Chapter 5 : Describing Orbits Flashcards
1. Define classical orbits elements and use them to describe an orbit 2. determine the COEs given the R and V vectors 3. Explain and use orbital ground tracks
What are the classical orbital elements?
set of variables used to describe an orbit
- a semimajor axis (size)
- e eccentricity (shape)
- i inclination (tilt)
- Ω RAAN (orientation)
- ω argument of perigee (location of perigee)
- ν true anomaly (location of spacecraft from perigee)
How do you determine orbital size?
specific mechanical energy (km^2/s^2) using the equation
ε = -μ/2*a
What does eccentricity describe, how do you determine eccentricity, and describe the eccentricity value perimeters for specific orbital shapes.
shape e = (2*c)/(2*a) circle e = 0 ellipse 0 < e < 1 parabola e = 1 hyperbola e > 1
What is used to find the tilt of an orbit?
inclination which is the angle from the K unit vector to the h vector (h is a vector perpendicular to the orbital plane)
What are the perimeters of inclination?
i = 0 or 180 equatorial orbit
i = 90 polar orbit
0 < i < 90 prograde orbit
90 < i < 180 retrograde orbit
Retrograde orbit is described as what?
an indirect orbit in which the spacecraft travels in the opposite direction of earths rotation
What is a prograde orbit?
a direct orbit in which the spacecraft travels in the same direction of earths rotation
Describe what RAAM is.
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
What is the argument of perigee?
ω, the angle from the ascending node to the perigee, along the orbital path in the direction of the flight path
What is ν?
true anomaly, which is the angle from the perigee to the spacecrafts position along the orbit in the direction of the flight path
A geosynchronous orbit is?
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)
What is a sun synchronous orbit?
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
The Molniya Orbit is?
an orbit that is highly eccentric (e = 0.7) that has ~ 12 hour orbit period, designed by the Russians for communication and intelligence
What is a low earth orbit?
orbit around earth with a up to 250 miles (6700 km), used for manned space missions, communications and reconnaissance.
e = 0
What is a semi-synchronous orbit?
synchronous orbit that increases coverage, app. 10,900 miles, and a period of 12 hours
A geostationary orbit is?
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
How do you compute the semimajor axis?
a = μ/-2ε
where ε = V^2/2 - μ/R
(specific mechanical energy)
What is μ and what is its value?
universal graviational constant multiplied by Earth’s mass
GM = μ = 3.986E5 km^3/s^2
In which direction does the satellites ground track shift?
if prograde - westerly movement
if retrograde - easterly movement
What is ∆N
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.
How much does earth rotate in degrees with respect to time?
360 deg / 24 hours
15 deg / 1 hour
0.25 deg / 1 min
The equation for the orbital period in hours is?
P (hours) = ∆N/(15deg/hour)
for direct orbits
What is the relation between the period, P, and the semimajor axis, a?
a = cubed root (μ(P/2pi)^2)
the cubed root of gravitational parameter multiplied by the quantity of the period divided by 2pi squared
Describe the relationship between the period, nodal displacement, ground track, and semimajor axis.
the bigger semimajor axis,
the longer period
the bigger nodal displacement,
ground track appears to be scrunched closer together
How do you determine the inclination from the ground track?
the highest degree of latitude on the ground track (direct orbits)
180 - max latitude (for retrograde orbits)
Explain the relationship between the velocity, perigee/apogee, and the ground track.
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.
