Tell me how to calculate these two astronomy questions

As much as I hate to use DV as my own personal network of tutors, I'm a highschool junior with my first college exam on Thursday and I could use some help.

1. A certain binary system is composed of two identical main sequence stars in circular orbit. The stars are separated by 3x10^8 km. Each star has a mass of 6x10^30 kg. What is the orbital period of the system?

2. The H-alpha Balmer line (656.3 nm) in the spectrum of a star is observed at a photon frequency of 456.5 Tera-Hz. What is the star's radial velocity? Is the star approaching or receding? Is the star red-shifted or blue shifted?

The first has something to do with Kepler's laws. But I don't know how to apply them. And these symbols! What do all these symbols mean!?!?. Help me, DV!

1. I suppose each star is going to be affected by a centripetal force of Gm^2/d^2, where m is the mass of the stars and d the distance between them. Then it's a case of plugging this into the centripetal force formula F = mv^2/(d/2) and solving to find v. Once you have v you can find out the orbital period using the velocity formula v = pi*d/t and solving for t.

2. Not sure, never done questions on this. I suppose you use c = lambda*f to find what the velocity is and then subtract this from c. Not sure.

What symbols are confusing you? km is length, kg mass, nm is length, THz is frequency.

I talked to my professor. Apparently it goes like this:

1. p^2=a^3/Mt
t is being used as a substitute for the sun symbol since this is the internet

Mt = The combined mass of both bodies. My paper actually has the sun symbol rather than a "t", but I cannot enter that here.

a=au

P=earth years

For Mt
2(6x10^30kg)
(12x10^30kg/1) (1Mt/2x10^30kg) = 6Mt

For a
(3x10^8km/1) (1au/1.5x10^8km) = 2au

2^3/6 = 8/6 = 4/3 = (square root of) 4/3 = 1.1547 years

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2.

λo/λs = (1+v/c)
λo/λs - 1 = v/c
c(λo/λs - ) = v

c = speed of light

λo = observed wavelength
λs = actual wavelength

Since λo isn't given, convert fo (observed frequency) into λo
fo = 456.5x10^12
λf = c

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I have to go to bed, so I'll just finish this tomorrow.

I just checked my method. If you do what I said you end up with the formula

t = sqrt2 * pi * (d^3 * G^-1 * m^-1)^(1/2).

Plugging in the variables you get the answer 1.16 years.

I think it's much better to do it my way because I didn't have to memorise any highly specific formulae or anything, I just worked it out from basic physics (namely centripetal force = mv^2/r, gravitational force = G(m1)(m2)/r^2). I've never studied astronomy.

If you just ask your professor what formula is required and then put in the numbers, that's just a lesson in how to use a calculator. It's not really physics and it won't help you to study for an exam.

Also, be careful with your significant figures. Were the original data written as '3' or '3.00'? If it was the former then you can only give your final answer to at most 2 significant figures, if it was the latter you should give it to 3. Those final digits you wrote down are meaningless, as the '3' you are initially given, if that's how it was originally given, represents a pretty massive potential error as the real figure could be anywhere between 2.5 and 3.5.

Remember, as a general rule, only give your answer to the least number of significant figures in the original data. There could well be marks for understanding this.

I appreciate your help, I really do.

Took the test. Think I did quite well. Luckily, because this is astronomy, the class doesn't focus heavily on physics. As such, the teacher emphasized the actual mathematical process itself and gave us the formulas and values for things like the speed of light. It was actually quite an easy test so long as you read the chapters. I now realize the worry that instigated this thread was unjustified. Although, I am glad I have this thread for future reference.

No problem. :)

Well done on the test.