# If the average distance between Earth and the Sun were doubled, what changes would occur in the sun's gravitational pull on Earth and Earth's period of revolution?

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Jan 7, 2017

Doubling the distance from the sun reduces gravitational pull and increases the orbital period.

#### Explanation:

Using Newton's model of gravity the force or pull $F$ is given by:

$F = \frac{G M m}{r} ^ 2$

Where G is the gravitational constant, M is the mass of the Sun, m is the mass of the Earth and r is the distance between Sun and Earth.

So, doubling the distance reduces the force by a factor of 4.

Kepler's third law relates the semi-major axis distance $a$ in AU(Astronomical Units) to the orbital period $P$ in years.

${P}^{2} = {a}^{3}$

In the case of Earth in its current position $P = 1$ and $a = 1$. If the distance was doubled then $a = 2$ and:

${P}^{2} = {2}^{3} = 8$

This would make the orbital period $P = 2.828$ years.

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