Question

Suppose Comet Wild 2 had a small satellite, like the asteroid Ida in Figure 9.32. If this satellite were to orbit at twice the radius of the comet, what would be its period of revolution? A. $0.93 \mathrm{~h}$ C. $5.8 \mathrm{~h}$ B. $2.9 \mathrm{~h}$ D. $8.2 \mathrm{~h}$

Name: Problem 118, Chapter 9: Pearson Physics
Uploaded: 2023-03-17T16:56:31-08:00
Duration: 3 min 23 s
Channel: Prabhat Tyagi
Description: Suppose Comet Wild 2 had a small satellite, like the asteroid Ida in Figure 9.32. If this satellite were to orbit at twice the radius of the comet, what would be its period of revolution? A. 0.93 h C. 5.8 h B. 2.9 h D. 8.2 h

   Suppose Comet Wild 2 had a small satellite, like the asteroid Ida in Figure 9.32. If this satellite were to orbit at twice the radius of the comet, what would be its period of revolution?
A. $0.93 \mathrm{~h}$
C. $5.8 \mathrm{~h}$
B. $2.9 \mathrm{~h}$
D. $8.2 \mathrm{~h}$

Pearson Physics

James S. Walker 1st Edition

Chapter 9, Problem 118

Instant Answer

Solved by Expert Prabhat Tyagi

03/17/2023

Step 1

1 \times 10^{14}$ kilograms. We are also given that the satellite is orbiting at twice the radius of the comet, which we can write as $2 \times 2.7 \times 10^{3}$ meters. Show more…

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Suppose Comet Wild 2 had a small satellite, like the asteroid Ida in Figure 9.32. If this satellite were to orbit at twice the radius of the comet, what would be its period of revolution? A. $0.93 \mathrm{~h}$ C. $5.8 \mathrm{~h}$ B. $2.9 \mathrm{~h}$ D. $8.2 \mathrm{~h}$

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Key Concepts

Kepler's Third Law

This law connects the orbital period of an object with its average distance from the body it is orbiting. It states that the square of the period is proportional to the cube of the semi?major axis of the orbit, which means that if the distance increases, the period increases following a specific scaling relation. This law is fundamental in understanding orbits in any gravitational system.

Scaling Relationship in Orbital Mechanics

In orbital mechanics, changing the distance (or radius) of an orbiting satellite affects the orbital period according to a specific power law derived from Kepler's third law. When the orbital radius is increased by a factor, the period increases by that factor raised to the power of 3/2, which illustrates how sensitive orbital periods are to the distance from the central body.

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