orbit concepts Flashcards
what do kepler’s laws provide?
reasonable approximation of the dynamics of a small body orbiting about a much larger body
what is kepler’s first law?
path of a planet is an ellipse whose radius vector is measured from the sun which is fixed at one focus
what is kepler’s second law?
time taken by a planet to reach a particular position is represented by the area swept out by the radius vector drawn from the fixed sun
true or false: the velocity of the spacecraft is constantly changing around the orbit
true
what is kepler’s third law?
the square of the period of any planet is proportional to the cube of the semi-major axis of the planet
circle, ellipse, parabola, hyperbola
provide the eccentricity and semi-major axis ranges for different conic sections
- circle: e = 0, a = r
- ellipse: 0 < e < 1, 0 < a < inf
- parabola: e = 1, a -> inf
- hyperbola: e > 1, a < 0
define lagrange points
points where the gravitational pull of two large masses equals the centripetal force required for a small object to move with them
true or false: forces are the strongest when they are together and the weakest when they are apart from each other
true
assuming that there are no other forces acting on the body, what can be said about gravitational and kinetic energies?
the sum of KE and PE remains constant throughout the orbit
what is the role of the vis-visa equation?
relates an orbiting body’s speed to its distance from the body it is orbiting
what assumptions does the 2 body problem consider?
- masses m and M are the only two bodies involved
- mass M»_space; mass m
- mass M spherically symmetrical
- gravity only force acting
define closed orbit
orbit where object in orbit is permanently associated with body being orbited and decribes a closed conic section such as circle or ellipse
what is the total energy of a closed orbit?
negative
can an object orbiting a body in a closed orbit escape?
no
define open orbit
orbit where the object is not permanently associated with the body being orbited and describes an open conic section, such as parabola or hyperbola
what is the total energy of a parabolic orbit?
0
what is the total energy of a hyperbolic orbit?
positive
in what plane does the earth orbit the sun?
ecliptic
what angle does the earth spin on its axis?
23.45º
what causes seasons?
earth’s spin angle of 23.45º
where are the tropics of cancer and capricorn located?
23.45º north and south
define vernal equinox
where equatorial and ecliptic planes intersect
define apparent solar day
time interval between two successive solar transits across a local meridian
what is responsible for the duration of the apparent solar day?
- rotation of earth around its axis
- earth’s revolution around the sun
define the mean solar day and its duration
- time taken for the sun to appear in the same position in the sky
- 24h per day
- 365.25 days a year
define sidereal time and its duration
- time required to rotate earth on its own axis with respect to fixed stars or inertial space
- 23h, 56m, 4s
define universal time
index mark for 24 time zones of 15º longitude each
list the keplerian orbit elements and what they determine
- semi major axis (SMA) = orbit size
- eccentricity (ECC) = orbit shape
- true anomaly (TA) = satellite position on orbit
- inclination (INC) = orbital plane orientation
- ascending node / right ascension (RAAN) = orbital plane orientation
- argument of perigee (AOP) = orbital plane orientation
define orbital inclination
orientation of orbit with respect to earth’s equatorial plane
define prograde and retrograde, and define their angles
- prograde = with the spin of the earth (if i = 0º-90º)
- retrograde = against the spin of the earth (if i = 90º-180º)
define the ascending node
defines the location of the line of nodes which are given by the intersection between the orbit plane and the equatorial plane
define the argument of perigee
defines an angle in the plane between the line of nodes and the periapsis
define the true anomaly
position of the satellite in the orbit, given as angle between the direction of periapsis and current position of body
define periapsis
point in orbit where orbiting object is closest to body it orbits
list the types of earth orbits
- low earth orbit (LEO)
- medium earth orbit (MEO)
- high earth orbit (HEO)
- geosynchronous orbit (GSO)
- geostationary orbit (GEO)
- highly elliptical orbit (MOLNIYA)
- sunsynchronous orbit (SSO)
altitude, velocity, orbit period, used for?, advantages, disadvantages
list the features of an LEO
- altitude = between 100 - 2000km
- velocity = between 7 and 7.8km/s
- orbit periods = between 90 and 130min
- used for detailed observation of earth’s surface and atmospheric measurements
- adv = high res imaging, low energy req, low comms power
- disadv = limited coverage, short periods of coverage, high atmospheric density, costly to re-position
altitude, velocity, orbit period, used for?, advantages, disadvantages
list the features of an MEO
- altitude = between 2000 - 35786km
- velocity = between 3.3 and 7km/s
- orbit periods = between 2 and 20h
- used for navigational systems, galileo at 20000km altitude
- adv = great coverage, more time on station, cheaper to change orbit
- disadv = high radiation and charged particle level
list the altitude of a high earth orbit HEO
35786km < altitude < 929000km
list the features of a gysynchronous orbit (GSO)
- altitude: between 2000 and 35786km
- period: 23h, 56m, 4s
- used for missions that require continuous coverage such as comms satellites
list the features of a geostationary earth orbit (GEO)
- orbit plane is in line with the equator such that the inclination and eccentricity are 0
- used for communication satellite missions, but do not have coverage over the poles
list the features of molniya orbits
- altitude: low perigee altitude (< 1000km) and high apogee altitude (< 35800km)
- adv: long dwell time over region below apogee, potential for no eclipse period during mission ops
- disadv: potential traverse through van allen belts, for continous coverage need more than one satellite, wide variation in range, range rate and coverage region
list the features of sun synchronous orbits (SSO)
- altitude: between 600-800km
- period: between 96 and 100min
- inclination: ~98º
- used for earth observation where similar lighting conditions are required, change in RAAN is same as Earth’s and solar angle is the same
define ground tracks
traces of the sub satellite point, on the surface of the earth that a satellite generates in one orbit about the earth
how can the inclination of an orbit be determined from ground tracks?
max latitude of orbit ground trace
when calculating the orbit period using ground tracks, we can assume the angular velocity of the earth to be?
0.25º/min
