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 $3\mathrm{.}0108$m$/$s$3\mathrm{.}0108$m$/$s$.$ Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of $230$ km$/$skm$/$s$.$

Part A

Assuming the orbit is circular, what is the period of the solar system's orbit?

Express your answer in years.

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Part B

Our solar system was formed roughly $5$ billion years ago. How many orbits has it completed?

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Part C

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?

Express your answer in kilograms.

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Part D

Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?

Note : Astronomers have spent many years trying to determine how many stars there are in the Milky Way. The number of stars seems to be only about $10\%$ of what you'll find in part d$.$ In other words, about $90\%$ of the mass of the galaxy appears to be in some form other than stars. This is called the dark matter of the universe. No one knows what the dark matter is$.$ This is one of the outstanding scientific questions of our day.