The solar system is 25,000 light years from the center of our galaxy (Milky Way)

Question

The solar system is 25,000 light years from the center of our galaxy (Milky Way). One year light is the distance light travels in one year at a speed of 3.0x108 m / s. The Astronomers have determined that the solar system is orbiting the center of the galaxy a speed of 230 km / s. to. Assume that the orbit is circular, what is the period of the orbit of the solar system? b. Our solar system formed about 5 billion years ago. How many orbits completed? c. The gravitational pull of the solar system is the net force due to all the matter within our orbit. Most of matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, as a giant star. What is the approximate mass of the galaxy center ?. d. Assume that the sun is a typical star with a mass. If the galactic matter is made of stars, how many stars are approximately in the center galaxy?

Explanation / Answer

we have the radius of our orbit is 25,000 ly. The distance our solar system must travel is:
D = 2 X pi X r
= 2 X 3.141592 X 25,000 ly
= 157,079.6 ly
Speed of light = 3.0 x 10^6 km/sec* 60 sec X 60 min X 24 hrs X 365.25 days) = 9,467,280,000,000km/year

a)

So, the distance in km our solar system must travel is:
157,079.6ly x 9,467,280,000,000km/year = 1.487 X 10^18km

b)

At 230km/sec, that's 7,258,248,000 km/year. So, it takes our solar system 1.487 X 10^18km / 7,258,248,000km/year = 204,886,434 years to complete a single orbit.
5,000,000,000 / 204,886,434 = 24.4 times.

c)

Vorbit = sqrt(GM/r)
230m/sec = sqrt((6.67384 x 10^-11 m^3/kg sec^2)M/1.487 X 10^21m)

M = 11.793*10^35 Kg

d)

Mass of sun is 1.989 × 10^30 kg

Total number of stars are 11.793*10^35 Kg / 1.989 × 10^30 kg = 592911

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