Page 50 - Intro to Space Sciences Spacecraft Applications

vp =J- Orbital Principles 37
(2 - 13)

Being associated with the minimum orbital radius, the periapsis
velocity vp is thefastest velocity in the orbit.

We now have enough information to analyze established orbits if given
just a few of the orbital parameters.

Example Problem:

Due to thrust limitations and the reaches of the atmosphere, the
Space Shuttle is limited to operations between about 200 km to 800
km altitudes. From this information, determine the orbital parame-
ters associated with an elliptical orbit between these two altitudes.

Solution:

a. Semi-major axis (equation 2-1):
a = 6,878 km

Note: altitudes must be converted to orbital radii by adding the
radius of the earth, & = 6,378 km for use in equation 2-1.

b. Orbital period (equation 2-6):
T = 5,677 sec = 94.6 min

Slightly over an hour and a half between sunrises!

c. Total specific energy (equation 2-9):
E = -28.98 km2/sec2

Note: Like eccentricity, knowledge of the total energy can indicate the
type of orbit as well. All “closed” (elliptical and circular) orbits have
negative values for total energy. Zero or positive total energies indi-
cate the “open” (parabolic or hyperbolic) orbits introduced earlier.

d. Eccentricity (using equation 2-3 or equation 2-5):
e = 0.0436