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A 1000 kg satellite and a 2000 kg satellite follow exactly
Chapter 13, Problem 3CQ(choose chapter or problem)
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?
Questions & Answers
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 \(\frac{F_{1}}{F_{2}}=\frac{1}{2}\).