Question

Sputnik, the first artificial satellite to orbit the Earth, had a mass of 83.6kg and travelled at 7574 m/s. The radius of the earth is 6371 km and its mass is 5.972 x 10^24 kg. What gravitational force did Sputnik apply to the earth during this orbit?

Answer 1

Answer:

690.6 N

Explanation:

The gravitational force that the Earth exerts on Sputnik acts as centripetal force to keep the satellite in motion, so we can write

$\frac{GMm}{r^2}=m\frac{v^2}{r}$

where

G is the gravitational constant

M = 5.972 x 10^24 kg is the Earth's mass

m = 83.6 kg is the satellite's mass

v = 7574 m/s is the satellite's speed

r is the distance of the satellite from the Earth's center

Solving for r, we find

$r=\frac{GM}{v^2}=\frac{(6.67\cdot 10^{-11})(5.972\cdot 10^{24})}{(7574)^2}=6.944\cdot 10^6 m$

Now we can find the gravitational force exerted by the Earth on Sputnik:

$F=\frac{GMm}{r^2}=\frac{(6.67\cdot 10^{-11})(5.972\cdot 10^{24})(83.6)}{(6.944\cdot 10^6)^2}=690.6 N$

And according to Newton 3rd law (action-reaction, the force exerted by Sputnik on the Earth is equal to the force exerted by the Earth on Sputnik, so this is the value of the force we are requested to find.