# What is the size of the gravitational force acting on the earth due to the sun?

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Consider the earth following its nearly circular orbit about the sun. The earth has mass earth = 5.98*10^24 kg and the sun has mass sun = 1.99*10^30 kg. They are separated, center to center, by r = 93 million miles = 150 million km.

Consider the earth following its nearly circular orbit about the sun. The earth has mass earth = 5.98*10^24 kg and the sun has mass sun = 1.99*10^30 kg. They are separated, center to center, by r = 93 million miles = 150 million km.

##### 1 Answer

Zero.

#### Explanation:

There is no such thing as a gravitational force. Newton described gravity in terms of a force. It is however just a good approximation.

Einstein's general theory of relativity describes gravity as curvature of 4 dimensional spacetime. The Sun's mass curves spacetime. The Earth has no force acting on it from the Sun. It travels along a geodesic which is the spacetime extension of a straight line.

The Earth appears to have an elliptical orbit but it is in fact the projection of the 4 dimensional geodesic onto our familiar 3 dimensions.