Calculating mass of Milky way Galaxy

[RyanH42]

I used the $v^2=MG/R$ to calculate mass of milky way.Now $v=225000$ m/s G=6.7 10^-11 and r is 16 kpc source (https://upload.wikimedia.org/wikipedia/commons/7/77/Rotation_curve_(Milky_Way).JPG)
If I plut them I get $50,625,000,000=v^2$ and the other side G=6.6 10^-11 and R =49.6 10¹⁹ so $M=v^2R/G$ that's equal 50,625,000,000/5.10²⁰.6.6 10^-11 which its ≅ 1.534 10^-3

Whats the point which I am missing

 

[PeterDonis]

Whats the point which I am missing

You forgot to include R in the numerator of your calculation, and I don't understand where the 5.10²⁰ in the denominator comes from.

 

[RyanH42]

Oh I made a huge mistake now I see it 5 10²⁰ comes from kpc-meter transformation.Then the answer will be 50,625 10⁶*5 10²⁰/6.6 10 ^-11.Which we get ≅40 10 ³⁶ which means 8 10⁶ M_sun

 

[RyanH42]

But again it false

 

[PeterDonis]

But again it false

Check your math. I get as a rough answer $\left( 5 \times 10^{10} \right) \left( 5 \times 10^{20} \right) / \left( 7 \times 10^{-11} \right)$, which comes out to about $4 \times 10^{41}$, or about $10^{11} M_{sun}$, which is about right. (As a rule of thumb, when using scientific notation, always adjust the exponent so that the number in front is between 1 and 10. You didn't do that for the $v^2$ factor and I think it confused you.)

 

[RyanH42]

Probably you are right.Thanks for help