(10%) Problem 7: The Sun orbits the center of the Milky Way galaxy once each 260

Question

(10%) Problem 7: The Sun orbits the center of the Milky Way galaxy once each 260 x 108 years, with a roughly circular orbit avernging 3.00 x 10* light years in radius. (A light year is the distance traveled by light in 1 y) 50% Part (a) Calculate the centripetal acceleration of the Sun in its galactic orbit in m/s. asin acos0 atan0 acotansinhO 0 coshO tan0 cotanho+ O Degrees O Radians Submit Hint I give up! Hints: 0% , deduction per hint. Hints remaining:-2 Feedback: 0% deduction per feedback. 50% Part (b) Calculate the average speed of the Sun in its galactic orbit in m/s.

Explanation / Answer

Centripetal acceleration is given by:

ac = V^2/R

V = w*R

w = 2*pi/T

ac = 4*pi^2*R/T^2

Now given that

period = 2.60*10^8 yr = 2.60*10^8 yr*(3.154*10^7 sec/1 yr)

period, T = 8.2*10^15 sec

Now distance of sun from center = 3*10^4 ly

1 ly = 9.46*10^15 m

R = 3*10^4 ly*(9.46*10^15 m/1 ly)

R = 2.84*10^20 m

So,

ac = 4*pi^2*R/T^2

ac = 4*pi^2*2.84*10^20/(8.2*10^15)^2

ac = 1.67*10^-10 m/sec^2

Part B.

Avg speed = V = length of orbit/time period

V = 2*pi*R/T

V = 2*pi*2.84*10^20/(8.2*10^15)

V = 2.18*10^5 m/sec

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