A 1000 kg satellite and a 2000 kg satellite follow exactly

Chapter 13, Problem 3CQ

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QUESTION:

Problem 3CQ

A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.

a. What is the ratio F 1 /F 2 of the force on the first satellite to that on the second satellite?

b. What is the ratio a 1 /a 2 of the acceleration of the first satellite to that of the second satellite?

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QUESTION:

Problem 3CQ

A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth.

a. What is the ratio F 1 /F 2 of the force on the first satellite to that on the second satellite?

b. What is the ratio a 1 /a 2 of the acceleration of the first satellite to that of the second satellite?

ANSWER:

Step 1 of 2

a) We need to find the ratio \(\frac{F_{1}}{F_{2}}\).

The force of the Earth on the first satellite,

\(F_{1}=\frac{G M_{e} m_{2}}{r_{1}^{2}}\)

While,

\(F_{1}=\frac{G M_{e} m_{2}}{r_{2}^{2}}\)

Since \(r_{1}=r_{2}\0,

\(\frac{F_{1}}{F_{2}}=\frac{m_{1}}{m_{2}}\)

Mass of the first satellite, \(m_{1}=1000 \mathrm{~kg}\)

Mass of the second satellite, \(m_{2}=2000 \mathrm{~kg}\)

\(\frac{F_{1}}{F_{2}}=\frac{1000 \mathrm{~kg}}{2000 \mathrm{~kg}}\)

\(\frac{F_{1}}{F_{2}}=\frac{1}{2}\)

Therefore, the ratio \(\frac{F_{1}}{F_{2}}=\frac{1}{2}\).

 

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