Quote your answers to at least 3 significant figures. Show your full algebra, in

Question

Quote your answers to at least 3 significant figures. Show your full algebra, including both numbers and units. Put a box around all final answers. It is ok to hand-write algebra if you are neat and organized (e.g., equal signs are lined up vertically). 1. Assume that the Sun’s distance from the center of the Milky Way is 26,000 light years, and that the Sun travels on a circular path around the center. Calculate the circumference of the Sun’s orbit. Quote your answer in (i) light years, and (ii) kilometers. 2. Use your answer in part (a), together with the Sun’s travel speed of 220 km/sec. Calculate the length of time required by the Sun to make one complete trip around the center of the Milky Way. Quote your answer in years. 3. Our solar system is 4.5 billion years old (billion = 109 ). Calculate how many trips around the Milky Way our solar system has made. 4. The oldest stars in the Milky Way are 12 billion years old. Calculate how many trips they have made around the Milky Way.

Explanation / Answer

here,

radius of the orbit of sun , r = 26000 light yr

a)

the circumference of the Sun’s orbit , C = 2 * pi * r

C = 2 * pi * 26000

C = 163280 light yr

b)

1 light yr = 9.46 * 10^12 km

the circumference of the Sun’s orbit , C = 163280 light yr

C= 1.54 * 10^18 Km

c)

speed , v = 220 km/s

the length of time for one complete revolution , t = C/ v

t = 1.54 * 10^18 /220

t = 7 * 10^15 s

t = 2.22 * 10^8 yr

d)

given time , T = 4.5 * 10^9 yr

number of revolutions , n = T/t

n = 20.27 revolutions

e)

given time , T = 12 * 10^9 yr

number of revolutions , n = T/t

n = 54 revolutions

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