Calculating Solar Sail Size for Propulsion Against Sun's Gravitational Force

[desibrij_1785]

whats up guys. help me out

NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low-mass sail and the energy and momentum of sunlight for propulsion.

The total power output of the sun is . How large a sail necessary to propel a 10,000-kg spacecraft against the gravitational force of the sun?

Answer must be in km^2

 

[HallsofIvy]

"The total power output of the sun is . " Was there supposed to be something at the end of that sentence? My guess is that you take the "total power output of the sun" and multiply by the ratio of the size of your sail to the size of the sphere around the sun at your distance (that gives the fraction of the total power that falls on your sail). That should be equal to the force of gravity at that distance.
In fact, if you are clever, you don't need to take distance into account:
Call the total power output (the thing missing from our sentence) "P" and the area of your solar sail "A". If you are "r" meters from the sun, then the total area of the sphere of radius r about the sun is 4πr² square meters. The fraction of the sun's power that is falling on your sail is A/(4πr²) so the power the sail is receiving is PA/(4πr²). The force of gravity you need to overcome at that distance is GMm/r². An important number missing from your information is the "efficiency" of your sail: k. The force on your sail due to the "solar wind" will be kPA/(4πr²)= GMm/r² and the "r²" cancels out: You must have A= 4πGMm/kP.

Apparently you were given "P" and should be able to look up "G" (the universal gravitational constant) and "M" (the mass of the sun). You will also need to know (be given) k (the "efficiency" constant for your sail) and m (the mass of your sail and payload).

 

[desibrij_1785]

power value is 3.9*10^26 and there is no efficiency of the sail. i tried your way and i got answer to be .04 m^2 but actual answer is 6.48 km^2. I got that answer by guessing...

Thanks anyways.

 

[Nereid]

The Planetary Society has a solar sail project. One section of their "Cosmos 1" website is http://www.planetary.org/solarsail/allaboutsolarsails.html , and contains a discussion of the factors of interest. It may not give you exactly what you want, but there's more than enough on the site for you to work out the rest yourself.