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Re: Orbit Transfer



On Fri, 14 May 1999, Dan Burns wrote:

The problem arises when we do Hohmann transfer problems. Take the following
numerical example. In a transfer from a 7E6 m radius orbit to a 1E7 radius
orbit about the Earth the required delta Vs are obtained by subtracting the
lower circular orbit speed from the perigee speed of the transfer orbit (8188
m/s - 7449 m/s = 639 m/s)

Misprint: "7449" should be "7549" so the energy change is

(1/2)(8188^2 - 7549^2) J = 5.03 MJ (with a 1 kg spacecraft)

and subtracting the apogee speed of the transfer orbit from the upper
circular orbit speed (6316 m/s - 5731 m/s = 585 m/s).

(1/2)(6316^2 - 5731^2)J = 3.62 MJ

For a total of (5.03 + 3.62) MJ = 8.65 MJ

... The energy of the lower circular orbit is -2.85E7 J, the energy of
the transfer orbit is -2.35E7 J, and the energy of the upper circular
orbit is -2.0E7 J.

So the energy difference between the final and initial orbits is

-20 MJ - (-28.5 MJ) = 8 or 9 MJ

within sig fig accuracy of the same value so no problem.

John
----------------------------------------------------------
A. John Mallinckrodt http://www.csupomona.edu/~ajm
Professor of Physics mailto:ajm@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223