# What is the Sun's gravitational pull strength?

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Oct 13, 2017

The strength of the Sun's gravitational field depends on the distance from the Sun.

#### Explanation:

The Sun, and any other body, has a gravitational field. This field causes any other body to accelerate. Newton described this with his inverse square law and his second law force $F$ equals mass $m$ times acceleration $a$.

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

$a = \frac{G M}{r} ^ 2$

This says that the acceleration $a$ due to gravity is independent of the mass of the body $m$ under gravity. Where $G M = 132 , 712$ is the gravitational constant multiplied by the mass of the Sun and $r$ is the distance from the Sun.

General Relativity (GR) redefines gravity. It is not a force, it is a consequence of space time being curved by mass, energy and momentum. For relatively small masses, which includes the Sun, and low speeds GR reduces to Newton's laws.

Everything in a gravitational field experiences an acceleration towards the centre of the body causing the gravitational field. Everything follows a geodesic, which is the 4 dimensional equivalent of a straight line in curved space time.

So, the Sun doesn't exert a pull strength, it simply bends space time because of its mass and motion.

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