Satellite A orbits a planet with a speed of 10,000

osteoblogda 2021-12-18 Answered
Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Assume that both orbits are circular.
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Expert Answer

Joseph Lewis
Answered 2021-12-19 Author has 43 answers
Step 1
Given values:
vA=10000ms
mB=2mA
rB=rA
The gravitational force is equal to:
FGA=GmAmrA2 (Equation 1.)
FGB=GmBmrB2
FGB=G2mAm2rA2
FGB=G2mAm4rA2 (Equation 2.)
According to the Newtons

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Matthew Rodriguez
Answered 2021-12-20 Author has 32 answers
vB=100002ms
Given:
OA=r;OB=2r
mA=m;mB=2m
vA=10000ms;vB=?
mp: mass of planet
mAgAmBgB=KmAmPr2mBmp4r2
yields gAgB=4mAmB(1)
mAgAmBgB=mAvA2r2mBvB24r2
yields gAgB=4vA2vB2(2)
so (1)=(2)
mAmB=vA2vB2
mA=m;mB=2m;
m2m=vA2vB2;vB2=2vA2;vB=vA2
vA=10000ms
vB=100002ms

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nick1337
Answered 2021-12-27 Author has 575 answers

Satellite B's mass is not relevant, but at twice the distance, its orbital period is greater by a factor of (2)3=22. But the distance it must travel during each period is also greater by a factor of 2. Thus, its speed is 222 less or 12 less.
VB=0.7071
VA=7.071ms7×103ms.

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