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) 9000 N
B) 61 N
C) 110 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, making 4R). The gravitational force (weight) decreases with the square of the distance, so at an altitude of 3R above the Earth's surface, the satellite's weight is reduced by a factor of $1/4^2 = 1/16$ compared to its weight on the Earth's surface. If the satellite's weight on the surface is taken as $mg$ with $g \approx 9.8 \, \text{m/s}^2$, its weight in orbit is significantly less due to the increased distance from the Earth's center. The exact value depends on the calculation using the given formula and the known values of $G$, $m_1$ (mass of the Earth), and $m_2$ (mass of the satellite), but without doing the calculation explicitly and knowing that gravitational force decreases with distance, option B is the most reasonable estimate given the options provided.

The Earth Has Radius R