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
[tex]\frac{GMm}{r^2}=m\frac{v^2}{r}[/tex]
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
[tex]r=\frac{GM}{v^2}=\frac{(6.67\cdot 10^{-11})(5.972\cdot 10^{24})}{(7574)^2}=6.944\cdot 10^6 m[/tex]
Now we can find the gravitational force exerted by the Earth on Sputnik:
[tex]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[/tex]
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.
