Question

The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?

Answer 1

what values have we got?
velocity of the solar system, mass of solar system....?

Answer 2

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 10^8 m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.

Answer 3

Sorry I didn't post that earlier, whoops!

Answer 4

good.
so the solar system (a point mass) is performing (assume like anything) a uniform circular motion about the galactic center (another point mass).
then, the centripetal force of the solar system is balanced by the gravitational force

Answer 5

\[
{\cancel{m_{\rm solar}}v^2\over \cancel{r}}=G{m_{\rm core}\cancel{m_{\rm solar}}\over r^\cancel{2}}
\]

Answer 6

\[v^2={Gm_{\rm core}\over r}\]

Answer 7

make sure all the values are in
kg, m, s, N, ...

Answer 8

what answer do you come to? I got an answer and it was wrong..

Answer 9

what was your answer?

Answer 10

1.88*10^32

Answer 11

\[\left(230\times10^3\right)^2=\frac{6.67\times10^{-11}\times m_{\rm core}}{25\times10^3\times3\times10^8}\]

Answer 12

I didn't change the 230 to m/s, stupid! sorry!

Answer 13

thought so,
and told you so :)

Answer 14

haha

Answer 15

what did you multiply the 25000 light years by?

Answer 16

speed of light

Answer 17

does that give distance in meters?

Answer 18

I used the exact formula provided and still wrong, came to 5.9*10^33

Answer 19

answer was 1.87*10^41

Answer 20

no idea how to get it, I am a biology person, not physics haha

Answer 21

my bad
\[
\left(230\times10^3\right)^2=\frac{6.67\times10^{-11}\times m_{\rm core}}{25\times10^3\times3\times10^8\color{red}{\times365\times24\times3600}}=1.876\times10^{41}{\rm kg}
\]
http://wolfr.am/XZbB3r