Question

At what distance from the Earth’s surface is a 10,000 kg satellite if its potential energy is equal to –5.58 x 1011 J? (choose the closest answer)
A 958 km

B 858.km

C 758 km

D 658 km

Answer 1

Answer:

Option D

Explanation:

As we know

Gravitational Constant (G) $= 6.67*10^{11}$

Mass of Earth (M) $= 5.98*10^{24}$

Weight of satellite (m) $= 10,000$ Kg

Radius of Earth (R) = $6.378*10^6$

Distance of satellite from Earth = $\frac{GMm}{R} - U$

Substituting the given values, we get

$D=\frac{(-((6.67*10^{11})(5.98*10^{24})(10000))}{(6.378*10^6)} - (-5.58*10^{11})\\\\0.625*10^{3}$Km

or 635 m

The correct answer is option D