The earth has radius R.A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface.What is the satellite's weight at the altitude of its orbit?
A)61 N
B)110 N
C)9000 N
D)16,000 N

Question

Quizplus · Accepted Answer

The weight of an object in orbit can be calculated using the formula for gravitational force: $F = \frac{Gm_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers. In this case, $r = 4R$ (since the satellite is 3R above the Earth's surface, the total distance from the Earth's center is the Earth's radius $R$ plus 3R). The gravitational force (weight) decreases with the square of the distance, so at 4R, the weight is $\frac{1}{16}$th of its weight on the surface (since $(4R)^2 = 16R^2$). If the satellite's weight on the surface is $980 N$ (using $g = 9.8 m/s^2$ for Earth's surface gravity), at 4R from the center, its weight would be $\frac{980 N}{16} = 61.25 N$, which rounds to $61 N$, making A the correct choice.

The Earth Has Radius R