1 Orbital Mechanics Flashcards
What is Kepler’s 1st Law?
Law of Ellipses
The centre of the larger of two orbiting bodies will one of the foci. With the orbital plane passing through that bodies centre.
What is Kepler’s 2nd Law?
Law of Equal Areas
A line joining a body and its orbiting satellite sweeps out equal areas in any given time. The satellite will therefore slow down at apogee and speed up at perigee.
What is Kepler’s 3rd Law?
Law of Harmonics
The square of the orbital period is proportional to the cube of the semi-major axis. Regardless of eccentricity, the period of an orbit is solely dependent on the size of the semi-major axis.
What is Newton’s 1st Law?
The Law of Inertia
An object will remain at rest or in constant motion in a straight line unless acted on by an external force.
What is Newton’s 2nd Law?
Law of Changing Momentum
The time rate of change of momentum (acceleration) is proportional to the force applied.
What is Newton’s 3rd Law?
Action - Reaction
For every action (force) there is an equal and opposite reaction.
What is the Law of Universal Gravitation?
The force of attraction between two bodies is…
directly proportional to the product of their masses…
and inversely proportional to the square of the distance between them.
Linear Momentum is…
Mass x Velocity
Angular Momentum is…
The resistance of a spinning object to change its spin rate/direction.
IMPORTANT: Angular momentum remains constant for an orbiting object which is not torqued.
Every orbit has an associated …. level.
Energy
Energy of a body in orbit is conversed. Transforming between ….. and ….. energy?
Kinetic and Potential
Mechanical energy =
KINETIC energy + POTENTIAL energy
Specific Mechanical Energy is….
ME normalised for satellite mass.
What is the difference between ME and SME?
Normalised for satellite mass
What coordinate reference frame do we use?
Earth Centred Inertial - ECI
What 4 things are used in the ECI reference system?
Origin (Centre of Gravity)
Fundamental Plane (Equatorial plane at 1200 01 Jan 2000 (J2000))
Principal Direction (Constant. Vernal Equinox - Quasars v. far away)
Normal Direction
What is Perigee?
Point at which an object is CLOSEST to the Earth in its orbit
What is Apogee?
Point at which an object is FURTHEST AWAY to the Earth in its orbit
Name the 6 COEs
Semi Major Axis Eccentricity Inclination Right Ascension of Ascending Node Argument of Perigee True Anomaly
In COE the Semi Major Axis describes what aspect of an orbit?
Size
In COE the Eccentricity describes what aspect of an orbit?
Shape
In COE the Inclination describes what aspect of an orbit?
Tilt
In COE the RAAN describes what aspect of an orbit?
Twist
In COE the Argument of Perigee describes what aspect of an orbit?
Rotation
In COE the True Anomaly describes what aspect of an orbit?
Satellite Position
What line of a TLE contains information about the satellite, launch, time of TLE etc?
Line 1
What line of a TLE contains information about the orbit of a satellite?
Line 2
What are the 4 different orbit types?
LEO
MEO
HEO
HEO
Describe a LEO (alt., per. and common uses)
Altitude - 150 km to 2,000 km
Period - approx. 90 mins
Polar Orbits
Sun-Synchronous Orbits
Describe a MEO (alt., per. and common uses)
Altitude - 2,000 km to 35,862 km
Period - approx. 11hr 58 mins
Semi-synchronous
Name the 2 HEOs
Molniya
Tundra
Describe a Molniya orbit (alt. and per.)
Altitude - 600 km to 40,000 km
Period - approx. 11 hr 58 mins
Describe a Tundra orbit (alt. and per.)
Altitude - 25,000 km to 46,000 km
Period - approx. 23 hr 56 mins
Inclination: 63.4 deg
Describe a GEO (alt. and per.)
Altitude - 35,862 km
Period - 23 hrs 56 mins
Describe a Polar Orbit
Passes over the N and S poles each revolution. Inclination = 90 deg
Altitude between 200 km to 1,000 km
Can observe the entire planet over a given period
Used for reconnaissance and Earth observation
Describe a Sun-Synchronous Orbit (SSO)
Near-Polar Orbit (inclination approx. 98 deg)
Passes over given point on Earth’s surface at same local mean solar time
Same surface illumination each time it passes overhead
Extensively used for IMINT gathering
Describe a Semi-Synchronous Orbit
Orbital period equal half that of the rotational period of the Earth (relative to the stars)
Assuming prograde orbit it will pass over the same point on Earth’s surface pass after pass
Typically used for GNSS such as GPS
Describe a Geosynchronous Earth Orbit (GEO)
Orbital period equal to that of the Earth’s rotational period
Describe a Geostationary Earth Orbit (GSO)
A special GEO that is perfectly aligned with the Earth’s equator
This means it will appear to ‘hover’ over the same point on the Earth’s surface
Define the Semi Major Axis COE
Half the distance from Apogee to Perigee
Define the Eccentricity COE
Ratio of the distance between foci of the elliptical orbit and the Major Axis
Define the Inclination COE
Angle between the FUNDAMENTAL and ORBITAL planes…
measured in a WESTWARD direction…
at the ASCENDING NODE.
0 deg or 180 deg = equatorial
90 deg = polar
<90 deg = prograde
Define the RAAN COE
The angle between the PRINCIPLE DIRECTION and the ASCENDING NODE…
measured in an EASTWARD direction.
0 deg <= RAAN < 360 deg
Define the Argument of Perigee COE
Angle between the ASCENDING NODE and the point of PERIGEE…
measured in the direction of travel.
Define the True Anomaly COE
Angle between PERIGEE and the objects position…
measured in the direction of travel.
What happens to an orbits ground track over time?
Travels Westward
From a ground track how can we determine an orbits INCLINATION?
Prograde: max latitude of ground track
Retrograde: 180 deg - max latitude of ground track
From a ground track how can we determine an orbits PERIOD?
By dividing nodal displacement by 15 deg/hr
From a ground track how can we determine an orbits Semi Major Axis?
From Kepler’s 3rd Law (harmonics). If the period is known.
From a ground track how can we determine an orbits ECCENTRICITY?
Circular orbits: Symmetrical
Eccentric: Asymmetrical
