Chapter 13: Q. 3 (page 353)

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

Expert verified

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

$F_{1} = m_{1} a ∣ F_{1} = 1000 \times a_{1} \dots . . . . . . . . . . . . . . . . . . . . . (4)$

Similarly on satellite 2

$F_{2} = m_{2} a_{2} F_{2} = 2000 \times a_{2} \dots . . . . . . . . . . . . . . . . . . . . . . . (5) \frac{F_{1}}{F_{2}} = \frac{1000 \times a_{1}}{2000 \times a_{2}} \frac{1}{2} = \frac{1}{2} \times \frac{a_{1}}{a_{2}} \frac{a_{1}}{a_{2}} = 1$

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Short Answer

Step by step solution

Part(a) Step 1: Given information

Part(a) Step 2 Explanation

Part(b) Step 1 : Given Information

Part(b) Step 2: Explanation

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