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Gmsmc

r2

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Example 1 - What is the velocity of orbit 250 miles above the earth?r = 6.38x106 m + (250 mi)(1609 m/mi) = 6782250 mmc = 5.97 x 1024 kg, use mv2/r = Gmm/r2

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=

msv2

r

or

ms42r T2

mc

ms

Orbit

Gmsmc

r2

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Example 2 - What is the radius of a geosynchronous orbit?T = 23:56:04 = 23(3600) + 56(60) + 4 = 86164 smc = 5.97 x 1024 kg, use m42r/T2 = Gmm/r2

Algebra

=

msv2

r

or

ms42r T2

mc

ms

Orbit

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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

W

= Gmsmc

r2

msv2

r

7436 m/s

7400 m/s

r

Gmv c

At what distance from the moon’s center is the orbital velocity 52.5 m/s? Mm = 7.36 x 1022 kg

1.78 x 109 m W

= Gmsmc

r2

msv2

r

1781086621 m

r = Gmc

v2

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?

1.2 x 1015 kg W

= Gmsmc

r2

ms42r T2

1.15223E+15 kg

mc = 42r3

GT2

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?

9.0 x 103 s W

= Gmsmc

r2

ms42r T2

8987.5 s

42r3

Gmc

T =