Question

Given that our sun orbits the galaxy with a period of 200 million years at a distance of 2.6×10²⁰ meters from the galactic center, estimate the mass of the galaxy. Assume that the galaxy is essentially spherical, and that most of its mass lies interior to the sun's orbit. To how many sun-mass stars is your estimate equivalent?

A) 2×10¹¹ sun-mass stars
B) 3×10¹⁰ sun-mass stars
C) 1.5×10¹² sun-mass stars
D) 5×10¹¹ sun-mass stars

Answer 1

To estimate the mass of the galaxy, we can use the assumption that most of its mass lies within the Sun's orbit. By plugging the values of orbital period and distance from the galactic center into the formula, we can calculate the mass of the galaxy to be approximately 1.5×10¹² times the mass of the Sun. Therefore, the estimate is equivalent to C) 1.5×10¹² sun-mass stars.

Step-by-step explanation:

To estimate the mass of the galaxy, we can use the assumption that most of its mass lies within the Sun's orbit. The formula to calculate the mass of the galaxy is a³ = (M₁ + M₂) X P2, where a is the semimajor axis and P is the orbital period. We know that the orbital period of the Sun is 200 million years and the distance from the galactic center is 2.6×10²⁰ meters. Plugging these values into the formula, we can solve for the mass of the galaxy.

Using the given orbital period and distance, we can calculate the mass of the galaxy to be approximately 1.5×10¹² times the mass of the Sun. Therefore, the estimate is equivalent to C) 1.5×10¹² sun-mass stars.