Mass of the Milky Way through the speed of a planet

[fawk3s]

Homework Statement

Is it possible to calculate the mass of the Milky Way knowing only the speed of a planet in a circular orbit? I fail to see how, but if yes, then how?

Thanks in advance

Homework Equations

The Attempt at a Solution

 

[SHISHKABOB]

The planet would have to be orbiting the Milky Way in the same way that the Sun and all the other stars in the MW are orbiting.

The relationship between a planet and the star its orbiting has no connection to the mass of the Milky Way.

 

[fawk3s]

I did type planet, indeed. Let it be a star then for clarity's sake. Think you get the point.

 

[SHISHKABOB]

well there's only one force acting on a something out in space (most of the time, let's just assume this is the case)

so if F_net = F_g

can you take it from there?

 

[fawk3s]

well there's only one force acting on a something out in space (most of the time, let's just assume this is the case)

so if F_net = F_g

can you take it from there?

Well, in a circular orbit,
F_centripetal=F_g

You are given only the speed v. The problem is how to get rid of the radius (r). Dunno how, and if possible.

 

[SHISHKABOB]

What's the exact problem and what values are you given?

 

[fawk3s]

Find the mass of the Milky Way, when an orbiting star's speed is 220 km/s.

 

[fawk3s]

Im guessing there's no way to solve it then? Because a friend of mine asked me for help with this, and I immediately asked if she had forgot to copy down the radius of the orbit or the period of the orbit. She said it was not given, so I got kind of confused. I still can't see a way to solve it.

 

[BruceW]

Well, in a circular orbit,
F_centripetal=F_g

You are given only the speed v. The problem is how to get rid of the radius (r). Dunno how, and if possible.

Exactly. If you don't have the radius, then you can't get the speed. You would need to find the radius some other way, or introduce other assumptions.

 

[fawk3s]

What kind of assumptions could be introduced here?

 

[BruceW]

for example, you could assume that the star fits the typical trend of other stars in orbit around the milky way, then you could work out the radius of the star. But from what you've said in previous posts, I am guessing you are not allowed any other information.

 

[fawk3s]

for example, you could assume that the star fits the typical trend of other stars in orbit around the milky way, then you could work out the radius of the star.

Could you elaborate on this please? Seems interesting, but don't think I follow. What kind of trend and how do you work out the radius from that?

Thanks in advance

 

[BruceW]

I just mean a trend of orbital radius and orbital speed. So for example, if a star has a certain orbital speed, then the trend would suggest a typical orbital radius for that star.

But your original problem was to find the mass of the milky way given only the orbital speed of the star, so this method would not be any help.