I am having trouble with one of the problems on my hw. The question is:(adsbygoogle = window.adsbygoogle || []).push({});

Because light carries momentum, it creates pressure when it shines on something. This has led people to propse using "solar sails" instead of conventional rocket engines on interplanetary or interstellar space craft.

A. Use dimensional analysis to estimate the light pressure at a ditance d from a star with luminosity L

B.What is the force on a solar sail with the area of 1km^2 that is the same distance from the sun as earth?

C.Suppose the sail is pulling a ton spacecraft. How long would it take to reach jupiter's orbit, which is 5.2 au from the sun? For this estimate you may assume the acceleration remains constant, even though we found above that the pressure varies with teh distance from the star.

The only part of this problem that is difficult for me is the relationship between luminosity pressure and distance. I feel once i can find the relationship between them I can solve the rest of the problem easily. Luminosity is J/sec which is M L^2 T^-3 ~ so we have to find Pressure and distance units that is equal to this right? I am having a problem figuring out how to do this.

Ive been looking at the examples in my notes. I understand how to we find the relationship between p and kT by dividing their units and seeing L^-3 which is n. We then get the relationship p~nKT but I dont understand how we can intuitively assume some other equations likeP~h^i c^j (kT)^l for a relativistic gas then solve and get P~(kT)^4/(hc)^3 . I understand the algebra but i just dont get how we can intuitively assume h c and (kT) will be factors in the equation for P and not anything else. I think if i can understand this example in the notes i will also get the question for the hw.

Sorry for the long question and thanks in advance

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# Dimensional analysis on Luminosity

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