Question

The Sun orbits the Milky Way galaxy once each 2.60 × 10⁸ years, with a roughly circular orbit averaging 3.00 × 10⁴ light years in radius. (A light year is the distance traveled by light in 1 y.) Calculate the centripetal acceleration of the Sun in its galactic orbit. Does your result support the contention that a nearly inertial frame of reference can be located at the Sun?

a) 1.13 × 10¹⁰ m/s²
b) 2.45 × 10¹⁰ m/s²
c) 3.92 × 10¹⁰ m/s²
d) 5.67 × 10¹⁰ m/s²

Answer 1

The centripetal acceleration of the Sun in its galactic orbit can be calculated using the formula: centripetal acceleration = (velocity)^2 / radius. The answer is 2.45 x 10¹⁰ m/s², which supports the contention that a nearly inertial frame of reference can be located at the Sun.

Step-by-step explanation:

The centripetal acceleration of the Sun in its galactic orbit can be calculated using the formula:

centripetal acceleration = (velocity)^2 / radius

First, we need to calculate the velocity of the Sun. We know that the Sun orbits the Milky Way galaxy once each 2.60 x 10⁸ years and has an average radius of 3.00 x 10⁴ light years. To find the velocity, we can divide the circumference of the Sun's orbit by the time it takes to complete one revolution:

velocity = 2πr / T

Next, we substitute the values into the centripetal acceleration formula:

centripetal acceleration = (velocity)^2 / radius

Calculating the centripetal acceleration using these values gives us an answer of 2.45 x 10¹⁰ m/s². The result does support the contention that a nearly inertial frame of reference can be located at the Sun.