Understanding Orbital Mechanics and Calculations
Explore examples and calculations related to orbital mechanics, including determining velocities and distances in various orbits around celestial bodies. Learn about geosynchronous orbits, spacecraft mass calculations, and orbital periods in different scenarios.
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Presentation Transcript
Orbit Orbit condition Example Whiteboards
Orbit msv2 r ms = Gmsmc r2 or mc ms4 2r T2 Example 1 - What is the velocity of orbit 250 miles above the earth? r = 6.38x106 m + (250 mi)(1609 m/mi) = 6782250 m mc = 5.98 x 1024 kg, use mv2/r = Gmm/r2 Do algebra first!!!!!!!! TOC
Orbit msv2 r ms = Gmsmc r2 or mc ms4 2r T2 Example 2 - What is the radius of a geosynchronous orbit? T = 23:56:04 = 23(3600) + 56(60) + 4 = 86164 s mc = 5.97 x 1024 kg, use m4 2r/T2 = Gmm/r2 TOC
Whiteboards: Orbit 1 | 2 | 3 | 4 TOC
What is the velocity of orbit 7.2 x 106 m from the earth s center for a 23.5 kg object? Me = 5.97 x 1024 kg msv2 r = Gmsmc r2 v = Gmc r 7437 m/s W 7400 m/s
At what distance from the moons center is the orbital velocity 52.5 m/s? Mm = 7.36 x 1022 kg msv2 r = Gmsmc r2 r = Gmc v2 1781086621 m W 1.78 x 109 m
You are orbiting 2.3 km from the center of an asteroid in a 24,600 kg spacecraft with a period of 2500 seconds. What must be the mass of the asteroid? ms4 2r T2 = Gmsmc r2 mc = 4 2r3 GT2 1.15223E+15 kg W 1.2 x 1015 kg
You are orbiting 8.5 x 106 m from the center of a planet with a mass of 4.5 x 1024 kg. Your spaceship has a mass of 45,120 kg. What is your period of motion? = Gmsmc r2 T2 ms4 2r 4 2r3 Gmc T = 8987.5 s W 9.0 x 103 s
