orbit concepts

Question 1

what do kepler’s laws provide?

Answer 1

reasonable approximation of the dynamics of a small body orbiting about a much larger body

Question 2

what is kepler’s first law?

Answer 2

path of a planet is an ellipse whose radius vector is measured from the sun which is fixed at one focus

Question 3

what is kepler’s second law?

Answer 3

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

Question 4

true or false: the velocity of the spacecraft is constantly changing around the orbit

Answer 4

true

Question 5

what is kepler’s third law?

Answer 5

the square of the period of any planet is proportional to the cube of the semi-major axis of the planet

Question 6

circle, ellipse, parabola, hyperbola

provide the eccentricity and semi-major axis ranges for different conic sections

Answer 6

• circle: e = 0, a = r
• ellipse: 0 < e < 1, 0 < a < inf
• parabola: e = 1, a -> inf
• hyperbola: e > 1, a < 0

Question 7

define lagrange points

Answer 7

points where the gravitational pull of two large masses equals the centripetal force required for a small object to move with them

Question 8

true or false: forces are the strongest when they are together and the weakest when they are apart from each other

Answer 8

true

Question 9

assuming that there are no other forces acting on the body, what can be said about gravitational and kinetic energies?

Answer 9

the sum of KE and PE remains constant throughout the orbit

Question 10

what is the role of the vis-visa equation?

Answer 10

relates an orbiting body’s speed to its distance from the body it is orbiting

Question 11

what assumptions does the 2 body problem consider?

Answer 11

• masses m and M are the only two bodies involved
• mass M&raquo_space; mass m
• mass M spherically symmetrical
• gravity only force acting

Question 12

define closed orbit

Answer 12

orbit where object in orbit is permanently associated with body being orbited and decribes a closed conic section such as circle or ellipse

Question 13

what is the total energy of a closed orbit?

Answer 13

negative

Question 14

can an object orbiting a body in a closed orbit escape?

Answer 14

no

Question 15

define open orbit

Answer 15

orbit where the object is not permanently associated with the body being orbited and describes an open conic section, such as parabola or hyperbola

Question 16

what is the total energy of a parabolic orbit?

Answer 16

0

Question 17

what is the total energy of a hyperbolic orbit?

Answer 17

positive

Question 18

in what plane does the earth orbit the sun?

Answer 18

ecliptic

Question 19

what angle does the earth spin on its axis?

Answer 19

23.45º

Question 20

what causes seasons?

Answer 20

earth’s spin angle of 23.45º

Question 21

where are the tropics of cancer and capricorn located?

Answer 21

23.45º north and south

Question 22

define vernal equinox

Answer 22

where equatorial and ecliptic planes intersect

Question 23

define apparent solar day

Answer 23

time interval between two successive solar transits across a local meridian

Question 24

what is responsible for the duration of the apparent solar day?

Answer 24

• rotation of earth around its axis
• earth’s revolution around the sun

Question 25

define the mean solar day and its duration

Answer 25

* time taken for the sun to appear in the same position in the sky * 24h per day * 365.25 days a year

Question 26

define sidereal time and its duration

Answer 26

* time required to rotate earth on its own axis with respect to fixed stars or inertial space * 23h, 56m, 4s

Question 27

define universal time

Answer 27

index mark for 24 time zones of 15º longitude each

Question 28

list the keplerian orbit elements and what they determine

Answer 28

* 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

Question 29

define orbital inclination

Answer 29

orientation of orbit with respect to earth's equatorial plane

Question 30

define prograde and retrograde, and define their angles

Answer 30

* prograde = with the spin of the earth (if i = 0º-90º) * retrograde = against the spin of the earth (if i = 90º-180º)

Question 31

define the ascending node

Answer 31

defines the location of the line of nodes which are given by the intersection between the orbit plane and the equatorial plane

Question 32

define the argument of perigee

Answer 32

defines an angle in the plane between the line of nodes and the periapsis

Question 33

define the true anomaly

Answer 33

position of the satellite in the orbit, given as angle between the direction of periapsis and current position of body

Question 34

define periapsis

Answer 34

point in orbit where orbiting object is closest to body it orbits

Question 35

list the types of earth orbits

Answer 35

* 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)

Question 36

# altitude, velocity, orbit period, used for?, advantages, disadvantages list the features of an LEO

Answer 36

* 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

Question 37

# altitude, velocity, orbit period, used for?, advantages, disadvantages list the features of an MEO

Answer 37

* 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

Question 38

list the altitude of a high earth orbit HEO

Answer 38

35786km < altitude < 929000km

Question 39

list the features of a gysynchronous orbit (GSO)

Answer 39

* altitude: between 2000 and 35786km * period: 23h, 56m, 4s * used for missions that require continuous coverage such as comms satellites

Question 40

list the features of a geostationary earth orbit (GEO)

Answer 40

* 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

Question 41

list the features of molniya orbits

Answer 41

* 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

Question 42

list the features of sun synchronous orbits (SSO)

Answer 42

* 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

Question 43

define ground tracks

Answer 43

traces of the sub satellite point, on the surface of the earth that a satellite generates in one orbit about the earth

Question 44

how can the inclination of an orbit be determined from ground tracks?

Answer 44

max latitude of orbit ground trace

Question 45

when calculating the orbit period using ground tracks, we can assume the angular velocity of the earth to be?

Answer 45

0.25º/min