According to Keplers 3rd Law, how would a planets orbital period change if the planets a)...

Question:

According to Keplers 3rd Law, how would a planets orbital period change if the planets

a) eccentricity doubled?

b) mass halved?

c) distance from the sun quadrupled?

Kepler's Law:

Kepler went through and developed three laws to describe planetary motion. These help to explain the shape, the varying speeds of orbit, and the period.

Answer and Explanation:

Kepler's Third Law:

{eq}P^2 = \frac{4 \pi^2 a^3}{GM} {/eq}

a.) Eccentricity would have no impact on the period as there are several other factors that would change to allow for this.

b.) If the mass is halved, the period would increase by about 1.4.

{eq}P^2 = \frac{1}{m} = \frac{1}{\frac{1}{2}} \\ P^2 = 2 \\ P = \sqrt{2} = 1.41 {/eq}

c.) If distance quadrupled, the period would increase by a factor of eight.

{eq}P^2 = a^3 = 4^3\\ P^2 = 64 \\ P = \sqrt{64} = 8 {/eq}


Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
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