# Estimating Galactic Mass of Andromeda

So I need to estimate the mass of the andromeda galaxy using: $$M = \frac{v^2r}{G}$$ where $$v$$ is the rotational velocity, $$r$$ the galaxy's radius and $$G$$ Netwon's gravitational constant. I'm told the following:

1. Distance (m) = 2.403×$$10^{22}$$
3. Velocity (km/s) = 300

I went so far as to convert the radius: $$\frac{12250.4}{60*57.3} = 3.563\ rad$$ then, calculated the radius: $$0.5*3.563*2.403\times10^{22} = 4.2757\times10^{22}$$ Then subbed into original formula to get: $$\frac{ 4.2757\times10^{22} \times 300^2}{G} = 1.7595\times10^{36} kg$$ It should be $$2\times10^{42}kg$$. where have I gone wrong?

• Andromeda does not have a radius of 204 degrees. – ProfRob Feb 10 '20 at 17:07
• What is it? I'm not sure how to calculate it – Roberto_1986 Feb 10 '20 at 17:08

You have gone wrong because the radius of Andromeda is not 12250.40 arcminutes. It is difficult to be more helpful. Possibly the units are arcseconds?

Neither do I see why you have inserted a factor of 0.5 in your second equation. or why you have inserted $$300^2$$ into the third equation, when $$v$$ is given in km/s, so it should be $$(3\times 10^5)^2$$.

• I think OP inserted 0.5 in the second calculation, because it's for radius. Not necessary, of course. He's just misunderstood radius. – Jim421616 Feb 10 '20 at 19:41
• @Jim421616 He?? – ProfRob Feb 10 '20 at 19:49
• He/she/it. There's no information in his/her/its profile. – Jim421616 Feb 10 '20 at 19:58

H98. There are a couple of issues we need to work through.

First, using your figures, I get a value of $$5.78\times10^{37}$$ kg, which is different to yours. I'm including here, the fact that the numbers are wrong. What value are you using for $$G$$?

Second,

a) I don't know where your information is coming from, but according to enter link description here, M31 has an angular radius of 178 arcminutes, not 12250.4 arcminutes.

b) One arcminute (written as $$1'$$) is $$\frac{1}{60}$$ of a degree, so $$178'=2.97^o$$.

c) To convert $$2.97^o$$ to metres, you'd use the formula $$S=D\theta$$

d) As @RobJeffries stated, the velocity is $$300$$ km/s, which is $$3\times10^5\rm{m/s}$$.

Have another go and let us know how you get on.