## anonymous 4 years ago Evil integration problem!

1. anonymous

Concerning the first law of gravitation, I am seeing whether the same result can be achieved by integration as if you treat a planet (orbiting the son) as a point-like particle (at its centre of mass)

2. anonymous

Firstly, consider the sun. If we draw a circle around the it, we can say that the same force will act on 1kg anywhere in the circle.|dw:1328041371179:dw|

3. anonymous

Now, consider a planet orbiting the sun|dw:1328041409993:dw| (Not to scale)

4. anonymous

|dw:1328041434214:dw| All the 'particles' in the arc will experience the same force. The area of the arc is, for any point x-t :$2\pi*q*\theta/360$ All terms in the drawing can be easily worked out as functions of x, taken that z and r are constants. What would you actually do to work out the area and the force acting on it due to Newton's First Law of Gravitation by integration?