Concepts explained in this course:
C1 - Newton's laws of motion
First law: In the absence of a force, a body either is at rest or moves in a straight line with constant speed.
Second law: A body experiencing a force will be subject to an acceleration such that the force is equal to the product of the mass of the body and the acceleration.
Third law: Whenever a first body exerts a force on a second body, the second body exerts a force equal in magnitude and opposite in direction on the first body.
The general form of Newton’s second law expresses that the force equals the time derivative of the momentum. The momentum is the mass of the body times its velocity.
This concept is explained in the following video: 1.2.1.
C2 - Inertial Frame
An inertial frame is a frame with respect to which Newton’s laws of motion are valid.
The direction of the axes of an inertial frame can be imagined as being fixed with respect to distant stars.
The center of the inertial frame, which is an orthogonal coordinate system, will depend on the application.
This concept is explained in the following video: 1.2.1.
C3 - Newton's law of gravitation
Newton's law of gravitation states that any two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
This concept is explained in the following video: 1.2.2.
C4 - Standard gravitational parameter
The standard gravitational parameter \( \mu \) of a celestial body is equal to the gravitational constant G times the mass M of the body. It is used throughout this course for the central body around which a spacecraft is on orbit.
This concept is explained in the following video: 1.2.2.
C5 - Laws of motion of a solid body in rotation, and precession
This concept is based on the Newton’s second law of motion applied for a rotation: the torque is equal to the time derivative of the angular momentum.
A torque-induced precession is a phenomenon in which the axis of a spinning object describes a cone in space when an external torque is applied to it. This can be explained by Newton’s second law for rotations.
This concept is explained in the following video: 1.2.2.
C6 - Conservation laws
Conservation of momentum in an isolated system (absence of forces).
Conservation of angular momentum in an isolated system (absence of torques).
Conservation of the mechanical energy, potential plus kinetic, in an isolated system, in a conservative force field (for instance a gravitational force field in the absence of dissipative forces).
This concept is explained in the following video: 1.2.3.
C7 - Structure and composition of the Earth’s atmosphere
Chemical composition in the lower layers: 78% of nitrogen, 21% of oxygen, 1% of argon, < 0.1% others.
Layers: Troposphere, stratosphere, mesosphere, thermosphere.
Tropopause: limit of the troposphere, 9 to 17 kilometers altitude, depending on the latitude.
Stratopause: limit of stratosphere, around 50 km altitude.
The limit of the atmosphere and the beginning of space is considered to be at 100 km altitude.
This concept is explained in the following video: 1.3.1.
C8 - Microgravity
Microgravity is the term used to characterize the very low acceleration level encountered inside a spacecraft in LEO (typically 10-6g at 300 km altitude).
This concept is explained in the following video: 1.3.1.
C9 - Transparency of the atmosphere
The atmosphere is opaque to electromagnetic radiation except in the visible part of the spectrum and in the radio part between about 3cm to 10m wavelength. It has limited transparency in the infrared, between 1micron and 10 microns wavelength.
This concept is explained in the following video: 1.3.2.
C10 - Airglow
Airglow: emission of light by the atmosphere due to the photoionization of oxygen atoms and de-excitation which produces a luminescence, mainly due to the oxygen, somewhat also to nitrogen and the radical OH.
The airglow is well visible from Low Earth Orbit (LEO) during the orbital night as a light emission layer at an altitude of about 100 kilometers.
This concept is explained in the following video: 1.3.2.
C11 - Earth’s Magnetic field, or geomagnetic field
Close to the Earth’s surface, the geomagnetic field is essentially a bipolar field slightly offset from the center of the Earth. The expression of the amplitude of the magnetic field is a function of the distance to the center of the Earth and of the magnetic latitude.
Radiation Belts (RB) or Van Allen belts: High energy protons and electrons trapped in two regions of the magnetosphere, Protons and electrons in the inner RB, electrons only in the outer RB.
The Earth's magnetic field is significantly distorted away from the surface of Earth toward the Sun (5, up to 10 Earth radii) and in the anti-Sun direction due to solar wind, made of charged particles flowing in all directions from the Sun.
This concept is explained in the following videos: 1.4.1.
C12 - Northern/Southern lights
Northern and Southern Lights are produced from the excitation of nitrogen and oxygen atoms by electrons and protons flowing from the solar wind and reaching the upper atmosphere along the magnetic field lines that are close to vertical in the magnetic polar regions.
This concept is explained in the following videos: 1.4.1.
C13 - Solar cycle - Influence on the Earth’s atmosphere
A solar cycle is a period of approximately 11 years, based on the sunspot number, which is changing over time with an increase of sunspot activity during 5 years until the solar maximum followed by 6 years of decrease until the solar minimum.
A better determination of the phase of the solar cycle is the solar radio flux. The solar radiation flux at a wavelength of 10.7 cm varies along the solar cycle and is often used as a measure of the level of the solar activity along the cycle.
The solar variations have a significant effect on the thickness of the atmosphere, respectively on the density of the Earth’s atmosphere at a given altitude.
This concept is explained in the following videos: 1.4.2.
C14 - Solar activity on its surface and solar corona
The Sun is an active star. Its surface is granular with prominences: flares and Coronal Mass Ejections or CMEs.
A solar prominence is a large, bright feature extending outward from the Sun’s surface, often in a loop shape. While the corona consists of extremely hot ionised gases, which do not emit much visible light, prominences contain much cooler plasma, similar in composition to that of the chromosphere.
This concept is explained in the following video: 1.4.3.
C15 - Solar and galactic particle flux
Following Coronal Mass Ejections or CMEs, there is a large amount of charged particles (mainly protons) that flow through the Solar System all the way to the Earth and beyond.
Galactic cosmic particles have often a high energy and can affect electronic systems onboard a spacecraft.
This concept is explained in the following video: 1.5.1.
C16 - South Atlantic Anomaly
The South Atlantic Anomaly (SAA) is an area where the Earth’s inner Van Allen radiation belt comes closest to the Earth’s surface.
This concept is explained in the following video: 1.5.1.
C17 - Physiological effects of radiation
Radiation dose is expressed in RAD - Radiation Absorbed Dose - which is the amount of energy absorbed or REM (Roentgen Equivalent Man), or Sievert (Sv = 100 REM).
Astronauts have to stay way below 100 REM, or one Sievert, which is the vomiting effective threshold. Medical problems start over 100 REM and become significant above 500 REM.
This concept is explained in the following video: 1.5.1.
C18 - Solar irradiance and Solar Constant
The total irradiance of the Sun is the total energy that it sends in the form of electromagnetic radiation every second on a square meter surface outside of the Earth's atmosphere.
The Solar Constant is a conventional measure of the mean total solar irradiance at a distance to the Sun of one Astronomical Unit. The Solar Constant was 1361 W/m2 in 2015, slowly decreasing.
The solar irradiance spectrum is the distribution of the solar radiation flux as a function of wavelength. It follows roughly the spectrum of a blackbody at 5250 °C.
Looking at the Sun from the Earth’s surface, the irradiance spectrum is generally depressed (because of the Albedo, see below), and with significant absorptions in the UV and in the infrared.
The total solar irradiance in the solar system decreases with the distance to the Sun, according to the inverse square law.
This concept is explained in the following video: 1.5.2.
C19 - Albedo
Albedo is the diffuse reflectivity or reflecting power of a surface measured from zero for a perfectly black surface, to 1 for perfect reflector.
The Earth’s Albedo is about 0.3 or 30%, which means that 30% of the solar radiation incident on the Earth is reflected back in space.
This concept is explained in the following video: 1.5.3.
C20 - Spectral irradiance from the Earth
The spectral irradiance from the Earth has 2 components:
- The irradiance from the stratosphere corresponding roughly to a blackbody of 218K or -55°C
- The irradiance from the Earth’s surface corresponding roughly to a blackbody of 288K or +15°C, and visible only in the wavelength bands for which the atmosphere is transparent
This concept is explained in the following video: 1.5.3.
C21 - Radiation balance for a spacecraft in the vicinity of the Earth
If we consider a spacecraft in the vicinity of the Earth, the dominant source of radiation it receives comes from the Sun. 30% of the radiation of the Sun impacting the Earth is coming back towards space (Albedo). The other source of radiation is the Earth infrared radiation, rather dim, and, also, the cosmic background radiation, extraordinarily dim (blackbody at 2.7K).
The total absorbed radiation by the spacecraft is equal to the emitted radiation in a balanced condition.
The Stefan-Boltzmann law gives the value of the emitted radiation per unit surface as a function of temperature in the case of a black body.
The spacecraft is not a black body and its emitted radiation depends on its IR emissivity.
The equation expressing the radiation balance can be used to determine the average temperature of a spacecraft, knowing its geometry, emissivity and absorptivity, and the solar irradiance value.
This concept is explained in the following video: 1.5.4.
C22 - Orbit decay - ballistic coefficient
The orbit decay is the reduction in the altitude of a spacecraft orbit. The major cause is the drag of the spacecraft in the Earth’s atmosphere, which is more important during the solar maximum at a given altitude.
The drag equation expresses the force experienced by an object moving through a fluid or a gas at a certain velocity
The ballistic coefficient is the measure of the resistance to orbit decay caused by atmospheric drag. It is propotional to the mass of the spacecraft and inversely proportional to the drag coefficient and to the frontal surface of the spacecraft.
This concept is explained in the following video: 1.6.1.
C23 - Space debris
Space debris is an object in space that is no longer functional and useful. There is a very large amount of space debris in LEO and GEO causing high risk of collision with active spacecraft.
Several rules have been put in place to regulate satellites allocation in certain areas and the end of missions: when a communication satellite in the geostationary orbit are is longer functional, it shall be moved to a graveyard orbit. Measures are in place to limit satellites lifetime in Low Earth Orbit to 25 years.
Two major break up events: Iridium-Cosmos in 2009 and Fengyun-1C in 2007 resulted in a significant increase of space debris density around 800 km altitude.
This concept is explained in the following video: 1.6.2.
C24 - Asteroid collision threat
Several asteroids collisions happened on Earth but also in other planets in the Solar System.
A major event was the Cretaceous-Paleogene extinction, 65 million years ago, large scale extinction of most of life on Earth, included dinosaurs from the impact of a large meteorite on Earth, probably in the region of the Yucatan peninsula, Mexico.
Different techniques to improve early detection of dangerous asteroids and to modify their trajectories to avoid collision with earth are currently being looked at.
This concept is explained in the following video: 1.6.3.
C25 - Gravitational acceleration profile inside and outside of Earth
Inside the Earth, considered homogeneous, the gravitational acceleration varies linearly from zero at the center to 9.81 meters per second square at the surface. From the surface on, it varies as 1/r2, r being the distance to the center of the Earth.
This concept is explained in the following video: 2.2.1.
C26 - Gravitational well
A gravitational well is a conceptual model of the gravitational field surrounding a body in space.
The work necessary to lift a unit mass from the surface of a spherical object such as Earth, to infinity, is equal to the work necessary to lift the same mass from the surface of the sphere over a distance equal to the object’s radius, with a constant force equal to the force at the surface.
The object’s radius is the depth of the object’s non-normalized gravitational well. The profile of the gravitational well is in 1/r.
This concept is explained in the following videos: 2.2.1. and 2.2.2.
C27 - Normalized gravitational well
The depth of gravitational well of any spherical objects in the solar system or elsewhere, is always normalized to the gravitational acceleration of the Earth for comparison purposes.
The depth of the normalized gravitational well of a spherical object is the radius of this object multiplied by the ratio of the gravitational acceleration values at the surface of this object and at the surface of the Earth.
This concept is explained in the following video: 2.2.2.
C28 - Escape velocity
The escape velocity from a celestial body’s surface is the velocity at which a spacecraft has to leave this surface (in the absence of an atmosphere) in order to reach infinity at a zero velocity. The escape velocity is independent of the direction of the initial impulse (as long as escape really takes place)
For Earth, the escape velocity from the surface is equal to 11.2 km/second. For higher altitudes, it varies as 1/square root of r.
This concept is explained in the following video: 2.2.3.
C29 - Circular velocity
The circular velocity is the velocity of a spacecraft on a circular orbit around an object such as the Earth. The circular velocity is equal to the square root of (GM divided by r), r being the distance to the center of the attracting body.
This concept is explained in the following video: 2.2.3
C30 - Gravitational well in terms of transfer velocity
The transfer velocity, for a given planet, is the velocity that has to be added to the planet’s circular velocity for a transfer to infinity with final zero velocity from this location in the Sun’s gravitational well, i.e. to just leave the solar system with no extra energy or velocity at infinity.
The gravitational well of the Sun can also be represented as a plot of transfer velocities vs. distance to the center of the Sun.
This concept is explained in the following video: 2.2.3.
C31 - Two-body problem
The two-body problem is to determine the motion of two bodies that only interact with each other, in the absence of other masses or diffuse matter.
This concept is explained in the following video: 2.3.1.
C32 - Kepler’s laws
First law: The orbit of every planet is an ellipse with the Sun at one of the two foci.
Second law: A line is joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Third law: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of the elliptical orbit.
This concept is explained in the following video: 2.3.1.
C33 - Generalization of the first law of Kepler
The first law of Kepler can be generalized in the case of a two-body problem: the orbit of the small body versus the large body is a conic, i.e. an ellipse (circle is a particular case), a parabola, or a hyperbola.
This concept is explained in the following video: 2.3.1.
C34 - Important orbital parameters: Periapsis, apoapsis, eccentricity, true anomaly
Periapsis and apoapsis are general terms. Periastris and apoastris are sometimes used for a star as central body. If the Earth is the central body, we talk about perigee and apogee; if it is the Sun, perihelion and aphelion.
If the eccentricity is equal to 0 the orbit is circular, if the distance from the focus to the center of the orbit increases, the eccentricity becomes closer to 1. If the eccentricity is equal to 1, the orbit is parabolic.
The true anomaly is the angle between the direction of the periapsis from the central body to the radius vector of the spacecraft or the planet.
This concept is explained in the following video: 2.4.1.
C35 - Mechanical energy of a body in an orbital motion
The total mechanical energy of a body in a gravitational field is the sum of its kinetic energy and its potential energy.
In the limit case of a very elongated ellipse, the total mechanical energy of the orbital motion is close to zero.
In the case of a parabolic orbit, the total mechanical energy is equal to zero. The velocity along a parabolic orbit is always equal to the escape velocity.
If the velocity is less that the escape velocity, which is always the case for a closed orbit, elliptical or circular, the total mechanical energy is negative.
The total mechanical energy for a closed orbit is given by \( \epsilon=-{\frac{\mu}{2a}}\)
If the orbit is hyperbolic (velocity >0 at infinity), the total mechanical energy is positive.
This concept is explained in the following video: 2.4.1.
C36 - Orbital velocity or “Vis Viva” equation for an elliptical orbit
Elliptical orbit \( V=\sqrt{\frac{2\mu}{r}-\frac{\mu}{a}}\)
Circular orbit \( V=\sqrt{\frac{\mu}{r}}\)
This concept is explained in the following video: 2.4.1.
C37 - Flight path angle
The flight path angle is the angle between the direction of the velocity vector and the perpendicular to the radius vector at the point where the spacecraft is located.
The variation of the flight path angle on an elliptical orbit is a function of the position of the spacecraft or planet. On an elliptical orbit, the flight path angle is positive from periapsis to apoapsis, and negative from apoapsis to periapsis.
This concept is explained in the following video: 2.4.1.
C38 - Elliptical orbits - Mean motion and Kepler’s equation
The mean motion n is the average angular speed required for a body to complete one orbit, it is expressed in radians per second.
E, the eccentric anomaly, is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit, measured from the center of the ellipse and not from a focus.
The Kepler’s equation is a transcendental equation that cannot be solved for E but expresses the time evolution of E, the eccentric anomaly, and, consequently, the time evolution of the true anomaly as well.
This concept is explained in the following video: 2.4.2.
C39 - Reference frames
The geographic coordinate system is used to define positions on the surface of the Earth, with longitude and latitude.
The geocentric-inertial coordinate system is an orthogonal reference frame centered at the center of the Earth. The plane of reference is the plane of the equator, where the direction of X is the direction of the vernal equinox for a given year, nowadays chosen to be the year 2000. Y is also in the equator and Z along the rotation axis of the Earth pointing to the North.
The heliocentric-inertial coordinate system has the same directions of axes as the geocentric-inertial coordinate system, but it is centered at the center of the Sun, and the plane of reference is the plane of the ecliptic, or the plane of orbit of the Earth around the Sun.
This concept is explained in the following video: 2.5.1.
C40 - Precession of the equinoxes
Axial precession is the change or orientation of the rotational axis of an astronomical body.
The Earth is not a perfect sphere, but has an equatorial bulge, and the gravitational force from the Sun and the Moon, on a non-spherical body, causes the Precession of the Equinoxes, a slow drift of the Vernal Equinox point on the celestial equator. The Earth goes through one such complete cycle in about 26000 years.
This concept is explained in the following video: 2.5.1.
C41 - Classical orbital parameters and spacecraft state vector
There are 6 orbital parameters used to describe an orbit: the eccentricity, the semi-major axis of the orbit, the inclination of the orbit, the longitude or Right Ascension of the Ascending Node (RAAN, in the plane of reference), the argument of periapsis (in the orbital plane), and the time of periapsis transit.
With the addition of the time t, the 6 orbital parameters provide us the exact position of the celestial body or satellite.
The spacecraft’s state vector (X, Y, Z, X-dot, Y-dot, Z-dot, t) is functionally equivalent to the six orbital parameters plus the time t.
This concept is explained in the following video: 2.5.2.
C42 - Mean solar day and sidereal day
The sidereal day is the time it takes for the Earth to make one full revolution with respect to the stars, or to the geocentric inertial coordinate system.
The mean solar day is the time it takes for the Earth to make one full revolution with respect to the Sun, averaged over a full year. The actual solar day duration varies along the year because the orbit of the Earth around the Sun is elliptical and not circular.
The duration of the mean solar day is 24 hours, and the duration of the sidereal day is 23h 56′ 04″.
This concept is explained in the following video: 2.5.2.
C43 - Julian days
Julian days are used for scientific programs by the astronomy community and for control of spacecraft trajectory by spacecraft operators. Julian days represent the interval of time in days and fractions of a day since January 1st, 4713 BC Greenwich at noon. The use of the Julian date is recommended for astronomical purposes by the International Astronomical Union.
On January 1st, 2000, 0h UT, it was the middle of Julian day 2451544.
This concept is explained in the following video: 2.5.2.
C44 - Maneuvers in-orbit
A maneuver on orbit is the modification of the orbit of a spacecraft by adding a vectorial velocity change (ΔV) at some point on the initial orbit. We also use the term “burn” for maneuvers because, in most cases, we use thrusters burning propellant mixed with an oxidizer to generate the ΔVs.
In this course, we will only consider instantaneous vectorial ΔVs.
This concept is explained in the following video: 3.2.1.
C45 - Hohmann Transfer
The Hohmann transfer is a transfer between one circular orbit to another circular orbit around the same central body, where the elliptical transfer orbit is tangent to both the departure orbit and the destination orbit.
This concept is explained in the following video: 3.2.1.
C46 - Hohmann transfer for small increments in speed or distance to the central body
This type of transfer is often used for rendezvous in Low Earth Orbit.
For a small \( \Delta V \) along the direction of \( V \) on a circular orbit, the change of altitude \( \Delta r \) of the resulting elliptical orbit, at the apoapsis or periapsis of the new orbit and half a revolution following the maneuver, will be expressed by:
\( \frac{\Delta r}{r} \cong 4 \frac{\Delta V}{V}\)
This is of course only half a Hohmann transfer. For a full Hohmann transfer, another \( \Delta V \) of the same amplitude as the initial one will have to be performed if it is desired to circularize the trajectory at the apoapsis or periapsis of the transfer orbit.
The Low Earth Orbit or LEO approximation is the previous expression where we have replaced \( r \) by the typical value for a LEO ( \( r = {6378km} + {400km} \) like for ISS) and \( V \) by a typical value for LEO (7.7 km/sec):
\( \Delta r \cong 3.5 \Delta V\) This is valid for LEO only, with \( \Delta r \) in kilometers, and \( \Delta V \) in meters/sec.
This concept is explained in the following video: 3.2.2.
C47 - Orbital plane change
For an orbit around the Earth, an orbital plane change is an orbital maneuver aimed at changing the inclination of the orbit of a spacecraft. Depending on the location of the maneuver, it may result in an instantaneous change of the Longitude (or Right Ascension) of the Ascending Node as well.
If it is desired to change only the inclination of an orbit around Earth, the best location to perform this is at equator crossing.
This concept is explained in the following video: 3.2.3.
C48 - Geosynchronous and geostationary orbits
A geosynchronous orbit is an orbit around the Earth with a period of revolution equal to one sidereal day.
A geostationary orbit is a geosynchronous circular orbit on the equatorial plane (eccentricity e = 0 and inclination i = 0).
A satellite on a geostationary orbit remains on a fixed position on the celestial sphere seen from a point on the surface of the Earth.
This concept is explained in the following video: 3.3.1.
C49 - Strategy for reaching a geostationary orbit
The general strategy to reach the geostationary orbit from a parking orbit around the Earth is the following: a Hohmann transfer initiated at equator crossing and with an apogee at the geostationary altitude (36,000 km above the Earth's surface, with a specific maneuver when reaching this apogee:
There are two options for this maneuver ending up in a geostationary condition:
- a plane change and then an acceleration to the circular velocity on that equatorial orbit (about 3 km/sec).
- a combined maneuver of plane change and acceleration to the circular velocity on the equatorial plane.
This concept is explained in the following video: 3.3.1.
C50 - Geometry of a launch from the Earth’s surface
If a spacecraft is launched to the east from a launch site of latitude L, then the orbit of the spacecraft will have an inclination equal to L. Examples are 7 degrees for a launch from Kourou in French Guyana, the European launch site; and 28.5 degrees if the launch takes place from Kennedy Space Center, Florida. For a launch in any other direction than east, the resulting orbit inclination will be larger than the latitude of the launch site. To reach a certain inclination of such an orbit, the azimuth of the launch track will have to be determined taking into account the inertial rotation rate of the Earth for latitude of the launch site.
This concept is explained in the following video: 3.3.1.
C51 - Nodal regression (or progression) of an orbit around the Earth
The Earth’s equatorial bulge results in a torque on any orbit around Earth other than a pure equatorial orbit (inclination zero degrees) or pure polar orbit (inclination 90 degrees). This will cause a drift of the line of nodes of this orbit.
For orbits with an inclination of less than 90 degrees, the line of nodes drifts to the west (nodal regression because dΩ/dt is negative).
For orbits with an inclination larger than 90 degrees and less than 180 degrees, the line of nodes drifts to the east (nodal progression because dΩ/dt is positive).
For a pure equatorial orbit, with inclination zero degrees, there is no line of nodes, so no regression nor progression!
This concept is explained in the following video: 3.3.2.
C52 - Sun synchronous orbit
A Sun-synchronous orbit is an orbit that keeps the same orientation versus the Sun as the Earth is going around the Sun in a full year. This condition requires a nodal progression (to the east) of a little less than one degree per day (360 degrees in 365.2422 days).
This concept is explained in the following video: 3.3.2.
C53 - Restricted three-body problem
The restricted three-body problem refers to the case of two relatively massive bodies (typically the Sun or planets or large natural satellites of planets) and a much smaller body, a spacecraft. The two main bodies are on circular orbits around the center of mass of the system. The third body is in an orbit contained in the plane of the orbits of the two main bodies.
This concept is explained in the following video: 3.3.3.
C54 - Lagrange points
In the restricted three-body problem, the Lagrange points are five positions where the small body keeps the same position with respect to the other two (large) bodies which are revolving around each other. There are five Lagrange points, designated L1, L2, L3, L4 and L5. For a spacecraft located at any of these points, the sum of the gravitational forces exercised by the two large bodies is equal in magnitude and opposite in direction of the inertial force in its curved (circular) trajectory.
The L1, L2 and L3 points are stable in directions perpendicular to the line joining the two large bodies, and unstable along this line. The L4 and L5 points are locally stable in all directions within the orbital plane of the two large bodies, so that dust, rocks or small asteroids could be captured there and stay in the vicinity of these points.
This concept is explained in the following video: 3.3.3.
C55 - Catch up rate for nearby orbits
For close circular orbits, the catch up rate per orbit for an object situated at a slightly lower orbit by a separation \( \Delta r \) to the target orbit is given by:
\( \Delta X \cong 3\pi\Delta r \) with \(\Delta r \ll r \)
If the object is on a slightly higher circular orbit than the target orbit, with a separation \( \Delta r \), the object will trail behind with the same value \( \Delta X \) after one full orbit.
For an object located on an elliptical orbit of semi-major axis \( a < r \), \( r \) being the radius of the circular target orbit, the catch up rate per orbit of this object is given by:
\(\Delta X \cong 3\pi(r-a)\) with \(|r-a|\ll r\)
If the object is on a slightly higher elliptical orbit with semi-major axis \( a > r \), then the object will trail behind with the same value \( \Delta X \) after one full orbit.
This concept is explained in the following video: 3.4.1.
C56 - Effects of posigrade, retrograde and radial burns
Posigrade burns increase altitude 180° from the burn point.
Retrograde burns decrease altitude 180° from the burn point.
Radial burns shift the semi-major axis without significantly altering other orbital parameters.
This concept is explained in the following video: 3.4.2.
C57 - Rendezvous in Earth’s Orbit - General strategy
The rendezvous is the action of bringing together two spacecraft, at the same location with the same vector velocities. Most of the time the initial conditions are a spacecraft on the ground, called the chaser, which is active and another spacecraft on orbit, the target, which is passive.
The target is initially on orbit and the chaser on the launch pad with latitude equal to, or less than the inclination of the orbit of the target.
The final conditions are chaser and target at the same location in space with the same vectorial velocity.
Example are the Space Shuttle and HST (Hubble Space Telescope), Space Shuttle and ISS, Soyuz and ISS, Dragon (resupply vehicle from SpaceX) and ISS.
This concept is explained in the following videos: 3.4.3. and 3.5.1.
C58 - Actions at the completion of the rendezvous
Depending of the types of space vehicles as chaser and target, one of the following actions takes place at the end of the rendezvous:
- Docking of the chaser vs. the target (example Soyuz with ISS).
- Capture of the target with a chaser-based robot arm and robot arm-controlled berthing of the target on the chaser (example Shuttle with HST).
- Capture of the chaser with a target-based robot arm and robot arm-controlled berthing of the chaser on the target (example Dragon with ISS).
This concept is explained in the following video: 3.4.3.
C59 - Degrees of freedom of a space vehicle
In principle, a space vehicle has 6 degrees of freedom while on orbit: 3 degrees of freedom rotation (pitch, yaw, and roll), and 3 degrees of freedom translation (up-down, left-right and forward-aft).
This is important for the final approach of an active chaser vs. a passive target in the Prox Ops (or Proximity Operation) portion of a rendezvous. An automatic or man-in-the loop control system both need to have the capability of controlling all 6 degrees of freedom for completing the actions at the end of the rendezvous.
This concept is explained in the following video: 3.4.3.
C60 - Phase angle and phasing rate
Phase angle is the angle between the chaser and target, measured from the center of the Earth. Phasing rate or catch-up rate is the rate at which phase angle changes. Phasing rate is a function of differential altitude.
This concept is explained in the following video: 3.4.4.
C61 - Coordinate system used to plot the relative trajectory of the chaser vs. target in a rendezvous
The profile of the relative trajectory of the chaser versus the target is represented in a plane which is the plane of the orbit of the target. The motion of the chaser relative to the target is depicted in a coordinate frame centered on the target, with the positive X-axis in the direction of the velocity vector of the target on a circular orbit, and the positive Z-axis to the Center of the Earth (COE).
In this representation, the X-axis is in fact a curvilinear axis always parallel to the surface of the Earth, but represented a straight horizontal line for practical purposes.
The Y-axis is not represented. It is perpendicular to the plane of the orbit in the general southern direction.
This concept is explained in the following video: 3.4.4.
C62 - Rendezvous profile (Shuttle)
The rendezvous profile normally has the chaser (Shuttle) initially behind and below the target (Hubble or ISS), the chaser slowly catching up with the target. The catch up rate and energy of the chaser’s orbit are gradually modified to complete the rendezvous within a certain time (for Shuttle was originally 48 hours, and only 6 hours in later missions).
On the plot of the relative motion of the chaser vs. the target for the final portion of the rendezvous, we have a set of loops tangent to the horizontal X-axis (the orbit of the target) and coming down under it. In this phase, the chaser is on an elliptical orbit with apogee at the height of the circular orbit of the target, and the perigee some distance lower. The total mechanical energy (per unit mass) of the chaser is less than that of the target, with the semi-major axis of the chaser’s orbit (a) less than the radius of the target’s orbit (r), and we have a positive catch up rate.
A posigrade burn of the Shuttle with respect to the target will result in a higher and slower orbit with a longer period, reducing the catch up rate.
Reaching the last apogee of the chaser’s orbit before rendezvous completion, at a certain distance behind the target, the total energy of the chaser will have to be increased to cover this distance exactly during the last relative orbit. The burn performed to accomplish this is designated the Ti or “Terminal insertion” burn and was always a very critical maneuver!
This concept is explained in the following video: 3.4.4.
C63 - Rendezvous navigation and control (Shuttle)
Rendezvous sensors are used to update the relative state vector of the target versus chaser using sensor data, for on-board calculation of the burns to be performed to follow the pre-planned rendezvous profile. These sensors also provide the crew with cues to control the vehicle in the manual Prox Ops phase.
We had 3 such sensors on the Space Shuttle: Star Trackers (S TRK), Rendezvous Radar (RR) and Crew Optical Alignment Sight (COAS).
The Shuttle was manually controlled using two controllers: the Rotational Hand Controller (RHC), to command vehicle rotation in pitch, roll and yaw, and the Translational Hand Controller (THC), to command translation along the X, Y and Z axis.
This concept is explained in the following video: 3.4.5.
C64 - Effects of burns on relative motion
We take an initial condition with the Shuttle and ISS at the same location and look at the relative motion of the Shuttle vs. ISS in case of small burns (1 fps or about 0.3 m/s) posigrade, retrograde, and radial to the Center of Earth and in the opposite direction towards the local zenith.
As our burn is of small amplitude, the resulting motion of the Shuttle and all numbers for the posigrade and retrograde cases can be entirely determined from concepts 45 (Hohmann transfer for small increments in speed or distance to the central body) and 54 (Catch up rate for nearby orbits).
For the posigrade burn, the Shuttle will initially move forward vs. ISS, then up, will then slow down and will be about 17,000 ft or a little more than 5 km behind ISS after one orbit!
For the retrograde burn, symmetrically, the Shuttle will initially move aft vs. ISS, then down, will accelerate and find itself about 17,000 ft or a little more than 5 km ahead of ISS after one orbit!
For the radial burns, as the total mechanical energy of the Shuttle remains unchanged, the period remains unchanged, and the Shuttle will follow a relative loop vs. ISS and come back to the same point after one orbit!
This concept is explained in the following video: 3.4.6.
C65 - Astronomical Unit
The Astronomical Unit is the average distance between the Sun and the Earth.
1 AU = 149.5978707 x 106 km
This concept is explained in the following video: 4.2.1.
C66 - Interplanetary trajectories - Patched conics approximation
In order to plan for and execute a mission to another planet, we will consider in this course the Sun, the planet of departure (the Earth), the planet of destination and the spacecraft. In a real case, perturbations by other planets in the solar system may have to be considered.
The spacecraft is initially on a parking orbit around the Earth, and is accelerated to leave the Earth’s sphere of influence. The trajectory of the spacecraft inside the sphere of influence is hyperbolic. The spacecraft will cross the surface of the sphere of influence with a non-zero velocity, the hyperbolic excess velocity, or \( v_d^\infty \) (\( d \) for departure).
From this point, the heliocentric trajectory of the spacecraft will be elliptical, a heliocentric Hohmann transfer half-orbit to the destination planet.
Upon arriving in the vicinity of the destination planet, or more precisely when crossing the boundary of the destination planet’s sphere of influence at a velocity \( v_a^\infty \) (\( a \) for arrival), the spacecraft enters a hyperbolic trajectory with respect to the destination planet. The parameters of this orbit will be adjusted depending on the intended objective of the mission.
This concept is explained in the following video: 4.2.1.
C67 - Sphere of influence
Sphere around a planet inside which the motion of a spacecraft is considered to be two-body Keplerian.
The radius \( R_s \) of the Sphere of influence of a planet has been determined by Laplace as: \( R_S = R (\frac{\mu_{Planet}}{\mu_{Sun}})^\frac{2}{5}\)
where \( R \) is the average distance between Sun and the planet.
This concept is explained in the following video: 4.2.1.
C68 - Departure from a planet
A journey to a destination in the solar system always starts with a parking orbit. Then the orbital velocity of the spacecraft is increased at some point to reach the departure velocity.
The departure velocity, larger than the escape velocity for the altitude of the parking orbit, will put the spacecraft on a hyperbolic trajectory with respect to the departure planet, and the spacecraft will intersect the planet’s sphere of influence at the velocity \( v_d^\infty \).
This concept is explained in the following videos: 4.2.2., 4.2.3. and 4.2.5.
C69 - Hyperbolic excess velocity
On its hyperbolic orbit, at a large distance from the Earth and when reaching the sphere of influence, the spacecraft comes to a near constant velocity \(v_d^\infty \) designated “hyperbolic excess velocity”. If the trajectory of the spacecraft was not “bent” by the Sun outside the Earth’s Sphere of influence, it would keep this constant velocity all the way to infinity!
We have the important relationship: \(v_d^2 = (v_d^\infty)^2 + v_{Erd}^2 \)
Where \(v_d \) is the departure velocity from the parking orbit and \( v_{Erd} \) the escape velocity from the parking orbit of radius \( r_d \).
This concept is explained in the following videos: 4.2.2. and 4.2.3.
C70 - Orbital velocity or “Vis Viva” equation for a hyperbolic orbit
For a hyperbolic orbit: \( V = \sqrt{ \frac{2\mu}{r} + \frac{\mu}{a}} \)
Remember that for an elliptical orbit we have: \( V = \sqrt{ \frac{2\mu}{r} - \frac{\mu}{a}} \)
This concept is explained in the following video: 4.2.3.
C71 - Arrival at a planet
At the completion of its heliocentric journey, the spacecraft arrives in the vicinity of the destination planet. It reaches the sphere of influence with a planetocentric velocity \( v_a^\infty \). Spacecraft controllers have to adjust its trajectory to have the desired values of \( d_\infty \), the impact parameter, and \( \vartheta \), in order to satisfy mission objectives.
Inside the sphere of influence the spacecraft will be on a hyperbolic orbit, and, similarly to the case of the departure from a planet, we have the following relationship between \( v_a^\infty \) and the velocity at the periapsis of the hyperbolic orbit \( v^p \), and the escape velocity \( v_E^p \) from the planet at the periapsis point:
\( (v_a^\infty)^2 + (v_E^p)^2 = (v^p)^2 \) with \( v_E^p = \sqrt{ \frac{2\mu}{r_p}} \)
\( r_p \) being the periapsis distance from the center of the planet.
At the periapsis point, a braking maneuver can and most of the time will be executed to put the spacecraft on an elliptical or circular orbit around the planet.
This concept is explained in the following videos: 4.2.4. and 4.2.5.
C72 - Aerobraking, aerocapture, aeroentry
All 3 techniques apply to the arrival at, or in the vicinity of a planet with an atmosphere.
Aerocapture: Transfers the spacecraft from a hyperbolic approach trajectory to an elliptical orbit around the target planet by a Δv generated through friction-caused braking in the high layers of the planet’s atmosphere in the vicinity of the periapsis. Further loss of energy will occur at every subsequent crossing of the periapsis if the orbit is not circularized at some point outside of the atmosphere of the planet.
Aerobraking: Transfers the spacecraft from an initial elliptical orbit to a less energetic (i.e. lower apoapsis) elliptical orbit through braking in the high layers of a planet’s atmosphere in the vicinity of the periapsis. It normally involves small Δv value and can be repeated several times to reach the intended apoapsis altitude.
Aeroentry: Transfers the spacecraft from either a hyperbolic, parabolic or elliptical approach orbit, breaking down the velocity through the atmosphere with intense heating all the way to a landing on the surface of the planet, or a splashdown in an ocean (Apollo example).
This concept is explained in the following video: 4.3.1.
C73 - Gravity assist or slingshot maneuver
When a spacecraft on a heliocentric trajectory approaches another planet and comes in close proximity to it, the gravity of that planet temporarily takes over, pulling the spacecraft in and altering its heliocentric velocity.
If properly planned and executed, this can result in a significant change in the energy of the spacecraft and a modification of its heliocentric trajectory allowing it to reach far regions of the solar system that would otherwise be very hard or impossible to access from Earth.
The geometry of the trajectory of the spacecraft inside the sphere of influence of the planet causing the deflection is exactly the same as in the case of the “arrival to a planet”, it is a hyperbolic orbit with planetocentric arrival and departure velocities of same amplitudes, but with different directions to achieve the desired heliocentric velocity when leaving the planet’s sphere of influence.
This concept is explained in the following video: 4.3.2
C74 - Tsiolkovsky or rocket equation
\( \Delta V = v_e \log_e(\frac{m_i}{m_f}) \)
\( \Delta V \) = change of velocity of the spacecraft caused by the thrust produced by the propulsion system.
\( v_e \) = exhaust velocity of the gas in the propulsion system.
\( m_i, m_f \) = initial and final mass of the spacecraft, the difference between the two being the mass of the propellant used for the maneuver.
The rocket equation is valid in free space. For an ascent to space from the surface of a planet, gravitational field-induced and drag-induced retarding \( \Delta V \)s will have to be considered to determine the real \( \Delta V \) that can be obtained on the ascent, which is always less than the pure propulsion-induced \( \Delta V \).
This concept is explained in the following video: 4.4.1.
C75 - Specific Impulse
\( I_{sp} \), the specific impulse, is a measure of the propulsion system efficiency, it is its thrust (kg-force) divided by the mass flow of propellants (fuel and oxidizer, in kg/s). It is expressed in seconds.
We have the relationship: \( v_e = g_0 I_{sp} \) with \( v_e \) the exhaust velocity, and \( g_0 \) the gravitational acceleration on the Earth surface 9.81 m/s2.
The highest \( I_{sp} \) for a chemical rocket engine is for the combination H2/O2, with a value of about 450 seconds, corresponding to an exhaust velocity of about 4.5 km/sec.
This concept is explained in the following video: 4.4.1.
C76 - Chemical propulsion
Chemical propulsion is normally used for all stages of an ascent from the Earth surface until orbit insertion because of the high thrust generated. We have two main types of chemical propulsion systems: monopropellant or bipropellant.
In a bipropellant propulsion system the fuel and the oxidizer are being fed in the combustion chamber in liquid form - alternatively a solid propellant can be used, containing both the fuel and the oxidizer in solid form.
An igniter system is needed except in hypergolic propulsion systems that require none. A hot gas is produced under high pressure, expanded in a nozzle in order to increase the velocity of the exhaust gas flow.
This concept is explained in the following videos: 4.4.1. and 4.4.2.
C77 - Nuclear propulsion
This system produces heating of the propellant with a nuclear reactor and control of the flux of neutrons with a reflector.
The exhaust velocity that can be reached is significantly higher than with a chemical rocket, so that the efficiency and Specific Impulse value are much higher.
Nuclear propulsion systems have been tested but never used operationally.
This concept is explained in the following video: 4.4.3.
C78 - Electric or ion propulsion
This propulsion system produces an ionization of the propellant gas and its acceleration with the electric field.
Higher exhaust velocities than with a liquid-fueled or solid propellant rocket engine can be reached.
The Specific Impulse can reach several thousands, but with a relatively low thrust, most of the time of the order of a fraction of a Newton.
Such a system can be used for propulsion of a spacecraft while in space, but not for leaving the Earth’s surface and bring a spacecraft to orbital conditions because of low thrust.
This concept is explained in the following video: 4.4.3
C79 - Strategies for ascent into orbit
The strategy is to shape the ascent trajectory to achieve the orbit insertion conditions (flight path angle close to zero, or slightly positive), and to minimize the combined set of gravity and drag losses during the initial part of the ascent.
Multistage rocket launch is clearly an advantage because we reduce in this way the initial mass for one or two segments of the launch profile beyond the initial segment. The advantage is easily understandable considering the rocket equation.
Direct insertion into orbit: Initial launch at the vertical, powered ascent with progressive tilt towards the desired orbit, using the propulsion system of either one, two or three stages until orbit insertion.
Transfer orbit insertion: The initial insertion is on an elliptical transfer orbit at the apogee of which a circularization burn is performed for final installation on the desired orbit (Shuttle ascent profile).
For a launch from the surface of the Earth, the ascent trajectory is lofted in order to reduce the time spent inside the drag-producing atmosphere. On a planet with a thinner atmosphere like Mars, less lofting is necessary because atmospheric drag is not a big issue. In case of a launch from a body without atmosphere, like the Moon, lofting is minimal.
This concept is explained in the following video: 4.5.1.
C80 - Strategy for reentry in the Earth’s atmosphere
From a Low Earth Orbit, reentry of a space vehicle is initiated by a deorbit burn reducing the velocity and inserting the spacecraft into a descending elliptical trajectory which, at some point, will enter the atmosphere. For the Space Shuttle, entry interface in the atmosphere was 400,000 feet or about 120 km altitude at a high angle of attack (40 degrees). Deceleration started to be felt by the crew after this point.
- Entering the atmosphere at a Mach number close to 26 will cause a lot of heating and deceleration in the lower layers of the atmosphere. The deceleration profile is a function of the drag profile during entry.
- We have entry requirements and constraints applicable for any reentry vehicle, which is not planned for a destructive reentry. In the phase of deceleration of a spacecraft with humans on board, the deceleration limit is about 10g for a short duration.
- Heating: Must withstand both total heat load and peak heating.
- Accuracy of landing or impact: Function primarily of trajectory and vehicle design.
- Size of the entry corridor: The size of the corridor depends on the three constraints: deceleration, heating and accuracy.
This concept is explained in the following video: 4.5.1.
C81 - Attitude measurement and control system
Man-made spacecraft or natural objects like an asteroid or a comet nucleus, are very slowly rotating subject to gravity gradient forces if located in the vicinity of a large body, to sun radiation, solar wind, atmospheric effect from a nearby planet or satellite, or magnetic effect.
The attitude measurement and control system (AMCS) consists in measuring and maintaining, or changing in a controlled manner, the orientation of a coordinate system attached to the spacecraft with respect to an inertial or any other reference system. In practice, the attitude is always maintained or controlled within a specified deadband.
This concept is explained in the following video: 5.2.1.
C82 - Coordinate systems attached to the Space Shuttle and ISS
For the Space Shuttle, like normally for an airplane, X was along the axis of the fuselage + forward, Y to the starboard side or right wing, and Z down perpendicular to X and Y.
For ISS, X is along the cluster of modules from the aft Russian segment to the US segment in the front, Y along the truss to starboard, and Z down perpendicular to X and Y.
This concept is explained in the following video: 5.2.1.
C83 - LVLH coordinate system
An LVLH coordinate system (Local Vertical Local Horizontal) is an orthogonal reference frame centered on the center of mass of a spacecraft, with Z to the center of the Earth (COE), X in the direction of the velocity vector for a circular orbit, and Y orthogonal to X and Z. An LVLH attitude (P,Y,R)=(0,0,0) for the Shuttle on a circular orbit meant that the spacecraft was orbiting the Earth with its orientation like an airplane (nose forward, wings level).
This concept is explained in the following video: 5.2.1.
C84 - Euler sequence
Rotations around axis X, Y, and Z are non commutative.
The sequence Yaw-Pitch-Roll is often used in space systems. For the Space Shuttle and ISS, including associated robotic system: the Euler sequence is Pitch-Yaw-Roll.
This concept is explained in the following video: 5.2.1.
C85 - Types of attitude control
Gravity gradient, thrusters, spinning spacecraft, momentum devices: reaction wheels or Control Momentum Gyros (CMG), magnetic torquers.
Gravity gradient is a passive attitude control system.
This concept is explained in the following video: 5.2.2.
C86 - Gravity gradient
An elongated object will take an orientation in orbit around the Earth such that its long axis will be along the local vertical, with possible swinging motion around the local vertical.
This concept is explained in the following video: 5.2.2.
C87 - Magnetic torquers
A magnetic torquer is an elongated bar with a wire coil wrapped around it and an external protection.
A current through the coil will produce a magnetic field, which will try to align itself along the geomagnetic field with a torque expressed by: \( T = N B A I \sin\theta \)
Magnetic torquers are used if the orientation to space track doesn’t need to be extremely precise and as a system to desaturate momentum wheels (on the Hubble Space telescope for example).
This concept is explained in the following video: 5.2.2.
C88 - Stabilization by rotation
The inertial orientation is maintained by spinning the spacecraft. Some of the early communication satellites were cylindrical in shape with the cylinder covered with solar cells. In this case the rotation axis was the axis of the cylinder oriented perpendicular to the Sun direction.
Advantages: cheap, propellant flow from tanks provided by inertial forces.
Disadvantages: low accuracy in controlled attitude (0.3-1°), translations only possible along the rotation axis, pointing of antennas and other devices impossible except in the direction of spin.
This concept is explained in the following video: 5.2.2.
C89 - Three-axis attitude control system
Advantages: Any orientation accessible, with high pointing accuracy possible. Allows independent pointing of instruments, antennas and solar arrays in an optimal manner.
For a thruster-based 3-axis attitude control system (example was the Space Shuttle), a minimum of 12 thrusters are needed (4 thrusters for each of the 3 axes). The Space Shuttle had 38 Reaction Control System (RCS) thrusters, distributed in the forward and the aft sections of the fuselage.
Disadvantages: complexity and price, complex redundancy architecture, need to insure propellant supply from the tanks by other means than using the inertial forces.
This concept is explained in the following videos: 5.2.2., 5.2.3. and 5.2.4.
C90 - Reaction wheel or Momentum wheel attitude control system
One large wheel for each axis, plus normally an extra wheel off the X, Y and Z axes for redundancy purposes. The Hubble Space Telescope uses such a system, together with data from a set of three optical Fine Guidance Systems (FGS) providing an extremely precise attitude control of the orbiting observatory.
A change in the angular rotation speed of a momentum wheel will cause a corresponding rotation of the spacecraft in the opposite direction around the same axis.
This concept is explained in the following videos: 5.2.3. and 5.2.5.
C91 - Control Momentum Gyro or CMG attitude control system
Uses the gyroscopic effect. The gyros are mounted on gimbals and have a constant angular velocity. A torque along the input axis of a gyro will produce a corresponding torque reaction around the output axis, according to the second law of Newton for rotations, and the spacecraft will react to this output torque and slowly change its orientation. The USOS (United States Orbital Segment) of ISS uses a CMG attitude control system.
This concept is explained in the following videos: 5.2.3. and 5.2.5.
C92 - Spacecraft electrical power sources
Primary batteries, fuel cells, solar arrays, radioisotopic thermal generators.
Rechargeable batteries: NiCd (Nickel Cadmium) currently replaced by Li-Ion (Lithium Ion) and NiH2 (Nickel Hydrogen).
Fuel cells convert chemical energy from reactants into electricity through a chemical reaction of positively charged hydrogen ions with oxygen (or other oxidizing agent). They require a continuous source of reactants to sustain the chemical reaction. The by-products of this reaction are water and heat.
A Radioisotope Thermoelectric Generator (RTG), uses the fact that radioactive materials (such as Plutonium 238) generate heat as they decay into non-radioactive materials. The heat is converted into electricity by an array of thermocouples.
This concept is explained in the following video: 5.3.1.
C93 - Tethered systems – concept and utilization
A space tether is a long cable, which is used to couple spacecraft to each other or to other objects in space, like an asteroid or a spent rocket upper stage.
Tethers are usually made of a strong material like high-strength fibers or Kevlar, with or without an electrically conducting material in the core.
Space tethers have several useful applications: Electrical power generation, Orbit transfers, Ionospheric studies, Variable gravity research, Space debris removal, Provision of artificial gravity for long journeys in the Solar System, Earth-Moon payload transfer, Space Elevator.
This concept is explained in the following videos: 5.3.2., 5.3.3. and 5.3.4.
C94 - Space tether as an electrical generator
This is based on the induced voltage caused by the motion of a conductive tether in the Earth’s (or any planet’s) magnetic field. It uses Faraday’s law of induction. For a tethered system on a low Earth orbit with a low inclination, the tether velocity vector, the tether alignment (local vertical) and the magnetic field vector are roughly perpendicular to each other and this maximizes the efficiency of the system. If the electrical circuit is closed via the ambient conducting ionosphere, the electron flow downwards inside the tether will cause a Lorentz retarding force on the tether, which will result in a slow erosion of the orbital altitude of the system.
This concept is explained in the following videos: 5.3.2. and 5.3.4.
C95 - Space tether as an electrical motor
For a tether on a low inclination and low altitude Earth orbit, it is theoretically possible to pump the electrons up the tether and create a posigrade Lorentz force which will slowly raise the orbit of the tether and attached objects at both ends. Electrons could be pumped up the tether using an electron gun in the upper body. This application has never been tested so far (April 2017).
This concept is explained in the following video: 5.3.2.
C96 - Gravity gradient and tether boost/deboost
Along an elongated object on a low Earth orbit, maintaining a local vertical orientation, we have a gravity gradient effect due to the reduction in the gravitational acceleration value as we go up along this object. This will cause a tension on a vertical tether, with the tension value roughly proportional to the tether length. We also have an extra centrifugal force generated within the object or tether by its rotation of one full revolution in 90 minutes with respect to inertial space.
If 2 objects are linked with a vertically oriented tether on orbit, a tether break will cause the upper object to be injected to a higher orbit, and the lower will come to a lower orbit (exchange of angular momentum). This purely mechanical characteristics of space tethers has numerous useful applications.
This concept is explained in the following videos: 5.3.2. and 5.3.3.
C97 - Space elevator
A space elevator consists in a cable anchored at a location on the equator, and longer than the geostationary distance, with a counterweight at the end, and a climber or lift system able to move upwards and downwards along this cable.
It would allow access to nearby space without using a rocket!
This concept is explained in the following videos: 5.3.2. and 5.3.3.
C98 - Reliability of space systems
Some definitions:
- MTTF = Mean Time To Failure, average time duration until first failure.
- MTBF = Mean Time Between Failures, average time duration between two consecutive failures.
- Failure rate λ = 1/MTBF , in hours-1 or months-1.
- Reliability R(t) is the probability that the system will not fail in the interval (0, t). It is equal to exp(-t/MTBF).
This concept is explained in the following video: 5.4.1.
C99 - Space Shuttle
The concept of the Space Shuttle was developed by NASA and the aerospace industry in the US already in the seventies, before the end of the Apollo program. The idea was to have a winged reusable spacecraft with access to Low Earth Orbit (LEO) to deploy commercial payloads, serve the needs of space exploration and utilization, and be available for Department of Defense (DoD) missions.
A fully reusable spacecraft would have induced quite high development cost for a relatively low operation cost, because everything was going to be reusable.
Due to budget limitations, NASA and the US government ended up with a partially reusable spacecraft concept only, meaning less development costs but a higher operational cost.
Europe participated in the Space Shuttle program in the form of the SPACELAB project, allowing the use of the Space Shuttle for scientific investigations in several disciplines. Canada provided the Space Shuttle robotic arm or Remote Manipulator System (RMS).
The Space Shuttle in its launch configuration consisted of the Orbiter spaceplane, the External Tank (ET), and two Solid Rocket Boosters (SRB). The Orbiter was equipped with three Space Shuttle Main Engines (SSME), fed in liquid H2 and O2 from the ET for the 8.5 minutes of ascent to orbit. The two SRBs were fully consumed and jettisoned after 2 minutes, recovered in the Atlantic Ocean by boats, and reused after some refurbishment. The ET was lost on every mission. The size and volume of the Orbiter payload bay, and the crossrange capability of the Orbiter, were specified by the DoD.
At the end of the mission, the Orbiter landed, manually controlled, on a runway at Kennedy Space Center (KSC), Florida, which also was the unique launch site used in this program.
The Approach and Landing Tests (ALT) were performed in 1977 with the non-space-qualified Orbiter Enterprise.
A total of 135 Shuttle missions were then executed between 1981 and 2011 (30 years) using the five Orbiters built: Columbia, Challenger, Discovery, Atlantis and Endeavour. Challenger was lost in January 1986 during launch and was eventually replaced by Endeavour. Columbia was lost during re-entry in February 2003. Following the Challenger accident, the Space Shuttle was used only for non-commercial and non-DoD missions.
Operational missions launched numerous satellites, interplanetary probes, and the Hubble Space Telescope (HST), and conducted numerous science experiments in orbit. The Space Shuttle was essential in servicing HST, and in the assembly of the International Space Station from 1998 to 2011.
This concept is explained in the following videos: 6.2.1., 6.2.2., 6.2.3., 6.2.4., 6.2.5., 6.3.1., 6.3.2., 6.3.3 and 6.3.4.
C100 - International Space Station (ISS)
Signature of ISS Agreements was in 1998 by 15 countries: US, Russian Federation, Japan, Canada and 11 ESA member states.
The idea was to design, assemble, and make available a world-class laboratory in Low Earth Orbit (LEO) for life science, materials science, Earth observations, solar physics, technology development and support of future human long-duration spaceflight in the Solar System.
In December 1998 the mating of the first two elements took place: Zarya Russian module and Unity node or Node 1, 1st US element, followed by another Russian module, Zvezda.
Two years after the beginning of the assembly of the Station, the first crew arrived by Soyuz.
The ISS has been permanently inhabited from that time on until now. Astronauts and cosmonauts from the various partner nations and Agencies normally stay for five to six months missions on board. Two crewmembers recently stayed for one full year in ISS.
ISS is currently on a 51.6 degrees inclination orbit, at around 400 km altitude, although this altitude varies with the slow orbital decay and periodic reboosts.
Until Shuttle retirement from service in July 2011, both Shuttle and the Russian Soyuz were used for ISS crew exchange. From that time on and until end of 2018, probably, Soyuz will remain the only space vehicle used for ISS crew exchange, until commercial vehicles from SpaceX (Crew Dragon) and from Boeing (CST-100 Starliner) will make the same possible from US soil.
Cargo resupply to ISS has been, and is still performed by the Russian Progress vehicle, the Japanese HTV, the SpaceX Dragon, and the Orbital ATK Cygnus vehicles. In the past and until the summer of 2014, ESA also was involved in ISS cargo resupply with the ATV or Automatic Transfer Vehicle, which was used on 5 occasions.
The Sierra Nevada Corporation in the US is also developing a winged vehicle, the “Dream Chaser” that could also be used for future crew/cargo resupply of ISS.
This concept is explained in the following videos: 6.4.1., 6.4.2. and 6.4.3.
C101 - Chinese human space program
Shenzhou ascent/reentry vehicle program starting with Shenzhou 5, first Chinese manned flight October 15, 2003. The crew was Yang Liwei, first Chinese in space. This flight was followed by Shenzhou 6, 7, 9, 10 and 11, with crew size increased to three crewmembers. Shenzhou 11 was in October-November 2016, to join the new Tiangong-2 Chinese space station.
Like Soyuz, Shenzhou consists of three modules: a forward orbital module, a reentry capsule in the middle, and an aft service module.
Tiangong-2 is the second space station in China’s Tiangong series and was placed in orbit in September 2016. The first space laboratory, Tiangong-1, was launched in 2011 and was used for two crewed missions. It is now discarded and is expected to perform a controlled destructive re-entry some time in 2017. A third, larger station, Tiangong-3, is expected to be sent to space in the 2020 time-frame.
All Tiangong orbiting laboratories are not permanently occupied and are thought be precursors for a larger space station that China is expected to launch later in the 2020’s. One of the goals of the China National Space Administration is to insure a permanent Chinese human presence in space.
This concept is explained in the following video: 6.4.2.
C102 - Extravehicular Activities (EVA) and spacesuits
Extravehicular activity (EVA) or spacewalk is any activity done by an astronaut or cosmonaut outside a spacecraft, and using a spacesuit or pressure suit.
The first spacewalk was done by the soviet cosmonaut Alexei Leonov in May 1965.
An EVA is typically of 5 to 7 hours duration, but some spacewalks exceeded 8 hours duration.
A spacewalker is normally holding some structural element of the spacecraft, typically handholds, but he or she can also use foot restraints or other spacecraft structural elements to hold the feet in place and be able to use both arms and hands to accomplish the planned task, most of the time using special tools designed to be operated with gloved hands. A platform at the end of a robot arm can also be used to hold the feet in place, the advantage being that the spacewalker can then be brought to a good working position by the robot arm operator (this was done on the Shuttle, and is still done on ISS).
Spacewalking capability, in terms of hardware and procedures, have been established in the US, Russia and China, but we have had spacewalkers from many nations, especially from the nations and Agencies participating in the ISS program.
Most EVAs have been and are still using safety lines and tethers to avoid situations where an astronaut or cosmonaut not holding the structure would float away from the spacecraft and not be able to come back, but, in 1984, a few untethered spacewalks were performed from the Space Shuttle using the Manned Manoeuvring Unit or MMU. The MMU was a personal spacecraft allowing autonomous displacements of a spacewalking astronaut using cold gas thrusters commanded by rotational and translational hand controllers.
The current US spacesuit is designated Extravehicular Mobility Unit or EMU. It was used during the Shuttle program already and is currently used on ISS. It is a modular suit with a life support system and a 4.3 PSI (or 300 HPa) pressure pure oxygen environment, and a liquid cooling garment worn by the astronaut.
The Russian Orlan spacesuit is a one-piece suit, easy to don or doff, with a 5.8 PSI (400 HPa) inside pressure. It is currently used on ISS for Russian segment based EVAs.
This concept is explained in the following videos: 7.2.1., 7.2.2. and 7.2.3.
C103 - Robotics for the Space Shuttle and ISS
The Shuttle Remote Manipulator System (SRMS) or Canadarm 1 had six joints. It was controlled from the port side of the aft Shuttle flight deck using a Robotic Workstation and relying primarily on direct vision by the arm operator, supplemented by camera vision scenes displayed on 2 monitors.
There was a one-to-one correlation between the six joint angle values and the end effector location (X,Y,Z) plus orientation (P,Y,R) with respect to a Shuttle Payload Bay reference frame.
The Space Station Remote Manipulator System (SSRMS) or Canadarm 2 has seven joints. It is controlled from the US Lab or the Cupola using a Robotic Workstation. From the US Lab, the arm operator is relying entirely on camera views, without direct vision. From the Cupola, some direct vision is possible, but reliance on several camera views is still high.
The seven joints of SSRMS allow some flexibility in the geometry of the arm while going from an initial to a final position + orientation.
The SSRMS is also perfectly symmetric. The shoulder cluster and wrist clusters are exactly the same, and each end, with 3 joints each, can be either base or end effector.
Both RMS have been manufactured in Canada.
This concept is explained in the following video: 7.3.1.
C104 - Suborbital spaceflight
A suborbital spaceflight is a flight in which the spacecraft reaches space (>100 km altitude in the case of the Earth), but does not even do one full orbit around the planet. The top part of the trajectory, done without propulsion and in weightless conditions, is in fact an arc of an ellipse with very large eccentricity (nearly one) and is very close in shape to a parabolic arc. A suborbital spaceflight is basically an up-and-down trip, reaching space.
If the trajectory of the suborbital spaceplane or capsule does not reach the 100 km mark, then we just have a suborbital flight and not spaceflight!
A suborbital flight or spaceflight can be used for technical or scientific experiments in microgravity conditions, giving more microgravity time (a few minutes) than a parabolic flight in an airplane (about 20 seconds per parabola), but significantly less than what you get in orbital conditions!
The current actors of suborbital spaceflights are: Virgin Galactic, XCOR Aerospace, and Blue Origin in the USA. The suborbital spaceflights they will soon offer (this is written in April 2017) will essentially be for space tourists. More on this to follow soon!
This concept is explained in the following video: 7.5.1.
C105 - Orion and Space Launch System
The Orion Multi-Purpose Crew Vehicle has been in development since 2005, in collaboration with ESA since 2013. Its purpose is to take astronauts to destinations at and beyond Low Earth Orbit (LEO). It consists of a crew module, a service module provided by ESA, and will be fitted with a Launch Abort System or launch Abort Tower during the early part of the ascent to orbit. Crew accommodation will be for up to 6 astronauts. It will be launched by the Space Launch System (SLS), see below.
In 2014, an early version of the Orion crew vehicle was successfully launched into space (using a Delta IV launcher) and retrieved at sea after splashdown on the Exploration Flight Test 1 (EFT-1).
The Space Launch System (SLS) is an American Space Shuttle-derived heavy expendable launch vehicle being designed by NASA. It will use several components of the retired Space Shuttle, like Solid Rocket Boosters (SRB) and Shuttle derived main engines (LH2 and LOX) for the first stage. Its payload capacity to LEO will be up to 130 t (metric ton).
Currently (April 2017), the first two flights of the SLS/Orion complex should be unmanned Exploration Mission 1 (EM-1) in November 2018 and Exploration Mission 2 (EM-2) with crew on board in August 2021, both with destination Moon without landing. There is discussion about delaying Mission EM-1 but with crew on board for the first time!
This concept is explained in the following video: 7.6.3.