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*Subject*: [amsat-bb] AO40 velocity*From*: "Stacey E. Mills" <w4sm@xxxxxxxxxx>*Date*: Thu, 29 Aug 2002 17:58:55 -0400

Bob said: >Hello >I was asked how fast "those things" go. I took a guess and probably was >fairly correct. That got me thinking how fast really is it. Given the >MA, at that part of the orbit is there a formula that would yield the >velocity at that point? Bob, rather than a function of MA, an easy approach is to calculate velocity as a function of distance from the center of the earth, given the semi-major axis of the orbit. This equation does that. I've plugged in values for AO-40. If I didn't make a math error, the results are shown for apogee and perigee, and comparison with a circular orbit at AO-40's perigee height. v^2 = G * M * ( 2/r - 1/a ) v = velocity at a point in the orbit G = gravitational constant (6.67e-11 in mkgs units) M = central mass (Earth masses 5.98e+24 kg) r = radial distance from the center of the Earth a = semi-major axis (3.6285e7 meters for AO-40) Re = radius of the earth (6.378e6 meters, mean) Hp = perigee height (1.155e6 meters for AO-40) Ha = apogee height (5.867e7 meters for AO-40) Therefore, for AO-40: v^2 = 6.67e-11 * 5.98e24 * (2/r - 1/3.6285e7) = 3.995e14 * (2/r - 2.756e-8) AO-40 velocity at perigee: r = Re + Hp r = 7.533e6 v^2 = 3.99e14 * (2/7.533e6 - 2.75e-8) v = 9744 meters/sec (35,078 km/hr) AO-40 velocity at apogee: r = Re + Ha r = 6.505e7 v^2 = 3.99e14 * (2/6.505e7 - 2.75e-8) v = 1138 meters/sec (4,096 km/hr) ******** For comparison, consider a satellite in a circular orbit at AO-40's perigee height of 1155 km: r = a = 1.155e6 + 6.378e6 r = a = 7.533e6 v^2 = 3.99e14 * 1/7.533e6 v = 7277 meters/sec (26,200 km/hr) AO-40 would zip past the "LEO" at: 9744 - 8277 = 1467 meter/sec (5,281 km/hr) -- ________________________________________________________________________ Stacey E. Mills, W4SM WWW: http://www.cstone.net/~w4sm/ham1.html Charlottesville, VA PGP key: http://www.cstone.net/~w4sm/key ________________________________________________________________________ ---- Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

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