Question

The Sun orbits the Milky Way galaxy once each 2.60 x 10^8 y, with a roughly circular orbit averaging 3.00 x 10^4 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..

Answer 1

a_c = 1.67 x 10⁻¹⁰ m/s²

Step-by-step explanation:

given,

time period = 2.60 x 10⁸ yr

T = 2.60 x 10⁸ x 365 x 24 x 60 x 60

T = 8.2 x 10¹⁵ s

radius, R = 3.00 x 10⁴ light year

R = 3 x 10⁴ x 3 x 10⁸ x 365 x 60 x 60 x 24

R = 2.84 x 10²⁰ m

now, angular velocity of sun

`\omega = (2\pi)/(T)`

`\omega = (2\pi)/(8.2* 10^(15))`

ω = 7.68 x 10⁻¹⁶ rad/s

centripetal acceleration

a_c = r ω²

a_c = (2.84 x 10²⁰) x (7.68 x 10⁻¹⁶)²

a_c = 1.67 x 10⁻¹⁰ m/s²

centripetal acceleration of the Sun in its galactic orbit is equal to

1.67 x 10⁻¹⁰ m/s².