I have finally cracked it!
Thanks for all the help gneill and BobG
After some algebra I found that the ratio
\frac{A}{m}=\frac{4\pic}{P(1+\kappa)}(\frac{v^2r}{2}-GM)
where A=Surface area of sail, m=mass of sail, P=irradiance or power of the Sun (constant)=3.846\times10^{26}W...
Cheers guys, I'm finally getting my head round it, I think I was trying to over complicate it by trying to find trajectories etc. I followed through these steps and got an answer of
\frac{A}{m}=\frac{1.355\times10^3}{1+q}
is this what you got?
If not, here are the steps I followed...
I can see three different ways of thinking about it with completely different answers and I don't know which one (if any) are correct:
1) the force pointing into the sun is
F=\frac{mv^2}{r}
The force out from the sun provided by the thrust from the sunlight is
F=\frac{2PA}{4\pi r^2...
If the only acceleration is radially, can i do this:
a=\frac{dv}{dt} and v=\frac{dr}{dt}
so dt=\frac{dv}{a}=\frac{dr}{v}
vdv=adr
\int{vdv}=\int{adr} with the limits on dv being u and v_e and the limits on dr being r'' and r' (i'm not sure about the limits)...
I have worked through some sums, got a bit further and got stuck again:
The escape velocity at a position r' is:
v_e=\sqrt{\frac{2GM}{r'}}
Say the sail is in circular orbit. Then Newtons 2nd law for centripetal force at a radius r'' is:
F_c=\frac{mu^2}{r''}
This force is only provided by...
It is part of a project I have to do at Uni but I'm stuck on this part!
I have gone back to the beginning to try to understand it more..I have the force produced by the sun's intensity (for a perfectly reflecting surface area A) is:
F_r=\frac{\2<I>A}{c}
where <I> is the time-averaged intensity...
I hadn't seen it that way..
So say the solar sail starts with an elliptical orbit around the Sun, even the smallest force would allow it to escape the Sun's gravitational pull?
If I wanted to incorporate the radiation pressure and initial orbit into an equation to show how a different surface...
Homework Statement
I am trying to work out the force on a solar sail at 1AU due to radiation pressure from the Sun, and also the force on it due to the Sun's gravity. I know G=6.67x10^-11; the mass of the sun M_s=2x10^30 kg; the distance from the Earth to the Sun r=1.5x10^11 meters; the speed...