- #1
Coco12
- 272
- 0
1. The problem statement, all variables and given/known
A star at the edge of the Andromeda galaxy appears to be orbiting the center of that galaxy at the speed of about 200km/s. The star is about g*10^9AU from the center of the galaxy. Calculate a rough estimate of the mass of the Andromeda galaxy. Earth orbital radius is 1.40*10^8
Fg=gm1m2/r^2
1 a.u. = 1.40*10^8 km = 1.40*10^11 m
For the mass of the entire galaxy, M, you will have to assume a spherical distribution of mass, with the star in question at the outside, at distance R. ( what does that mean by assume spherical)
In that case, the centripetal acceleration of the star is
V^2/R = G M/R2
Solve for M.
M = R V^2/G
I got this solution from a web page however I'm trying to understand how it works.
Isn't fg=Gm1m2/r^2
And then that will be equal to centripetal force
Why in the above solution did they omit the one of the mass??
A star at the edge of the Andromeda galaxy appears to be orbiting the center of that galaxy at the speed of about 200km/s. The star is about g*10^9AU from the center of the galaxy. Calculate a rough estimate of the mass of the Andromeda galaxy. Earth orbital radius is 1.40*10^8
Homework Equations
Fg=gm1m2/r^2
The Attempt at a Solution
1 a.u. = 1.40*10^8 km = 1.40*10^11 m
For the mass of the entire galaxy, M, you will have to assume a spherical distribution of mass, with the star in question at the outside, at distance R. ( what does that mean by assume spherical)
In that case, the centripetal acceleration of the star is
V^2/R = G M/R2
Solve for M.
M = R V^2/G
I got this solution from a web page however I'm trying to understand how it works.
Isn't fg=Gm1m2/r^2
And then that will be equal to centripetal force
Why in the above solution did they omit the one of the mass??