Question

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

Short answer

a) The ratio F₁/F₂ = ½

b) Ratio a₁/a₂ =1

Step-by-step solution

Part(a) Step 1: Given information

Mass of satellite 1 = 1000 kg

Mass of satellite 2 = 2000 kg

Follow exactly the same orbit around the earth.

Part(a) Step 2 Explanation

Calculate gravitation force on each satellite and find the ratio

Gravitational force on Satellite 1

F₁= m₁g = 1000 kg x g --------------------------(1)

Gravitational force on Satellite 2

F₂= m₂g = 2000 kg x g --------------------------(2)

Divide equation (1) and (2) we get

F₁ /F₂ = 1/2

Part(b) Step 1 : Given Information

Mass of satellite 1 = 1000 kg

Mass of satellite 2 = 2000 kg

Follow exactly the same orbit around the earth.

Part(b) Step 2: Explanation

Find a for each satellite and find the ratio

Force on Satellite 1

$$\begin{gathered} F_1=m_{1}a\mid \\ {F}_1=1000\times a_1\dots .....................\left(4\right) \end{gathered}$$

Similarly on satellite 2

$$\begin{gathered} F_2=m_2{a}_2 \\ {F}_2=2000\times a_2\dots .......................\left(5\right) \\ \frac{F_1}{F_2}=\frac{1000\times a_1}{2000\times a_2} \\ \frac{1}{2}=\frac{1}{2}\times \frac{a_1}{a_2} \\ \frac{a_1}{a_2}=1 \end{gathered}$$