L1 - State Kepler’s three laws of orbital motion
L1 - State Newton’s law of gravitation
Newton’s Law of Universal Gravitation:
Any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square distance between them

L1 - Describe the restricted two-body problem
Restricted Two-Body Problem:
If there are only two bodies which have constant mass and are both exactly spherical, then the small one will follow a trajectory which is a conic section - a circle, ellipse, parabola or hyperbola.
If we apply Newton’s laws where:
We find a small body will fly around a big one on a trajectory which is one of:
Eccentricity (e) is a measure of how non-circular the orbit/trajectory is.
Key Facts:

L1 - Describe the geocentric equatorial (ECI) co-ordinate system - PART 1
For Earth orbiting spacecraft we use the geocentric equatorial (ECI) system:
(For Sun-orbiting spacecraft we use the heliocentric ecliptic system)

L1 - Describe the geocentric equatorial (ECI) coordinate system - PART 2
But what is the vernal equinox/FPA?

L1 - Explain different general types of orbit
Circular Orbit:
the smaller body has a close orbit around the bigger body, the altitude at the apoapsis equals the one of the periapsis and the eccentricity equals zero.
E.g.: a body in a circular orbit around Earth at 222 km altitude must have a velocity of 7,77 km/s
Excentricity: e = 0
Elliptical Orbit:
the smaller body has a close orbit around the bigger body, the altitude of the apoapsis is greater than the one of the periapsis and the eccentricity is greater than zero and smaller than one.
Excentricity: 0 < e < 1
Parabola Orbit:
the smaller body has an open orbit with respect to the bigger body, it moves upon the minimum escape trajectory and the eccentricity is strictly equal to one.
Excentricity: e = 1
Hyperbola Orbit:
the smaller body has an open orbit with respect to the bigger body, it moves upon an escape trajectory and the eccentricity is greater than one.
Excentricity: e > 1
ISS - Low Earth Orbit
GPS - Medium Earth Orbit
Geosynchronous Orbit
Inclination can vary between 0o and 180o and is used to classify a variety of
different sorts of orbit:

L1 - Draw and label an orbit diagram

L1 - Use the Classical Orbital Elements (COEs) to define orbits
The orbit of a spacecraft is usually described using the Classical Orbital Elements:
(position)
(velocity)

L1R - Define Orbital Velocity
Orbital velocity is constant only in circular orbits. In elliptical orbits it is greatest at perigee and smallest at apogee
L1R - Circular orbit period and velocity
For circular orbits, the period increases with altitude while the velocity decreases.
L1R - Co-ordinate Systems
L1R - Orbital Elements: What do we need to know to describe the motion of a satellite?
Six pieces of information: x,y,z (position) and x’,y’,z’ (velocity)
L2 - Explain what is 3-level model of Space systems Engineering
L2 - Understand program definition
Program definition can be a very simple statement with task(s) to be performed with all necessary information to begin work:
Example: the Apollo Program
Program Definition
Space Program Level:
The Program level may integrate multiple
missions along with:
The ideal architect should be a man of letters, a skilled draftsman, familiar with historical studies, a diligent student of philosophy, acquainted with music; not ignorant of medicine, learned in the responsibilities of jurisconsults, familiar with astronomy and astronomical calculations. - Vitruvius, 25 B.C.
Space Program Architecture:
L2 - Understand Space mission characteristics
Space mission:
Space mission refers to human activity for the exploration, development and utilization of space and celestial resources outside the Earth, which is an engineering project that uses space technologies to achieve specific goals and covers a wide range of areas.
Space and Celestial Resources:
The vast expanse of space has unique resources not available on Earth, such as
high and remote positions, high vacuum, ultra low temperature, microgravity,
ultra cleanliness, electromagnetic spectrum, solar power and celestial bodies.
Mission Design Level
Mission Example:
Chang’e 4
Mission definition:
The Chang’e 4 is a mission of Chinese Lunar Exploration program (2nd phase) for the soft-landing and robotic exploration on the far side of the moon.
Mission configuration is comprised of a lander, a rover and a relay satellite:
Features of Space Missions:

L2 - Describe space system breakdown
Space system: is a system integration which consists of spacecraft; space transportation system; launching site; ground operation and control system(TT&C* network); recovery and landing site; astronaut system(for manned missions) and application system to complete specific space missions.
*Telemetry, Tracking, and Command
Space System
Space System Design
System design brings together many design elements to create a successful, end-to-end (pre-launch to payload disposal) space mission. See the 5 areas below:
Communications infrastructure / Mission control facilities Success can be measured by the accomplishment of all the mission-level requirements within the mission constraints.
The core of space system design is to provide the optimal system solution and product under specified constraints including timeline, funding etc.
Space System Design Content
The main tasks of system design :
Space engineering requirements and trade-off study are the basic methods for system design. (ENG L06 and L10)

L2 - Describe how space projects are broken down into major phases
A space mission could be broken down into 7 phases:
Phase 0 and A:
Phase B:
Phase C/D
Phase E/F
This phase usually accounts for most of the cost of the mission – an important factor in optimization.
L2 - List important tasks that a system engineer carries out in a project team
Basic Requirements:
The tasks of mission design normally are done under the leadership of the systems engineer with team efforts.
Key Tasks
L2 - Explain the term ‘system budget’ and list important parameters for which budgets are prepared.
About Budgets:
Budgets are used to ensure that all the elements are considered.
System Budgets
Safety and reliability budgets:
Financial Budgets:
Understand System Budgets:
Major budgets at the spacecraft system engineering level:
L3 - Characterise common Earth applications orbits
L3 - Interpret orbits based on spacecraft groundtracks
Ground Track
MORE:
The six COEs (classical orbital elements) allow us to visualise orbits in space, but it is important to be able visualise how orbits are seen from/on the Earth.
A ground track is the trace of the path that the satellite takes over the Earth’s surface.
All ground tracks are great circles, because the satellite orbits the centre of the Earth and so the orbit plane must also pass through this point.
The main complexity when interpreting ground tracks arises from the fact that:
Each time the satellite completes one orbit, the Earth has turned eastward underneath it, so the ground track shifts to the west.
See Image
We can determine useful information from this shift:
We can also determine the orbit inclination by looking at the ground track.
Inclination is very important in deciding on coverage patterns for satellites.
SEE image(in Slide p19)
All these orbits have a period of 4 hours, but they have different inclinations.
This can be seen by looking at the maximum latitude of their respective tracks.
Elliptical orbits ones are not symmetrical - they look different above and below the equator.
SEE image(in Slide p21)
Both orbits have P = 11.3 hours, i = 50o and e = 0.5.
However, the yellow has its perigee over the northern hemisphere, and red over the southern hemisphere.
L3 - Explain the major perturbations to Earth-orbiting satellites and their implications for the design of space missions
In the real life, a pure Keplerian orbit can never exists because of perturbations by forces other than central body gravity.
Peturbations:
Disturbing forces that act on a spacecraft to alter its orbit in some way
The primary forces perturbing the orbit are:
Lead to:
L4 - List and describe 5 different types of spacecraft
A spacecraft is composed of Spacecraft Bus (or platform) and Payload.
L4 - List the main subsystems that make up a spacecraft
Main subsystems of Platform:
Satellite platform is subsystems of Spacecraft to provide supporting functions necessary to make the payload work in all phases (launching, in-orbit operation and disposal).
