# Phun Question, or Using an Orbit to Find the Mass of a Sun

Registered User
edited February 2009
So here's the deal.

You are an alien on an alien planet orbitting the planet's sun in a circular orbit. You want to find the mass of your sun. You "triangulate" the center-to-center distance between your planet and sun to be 3.52E+10 meters. The period of motion of your planet (the length of your year) is 1.81E+7 seconds. You know G = 6.67E−11 Nm^2/kg^2. What is the mass of your sun?

Given: R = 3.52E+10 m, T = 1.81E+7 s, G = 6.67E−11 Nm^2/kg^2
Want: M (as opposed to m)
Equation: F = GmM/r^2, ?, ?

We have three unknowns, M, m, and F. With T, one could potentially solve for angular velocity (omega = 2PI(1/T)) and go from there.

Anyone up for some phun?

Golden Leg on

## Posts

• Registered User regular
edited February 2009
Golden Leg wrote: »
So here's the deal.

You are an alien on an alien planet orbitting the planet's sun in a circular orbit. You want to find the mass of your sun. You "triangulate" the center-to-center distance between your planet and sun to be 3.52E+10 meters. The period of motion of your planet (the length of your year) is 1.81E+7 seconds. You know G = 6.67E−11 Nm^2/kg^2. What is the mass of your sun?

Given: R = 3.52E+10 m, T = 1.81E+7 s, G = 6.67E−11 Nm^2/kg^2
Want: M (as opposed to m)
Equation: F = GmM/r^2, ?, ?

We have three unknowns, M, m, and F. With T, one could potentially solve for angular velocity (omega = 2PI(1/T)) and go from there.

Anyone up for some phun?

this sounds more like someone's homework than phun

thisisntwally on
#someshit
• Registered User
edited February 2009
You're crazy!

Golden Leg on
• Registered User regular
edited February 2009
actually I'm an economist. If I live a good life, perhaps I can come back as a physicist in my next life, and help you with your homework.

thisisntwally on
#someshit
• Registered User
edited February 2009

you are given a circular orbit which is pretty good; that makes things easy. I don't think Newton's law of universal gravitation is the right way to go on this one. this was just a quick google search so ill just hook you up here. Apparently:

the orbital period of something in a circular orbit is: T=(2pi)(r^3/(G*M))^(1/2). where M's the mass of the thing you are orbiting. You should be able to algebrate that and solve for what you need.

Fuzzywhale on
• Registered User regular
edited February 2009
That formula is derived using newtons law of gravitation. This Site and This Site should give you everything that you need that's not in the OP. Just be mindful of the difference between angular velocity and tangential velocity.

Steam - Backpack - Bnet: SirHeadless #1154
• Registered User regular
edited February 2009
all these threads do is make me realize that I know nothing.

Absolutely nothing.

Sentry on
[SIGPIC][/SIGPIC]
wrote:
When I was a little kid, I always pretended I was the hero,' Skip said.
'Fuck yeah, me too. What little kid ever pretended to be part of the lynch-mob?'
• Registered User regular
edited February 2009
Use centripetal force and set it equal to gravitational force.

Steam & GT

GT: Tanky the Tank
Black: 1377 6749 7425
• Registered User
edited February 2009
You guys are terrific.

The equation F = GmM/r^2 can be set to solve for M, rendering M = Fr^2/Gm. F is equal to the centripetal force, and Fcentripetal = (OMEGA)^2(r). Angular velocity, or OMEGA, equals 2PI/T. Solving for OMEGA and plugging into the equation for M gives us M = [(OMEGA)^2*(r)^3]/G.

Turns out the mass of that sun equals 6.55x10^29 kg.

Golden Leg on
• Daddliest Catch Registered User regular
edited February 2009
Sentry wrote: »
all these threads do is make me realize that I know nothing.

Absolutely nothing.

Aridhol on
• Registered User
edited February 2009
I did a similar lab last night with Jupiter using the motion of its moons. Unfortunantly for this I turned said lab in last night as well. The problem is none of your formulas look anything like what we used last night. Your final answer looks good though. There is nothing sadder than watching people try to do calculations like this on their celphones.

locomotiveman on
aquabat wrote:
I actually worked at work on Saturday. Also I went out on a date with a real life girl.

Can you like, permanently break the forums?