Assuming that the mass of the Milky Way Galaxy is times that of the Sun and that the Sun is meters from its center, what is...

Hello!

Kepler's first law states that an orbit of a planet around the Sun is an ellipse with the Sun being at one focus of it. Our problem is close enough: the Milky Way Galaxy may be considered as a sun (large central body), and the Sun may be considered as a planet orbiting it. I assume this ellipse is almost a circle, because in the opposite case the speed of the Sun would be different...

Hello!

Kepler's first law states that an orbit of a planet around the Sun is an ellipse with the Sun being at one focus of it. Our problem is close enough: the Milky Way Galaxy may be considered as a sun (large central body), and the Sun may be considered as a planet orbiting it. I assume this ellipse is almost a circle, because in the opposite case the speed of the Sun would be different at the different points of its trajectory.

Denote the radius of this orbit as it is given, and the speed as it is unknown. Also denote the given mass of the Milky Way Galaxy as and the Sun's mass as it is about Then the Newton's Law of Universal Gravitation tells us that the gravity force is so by Newton's second law the acceleration is

We also know that the acceleration of a body in uniform circle motion is so or or

Numerically it is about

or about 230 km/s.

The time needed is about 212,000,000 years.