Ask Question
26 December, 18:53

A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth. What is the ratio F1/F2 of the gravitational force on the first satellite to that on the second satellite? What is the ratio a1/a2 of the acceleration of the first satellite to that of the second satellite?

+4
Answers (1)
  1. 26 December, 19:20
    0
    the ratio F1/F2 = 1/2

    the ratio a1/a2 = 1

    Explanation:

    The force that both satellites experience is:

    F1 = G M_e m1 / r² and

    F2 = G M_e m2 / r²

    where

    m1 is the mass of satellite 1 m2 is the mass of satellite 2 r is the orbital radius M_e is the mass of Earth

    Therefore,

    F1/F2 = [G M_e m1 / r²] / [G M_e m2 / r²]

    F1/F2 = [G M_e m1 / r²] * [r² / G M_e m2]

    F1/F2 = m1/m2

    F1/F2 = 1000/2000

    F1/F2 = 1/2

    The other force that the two satellites experience is the centripetal force. Therefore,

    F1c = m1 v² / r and

    F2c = m2 v² / r

    where

    m1 is the mass of satellite 1 m2 is the mass of satellite 2 v is the orbital velocity r is the orbital velocity

    Thus,

    a1 = v² / r ⇒ v² = r a1 and

    a2 = v² / r ⇒ v² = r a2

    Therefore,

    F1c = m1 a1 r / r = m1 a1

    F2c = m2 a2 r / r = m2 a2

    In order for the satellites to stay in orbit, the gravitational force must equal the centripetal force. Thus,

    F1 = F1c

    G M_e m1 / r² = m1 a1

    a1 = G M_e / r²

    also

    a2 = G M_e / r²

    Thus,

    a1/a2 = [G M_e / r²] / [G M_e / r²]

    a1/a2 = 1
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth. What is the ratio F1/F2 of the gravitational ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers