Our solar system is 25,000 light years away from the center of our Milky Way gal
ID: 1463426 • Letter: O
Question
Our solar system is 25,000 light years away from the center of our Milky Way galaxy, and astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s. One light year is the spatial distance traveled by light in one (earth) year at a speed of 3.0 Times 10^8 m/s. Show your work in calculating the conversion from light years to meters. Assuming the orbit is circular, what is the period of the solar system's orbit? Give your answer in years. Evidence suggests that our solar system was formed roughly 5 billion years ago. How many compete orbits has it completed?Explanation / Answer
A lightyear is the distance that light travels in one year. Since there are various definitions for the length of a year, there are correspondingly slightly different values for a lightyear. One lightyear corresponds to about 9.461*1015 m
We know that the Distance(m) = Velocity(m/s) * time(s)
Time = 25,000 years=7.88*1011 s
Velocity = 3.0*108 m/s
distance=3.0*108 m/s/7.88*1011 s=3.8*10-4 m
The period equals the distance traveled, divided by the velocity.
Change the distance to the center of the galaxy from light years to kilometers. That will be the radius of your circular orbit.
1 kiloparsec = 3.08568025 × 1016 kilometers
circular orbit, therefore circumference is given by 2*pi*r
2*pi*8(3.08568025 × 1016)=1.55103206 × 1018 km
distance=s velocity=v time =t
v*t=s
t=s/v
t=1.55103206 × 1018 km / 230 km/s
t=6.73× 1015 seconds
86,400 seconds per day so
31,536,000 seconds per year (365 days approximately per year)
So divide seconds by 31,536,000 to get years
6.73*1015 / 3.1536*107 = 213244613 years
b. Sun has been around 5 billion years (5*109) divide this by the time it takes to do one rotation.
5*109/213244613=23.44 So about 23 times.
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