Question

(a) The Sun orbits the Milky Way galaxy once each 2.60 x 108y , with a roughly circular orbit averaging 3.00 x 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? (b) Calculate the average speed of the Sun in its galactic orbit. Does the answer surprise you?

Answer 1

Part a)

`a_c = 1.67 * 10^(-10) m/s^2`

Part b)

`v = 2.18 * 10^5 m/s`

Step-by-step explanation:

Time period of sun is given as

`T = 2.60 * 10^8 years`

`T = 2.60 * 10^8 (365 * 24 * 3600) s`

`T = 8.2 * 10^(15) s`

Now the radius of the orbit of sun is given as

`R = 3.00 * 10^4 Ly`

`R = 3.00 * 10^4 (3* 10^8)(365 * 24 * 3600)m`

`R = 2.84 * 10^20 m`

Part a)

centripetal acceleration is given as

`a_c = \omega^2 R`

`a_c = (4\pi^2)/(T^2) R`

`a_c = (4\pi^2)/((8.2* 10^(15))^2)(2.84 * 10^(20))`

`a_c = 1.67 * 10^(-10) m/s^2`

Part b)

orbital speed is given as

`v = (2\pi R)/(T)`

`v = (2\pi (2.84 * 10^(20)))/(8.2 * 10^(15))`

`v = 2.18 * 10^5 m/s`