# Energy and gravitation problem

1. Oct 11, 2011

### NewtonianAlch

1. The problem statement, all variables and given/known data
NASA is considering solar sailing: using the momentum of light and of massive particles emitted from the sun to help push a space craft equipped with large, diaphanous sails. Assume that the density of the material from which the sails are made is about 1000kg.m$^{-3}$.

a) What is the minimum thickness of a sail such that the use of the momentum from the sun's light is enough to balance the gravitational attraction (of the sail alone) towards the sun? At the Earth's orbit (150 million km), the "solar constant" or intensity of solar radiation is: 1.4kW.m$^{-2}$.

m$_{sun}$ = 1.99E30, G = 6.67E-11

b) How does the answer depend on distance from the sun?

2. Relevant equations

Force = Gmm/r^2
Volume = Area x Thickness
Density = Mass/Volume

3. The attempt at a solution

I'm not entirely sure how to start this. I guess I would need to find out the Area somehow, as well as the mass of the sail, that could help determine the gravitational attraction.

2. Oct 12, 2011

### ehild

Consider the area 1 m^2.

ehild

3. Oct 12, 2011

### Staff: Mentor

You might also want to investigate "radiation pressure".

4. Oct 14, 2011

### NewtonianAlch

Where did you get that from?

5. Oct 14, 2011

### ehild

The given data are the density of the sail material and the intensity of the light. So both mass and force are directly proportional to the area of the sail. The area will cancel from the equation of equilibrium, just like it cancels in the equation of planetary motion: it does not matter if a fly orbits around a planet or a big space station, they move with the same velocity at the same orbit. If you do not like 1m2 for the area, just call it A.

ehild