Question

How does the law of universal gravitation apply to planet motion around the Sun?

Answer 1

The Sun's gravitational force pulls on the planets which move perpendicular to this force at all times creating a elliptical (ideally circular) path around the Sun.

Explanation:

Let's use the Earth as an example:
As the Sun pulls the Earth towards it, the Earth moves very quickly (velocity around 30km/s) perpendicular to the force of gravity. These two forces create a resultant force pointed between the Sun and the Earth's path (let's just say this 30 degrees). Therefore, at all points around the Sun, the Earth will move at a 30 degree angle, creating a circle with radius r (r=93 million miles).