## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 1 - Problems - Page 23: 82

#### Answer

The period of Mars is about 2.8 times the period of Venus.

#### Work Step by Step

$T^2 = c~r^3$, where $c$ is a constant $T = \sqrt{c~r^3}$ We can write an expression for the period of Mars: $T_m = \sqrt{c~r_m^3}$ We can write an expression for the period of Venus: $T_v = \sqrt{c~r_v^3}$ We can divide the period of Mars by the period of Venus: $\frac{T_m}{T_v} = \sqrt{\frac{c~r_m^3}{c~r_v^3}}$ $\frac{T_m}{T_v} = \sqrt{\frac{(2~r_v)^3}{r_v^3}}$ $\frac{T_m}{T_v} = \sqrt{8}$ $\frac{T_m}{T_v} = 2.8$ The period of Mars is about 2.8 times the period of Venus.

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