Chapter 16, Problem 4E

### An Introduction to Physical Science

14th Edition
James Shipman + 3 others
ISBN: 9781305079137

Chapter
Section

### An Introduction to Physical Science

14th Edition
James Shipman + 3 others
ISBN: 9781305079137
Textbook Problem

# Calculate the length R of the semimajor axis of a planet whose period is 165 years.

To determine
Length of semi-major axis having a time period 165 years .

Explanation

Given info: Period of the planet is 165Â years .

Explanation:

Keplerâ€™s third law is also known as the harmonic law. It states that the square of the time period of the object is directly proportional to the cube of the semi-major axis.

It is represented mathematically as follows,

T2=kR3

Here,

T is the orbital time period

R is the semi-major axis

k is the proportionality constant

Rearrange the above equation to get an expression for the semi-major axis.

R3=T2k

Substitute 165Â years for T and 1Â years2(AU)3 for k

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