Question

If the speed of a satellite orbiting the Earth at a distance r from the center of the Earth is v, what is the speed of a second satellite orbiting the Earth at a distance 2r from the center of the Earth? (A) 2 $\mathrm{V}$ (B) $\sqrt{2} \mathrm{v}$ (C) $\frac{1}{\sqrt{2}} v$ (D) $\frac{1}{2} v$

Name: Problem 28, Chapter 14: Cracking The AP Physics 1 Exam
Uploaded: 2021-04-08T17:37:46-08:00
Duration: 58 s
Channel: Sachin Rao
Description: If the speed of a satellite orbiting the Earth at a distance r from the center of the Earth is v, what is the speed of a second satellite orbiting the Earth at a distance 2r from the center of the Earth? (A) 2 V (B) √(2) v (C) (1)/(√(2)) v (D) (1)/(2) v

   If the speed of a satellite orbiting the Earth at a distance r from the center of the Earth is v, what is the speed of a second satellite orbiting the Earth at a distance 2r from the center of the Earth?
(A) 2 $\mathrm{V}$
(B) $\sqrt{2} \mathrm{v}$
(C) $\frac{1}{\sqrt{2}} v$
(D) $\frac{1}{2} v$

Cracking The AP Physics 1 Exam

Robert Franek 1st Edition

Chapter 14, Problem 28

Instant Answer

Solved by Expert Sachin Rao

04/08/2021

Step 1

Step 1: The speed of a satellite orbiting the Earth at a distance r from the center of the Earth is given by the formula $v = \sqrt{\frac{GM}{r}}$, where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Show more…

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If the speed of a satellite orbiting the Earth at a distance r from the center of the Earth is v, what is the speed of a second satellite orbiting the Earth at a distance 2r from the center of the Earth? (A) 2 $\mathrm{V}$ (B) $\sqrt{2} \mathrm{v}$ (C) $\frac{1}{\sqrt{2}} v$ (D) $\frac{1}{2} v$

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Key Concepts

Orbital Speed and Radius Relationship

The orbital speed of an object in a circular orbit is given by the formula v = ?(GM/r), which shows that the speed is inversely proportional to the square root of the orbit's radius. This relationship is essential for comparing orbital speeds at different radii, as a larger orbital distance results in a lower orbital speed.

Newton's Law of Universal Gravitation

This law states that every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. It is fundamental in understanding how gravitational forces operate on celestial bodies.

Centripetal Force in Circular Orbits

For an object to maintain a circular orbit, the inward gravitational force must exactly equal the required centripetal force. This balance allows the derivation of the orbital speed formula, making it clear how the gravitational force keeps the satellite in orbit.

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