Circular motion homework

Answer the following Qs on lined paper.  They combine the circular motion and gravitational force topics.

1. Show that the centripetal force needed to make the Earth orbit the Sun and the gravitational force between the Earth and the Sun are the same size.  149.6x10^6 km seperation.
2. Show this is also true for Neptune.  Neptune’s mass is 1.02×10^26 kg and it is 4.498x10^9 km
3. If planet X existed at 1000 times the distance from the Sun that the Earth is and was 10 times the mass, what length would its year be?
4. How would this year change if it was 100 x the Earth’s mass?

Due Thursday 29th Sept.