Newton's laws - The Earth and the Sun

Problem Statement:

The Earth describes an elliptical orbit during its motion around the Sun as shown in the figure. Draw the forces that act on the Earth and the Sun.

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Solution:

The only force that acts in this case on both the Earth and the Sun is the gravitational force. The action of this force on the two bodies constitutes an action-reaction pair, because it corresponds to the mutual interaction that the two bodies experience.

Since Newton’s third law must be fulfilled, both will have the same magnitude and opposite directions:

Even if the norm is the same for both forces, the acceleration that this force causes on the Earth is not the same as on the Sun because the two bodies have different masses.

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Note that although the only force acting on the Earth is directed towards the Sun, the Earth does not move in that direction. The force changes the direction of the velocity vector (tangent to the trajectory), it does not cause the Earth to be directed towards the Sun, but that the Earth has an elliptical trajectory.

The Earth has a normal and a tangential acceleration in its motion around the Sun, these two accelerations change the magnitude and the direction of the velocity vector.

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