Question

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 × 10¹¹ solar masses. A star orbiting on the galaxy’s periphery is about 6.0 × 10⁴ light years from its center.

What should the orbital period of that star be?
a) 4.19 × 10⁸ years
b) 5.82 × 10⁸ years
c) 7.01 × 10⁸ years
d) 8.38 × 10⁸ years

Answer 1

The orbital period of the star orbiting the Milky Way galaxy's periphery can be calculated using Kepler's third law. Plugging in the values, we get an orbital period of approximately 4.19 × 10⁸ years.

Step-by-step explanation:

To calculate the orbital period of a star orbiting the Milky Way galaxy's periphery, we can use Kepler's third law, which states that the square of a planet's orbital period is proportional to the cube of its average distance from the center of the galaxy.

Given that the star is about 6.0 × 10⁴ light-years from the center of the galaxy, and the mass of the galaxy is about 8.0 × 10¹¹ solar masses, we can calculate the orbital period using the formula T = 2π√(r³/GM), where T is the orbital period, r is the average distance, G is the gravitational constant, and M is the mass of the galaxy.

Plugging in the values, we get T = 2π√((6.0 × 10⁴ ly)³ / (6.67 × 10⁻¹¹ N m²/kg²)(8.0 × 10¹¹ M☉)). Solving this equation gives us an orbital period of approximately 4.19 × 10⁸ years. Therefore, the correct answer is (a) 4.19 × 10⁸ years.