Chapter 5 : Describing Orbits

Question 1

What are the classical orbital elements?

Answer 1

set of variables used to describe an orbit

1. a semimajor axis (size)
2. e eccentricity (shape)
3. i inclination (tilt)
4. Ω RAAN (orientation)
5. ω argument of perigee (location of perigee)
6. ν true anomaly (location of spacecraft from perigee)

Question 2

How do you determine orbital size?

Answer 2

specific mechanical energy (km^2/s^2) using the equation

ε = -μ/2*a

Question 3

What does eccentricity describe, how do you determine eccentricity, and describe the eccentricity value perimeters for specific orbital shapes.

Answer 3

shape
e = (2*c)/(2*a)
circle e = 0
ellipse 0 < e < 1
parabola e = 1
hyperbola e > 1

Question 4

What is used to find the tilt of an orbit?

Answer 4

inclination which is the angle from the K unit vector to the h vector (h is a vector perpendicular to the orbital plane)

Question 5

What are the perimeters of inclination?

Answer 5

i = 0 or 180 equatorial orbit
i = 90 polar orbit
0 < i < 90 prograde orbit
90 < i < 180 retrograde orbit

Question 6

Retrograde orbit is described as what?

Answer 6

an indirect orbit in which the spacecraft travels in the opposite direction of earths rotation

Question 7

What is a prograde orbit?

Answer 7

a direct orbit in which the spacecraft travels in the same direction of earths rotation

Question 8

Describe what RAAM is.

Answer 8

Right ascension of the ascending node, Ω, is the angle b/w the vernal equinox to where the equatorial plane bisects the orbital plane. RAAN describes the swivel of the orbit

Question 9

What is the argument of perigee?

Answer 9

ω, the angle from the ascending node to the perigee, along the orbital path in the direction of the flight path

Question 10

What is ν?

Answer 10

true anomaly, which is the angle from the perigee to the spacecrafts position along the orbit in the direction of the flight path

Question 11

A geosynchronous orbit is?

Answer 11

an inclined orbit
about 24 hour period
around 22,300 miles 
∆N = 360
ground track appears as a figure 8 unless i = 0, then it is a point on the equator (geostationary orbit)

Question 12

What is a sun synchronous orbit?

Answer 12

a retrograde, low earth orbit, with ~ 95 < i < 105, near polar (i = 90) orbit, that passes over Earth with the same sun angle every day (there are never knew shadows) The sun is always in the same position in relation to the spacecrafts ground track. Used for weather, and remote sensing. App altitude = 460-520 miles

Question 13

The Molniya Orbit is?

Answer 13

an orbit that is highly eccentric (e = 0.7) that has ~ 12 hour orbit period, designed by the Russians for communication and intelligence

Question 14

What is a low earth orbit?

Answer 14

orbit around earth with a up to 250 miles (6700 km), used for manned space missions, communications and reconnaissance.
e = 0

Question 15

What is a semi-synchronous orbit?

Answer 15

synchronous orbit that increases coverage, app. 10,900 miles, and a period of 12 hours

Question 16

A geostationary orbit is?

Answer 16

orbit with inclination near 0 (i = 0) so that the orbit is close alignment with the equatorial plane.
Circular orbit, e = 0
ground track is a single point on the equator

Question 17

How do you compute the semimajor axis?

Answer 17

a = μ/-2ε
where ε = V^2/2 - μ/R
(specific mechanical energy)

Question 18

What is μ and what is its value?

Answer 18

universal graviational constant multiplied by Earth’s mass

GM = μ = 3.986E5 km^3/s^2

Question 19

In which direction does the satellites ground track shift?

Answer 19

if prograde - westerly movement

if retrograde - easterly movement

Question 20

What is ∆N

Answer 20

nodal displacement, which is the lateral change of the ground track (how much the ground track shifts).
∆N = 360 - longitudinal degrees b/w successive ascending nodes.

Question 21

How much does earth rotate in degrees with respect to time?

Answer 21

360 deg / 24 hours
15 deg / 1 hour
0.25 deg / 1 min

Question 22

The equation for the orbital period in hours is?

Answer 22

P (hours) = ∆N/(15deg/hour)

for direct orbits

Question 23

What is the relation between the period, P, and the semimajor axis, a?

Answer 23

a = cubed root (μ(P/2pi)^2)

the cubed root of gravitational parameter multiplied by the quantity of the period divided by 2pi squared

Question 24

Describe the relationship between the period, nodal displacement, ground track, and semimajor axis.

Answer 24

the bigger semimajor axis,
the longer period
the bigger nodal displacement,
ground track appears to be scrunched closer together

Question 25

How do you determine the inclination from the ground track?

Answer 25

the highest degree of latitude on the ground track (direct orbits)
180 - max latitude (for retrograde orbits)

Question 26

Explain the relationship between the velocity, perigee/apogee, and the ground track.

Answer 26

the faster the velocity, the more spread out the ground track is, the satellite is at perigee
the slower the velocity, the closer the ground track, the satellite is at apogee.