Three satellites orbit a planet of radius R , as shown in the figure. Satellites

Question

Three satellites orbit a planet of radius R, as shown in the figure. Satellites S1 and S3 have mass m. Satellite S2 has mass 2 m. Satellite S1orbits in 240 minutes and the force on S1 is 10,000 N.

a) What is the magnitude of the net gravitational force on the m1=20kg mass? Assume m2=10kg and m3=15kg.

b)What is the direction of the net gravitational force on the m1=20kg mass? Assume m2=10kg and m3=15kg.

c) What is the magnitude of the net gravitational force on the m2=10kg mass? Assume m1=20kg and m3=15kg.

my correct answer
F =

5.20×10?7N

D) What is the direction of the net gravitational force on the m2=10kg mass? Assume m1=20kg and m3=15kg.

please explain it out so I'll understand and learn please. thanks :)

Explanation / Answer

we know that,

T 2 = ( 4 2 /G M ) r3 So, 8R = (GMT2/42)1/3 = {(6.67 x 10-11x 2 x 1030 x144002 / (39.5)}1/3 =(7 x 1026)1/3

=1.91 x 102.96 m or 1742 m So,R = 217.8 m (approximately)

F1 = {(G/R2)(m1m2)+(G/4R2)m1m3} = (6.67 x 10-11/217.82)(m1m2+m1m3)

= 1.4x 10-15 (m1m2)+0.35x10-15 *(m1m3) =1.75 x 10-15 (500) = 8.75 x 10-13 N

Similarly,Other things will be calculated by replacing the values

like , F2 = {(G/R2)(m2m1)+(G/R2)m2m3} = 2F1

And F3 = {(G/4R2)(m1m3)+(G/R2)m2m3} =F1

And direction is Towards centre of planet and bounded

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