how pv solar works
star velocity problem? on TODAYS exam!!!?
hi, im having trouble working this out, but i think that my real trouble is with the units. here’s what i have to do.
2 stars in a binary system, of masses 2.5 and 0.7 solar masses (m1 and m2), orbit a common centre of mass with a 4 day period P. their orbit is inclined 40 degrees (i) to the sky’s plane. i have to find their maximum radial velocity.
i converted the period to years, left the angle in degrees and didnt know the Sun’s mass. (i think this problem wants me to solve this without needing to know that). then i rearranged the equation
Pv^3 / 2pi = (m2 / (m1 + m2))sin i
for v, and i ended up with 80.6 somethings. i do not know the units. (i also realise this is only a component of the actual velocity of one of the stars, but that isnt what im having trouble with).
can anybody show me the definitive way to solve this?
its on an exam i am sitting in about 3 hours.
thanks.
Probably a bit late, but anyways:
You can start with Kepler’s third law P^2=4 pi^2 / (GM) a^3
and derive the expression you have assuming circular orbits. I tried to do this and got a slightly different result, so either you typed it wrong or some extra assumptions were made that I was not aware of.
It’s easiest to use some system of units like cgs or MKS, but then you need to know the mass of the Sun (2×10^33 grams) as well as the values of constants like G.
For Kepler’s law, if P is in years and a in AU then 4pi^2/GM = 1. I suppose that if that’s the case then velocity v =2pi a/P would have units of astronomical units per year. Converting your answer of 80 would then give something like 380 km/s which is quite fast, but not crazy (the Earth is going around at 30km/s).
I’d still check where the equation came from and make sure you din’t miss any terms or constants.
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