Appendix C, Orbital Velocities and Time

from: Infrared Design Examples

Author(s): William L. Wolfe

Published: 15 July 1999

Chapter DOI: http://dx.doi.org/10.1117/3.343801.apc

Chapter Page Count: 2 pages

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Front Matter

1. Review of Design Fundamentals

2. The MX Shell Game

3. The Space Campout

4. An Infrared Night-Driving System

5. The Broad Ocean Surveillance System (BOSS)

6. Collision Avoidance Reaction Equipment (CARE)

A. Scanners

B. Optical Systems

C. Orbital Velocities and Time

Back Matter

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Excerpt

Orbital velocities and periods can be calculated by a more accurate formula than that used in the text. The formula is

where v is the orbital velocity, g is the gravitational force, R_E is the radius of the Earth, R is the instantaneous satellite height, measured from the center of the earth, R_ave is the average radius of the orbit, also measured from the center of the Earth. The orbital period is given by

The calculation is made in Fig. C-1.

The velocity at orbital altitude is a function of the altitudes of apogee and perigee, with the subscripts ap and per, as measured from the center of the earth. That is why the altitudes from the surface have added to them the radius of the Earth. The velocity one needs for the scanner calculations is the linear velocity on the surface of the Earth; it is different from that at altitude. The angular velocity is constant, so the two velocities are related by the ratio of radii. Notice that for a 200 km altitude, the velocity is about 7.6 km∕s, very close to the approximation made in the main part of the text.

http://dx.doi.org/10.1117/3.343801.apc

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