Why does the earth orbit the sun rather than be pulled into it?

Answer 1

This is a very good question!

I'll try to give you a visual example first (not mine but from the master, I. Newton):

We can see that the object (in this case a bullet) fired from the mountain at #V# falls back on the surface of Earth being attracted by it (gravitational pull); BUT if the initial velocity is high enough (and no friction) it "will keep on falling" without ever reaching the surface (=orbiting).
On the other hand if the initial velocity is too high the bullet will spiral out and escape.

Transfer this to the Sun-Earth system; at the start of s8lar system formation Earth acquired enough velocity to continuously fall like the bullet.

Hope it helps.

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Answer 2

Clara Avalos

The Earth orbits the Sun due to the gravitational force between them, counteracted by the Earth's tangential velocity, resulting in a stable orbit.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.