A satellite orbits Earth at a height of 2r Earth . What is the acceleration due to gravity on t

step 1 In this question, we have a satellite orbiting around the Earth, K at twice the radius. So this

A satellite orbits Earth at a height of 2r Earth . What is...

A satellite orbits Earth at a height of 2$r_{\text { Earth }} .$ What is the acceleration due to gravity on this satellite toward Earth in terms of Earth's surface gravity, $g ?$
(A) $\frac{1}{8} g$
(B) $\frac{1}{4} g$
(C) $\frac{1}{2} g$
(D) $g$
(E) 2$g$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Newton’s Law of Universal Gravitation

This principle states that every mass attracts every other mass in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It provides the fundamental framework for understanding how gravitational forces govern the motion of objects, including satellites orbiting a planet.

Inverse Square Law

The inverse square law is the mathematical relationship indicating that a physical quantity or intensity (in this case, gravitational force) is inversely proportional to the square of the distance from its source. This concept is critical for determining how the gravitational acceleration experienced by an orbiting satellite compares to the acceleration due to gravity at Earth’s surface.

Gravitational Acceleration Comparison

Using the inverse square law, one can compare the gravitational acceleration at different distances from the center of the Earth. By expressing the acceleration as GM/r² (with g as GM/r?² at Earth’s surface), it becomes possible to determine the satellite’s gravitational acceleration in terms of g by adjusting for the ratio of the distances squared. This comparison is essential for solving problems involving satellites at various orbital distances.

Please give Ace some feedback