<p>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?</p>

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

CC BY-SA 4.0
2020-02-10T19:41:26.280Z
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
CC BY-SA 4.0
2020-02-10T19:49:49.400Z
@Jim421616 He??
ProfRob
CC BY-SA 4.0
2020-02-10T19:58:37.613Z
He/she/it. There's no information in his/her/its profile.
Jim421616
CC BY-SA 4.0
2020-02-10T17:11:58.400Z
2020-02-10T17:11:58.400Z
ProfRob
<p>H98. There are a couple of issues we need to work through.</p>

<p>First, using your figures, I get a value of <span class="math-container">$5.78\times10^{37}$</span> kg, which is different to yours. I'm including here, the fact that the numbers are wrong. What value are you using for <span class="math-container">$G$</span>?</p>

<p>Second,</p>

<p>a) I don't know where your information is coming from, but according to <a href="http://astropixels.com/galaxies/M31-01.html" rel="nofollow noreferrer">enter link description here</a>, M31 has an angular radius of 178 arcminutes, not 12250.4 arcminutes.</p>

<p>b) One arcminute (written as <span class="math-container">$1'$</span>) is <span class="math-container">$\frac{1}{60}$</span> of a degree, so <span class="math-container">$178'=2.97^o$</span>.</p>

<p>c) To convert <span class="math-container">$2.97^o$</span> to metres, you'd use the formula <span class="math-container">$S=D\theta$</span></p>

<p>d) As @RobJeffries stated, the velocity is <span class="math-container">$300$</span> <strong>km/s</strong>, which is <span class="math-container">$3\times10^5\rm{m/s}$</span>. </p>

<p>Have another go and let us know how you get on.</p>

CC BY-SA 4.0
2020-02-10T19:57:44.473Z
2020-02-10T19:57:44.473Z
Jim421616
<p>So I need to estimate the mass of the andromeda galaxy using: 
<span class="math-container">$$ M = \frac{v^2r}{G}$$</span>
where <span class="math-container">$v$</span> is the rotational velocity, <span class="math-container">$r$</span> the galaxy's radius and <span class="math-container">$G$</span> Netwon's gravitational constant. I'm told the following:</p>

<ol>
<li>Distance (m) = 2.403×<span class="math-container">$10^{22}$</span> </li>
<li>Radius (arcmin) = 12250.40</li>
<li>Velocity (km/s) = 300</li>
</ol>

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

CC BY-SA 4.0
2020-02-10T17:07:18.807Z
Andromeda does not have a radius of 204 degrees.
ProfRob
CC BY-SA 4.0
2020-02-10T17:08:29.533Z
What is it? I'm not sure how to calculate it
Roberto_1986
<mass>
Estimating Galactic Mass of Andromeda
Roberto_1986
# Estimating Galactic Mass of Andromeda

(Asked by: username_0 on 2020-02-10)

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×$10^{22}$
2. Radius (arcmin) = 12250.40
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?

**Tags:** mass
> **Comments:**
> **username_1**: Andromeda does not have a radius of 204 degrees.  
> **username_0**: What is it? I'm not sure how to calculate it  

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## 2 answers

### Answer by username_1 on 2020-02-10. Score: 2

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 $(3\times 10^5)^2$.

> **Comments:**
> **username_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.  
> **username_1**: @Jim421616 He??  
> **username_2**: He/she/it. There's no information in his/her/its profile.  

---

### Answer by username_2 on 2020-02-10. Score: 1

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](http://astropixels.com/galaxies/M31-01.html), 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.


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