The sun is a satellite of Milky Way's galactic central cluster. The sun revolves around this center with a radius of 2.28x10^20 m. and with a period of 2.52x10^8 years. If the universe is 16 billion years old. a) How many times has the galaxy rotated and b)with what speed is the sun traveling around the galactic cluster in m/s?
r=2.28x10^20 m.
T= 2.52x10^8 yrs.-> 7.94x10^15 s.
15 billion years -> 4.73x10^15 s.
Any chance you got the answer to this question?
I have a professor who gave me a homework question that is IDENTICAL to this minus a few figure changes.
I cant seem to figure out the formula for the galaxy rotation.
To find out how many times the galaxy has rotated, we need to calculate the number of periods the sun has completed.
a) Number of times the galaxy has rotated:
To find the number of times the galaxy has rotated, also known as the number of periods completed by the sun, we can divide the total age of the universe by the period of the sun's revolution.
Total age of the universe: 16 billion years = 16 x 10^9 years
Total age of the universe in seconds: 16 x 10^9 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute = 5.04 x 10^17 seconds
Number of times the galaxy has rotated = Total age of the universe / Period of revolution
Number of times the galaxy has rotated = 5.04 x 10^17 s / 7.94 x 10^15 s
Now, divide these two numbers to find the answer:
Number of times the galaxy has rotated ≈ 63.5 times
Therefore, the galaxy has rotated approximately 63.5 times.
b) Speed of the sun around the galactic cluster:
To find the speed of the sun around the galactic cluster, we can use the formula:
v = 2πr / T
where v is the velocity, r is the radius of revolution, and T is the period of revolution.
Substituting the given values:
v = 2 x 3.14159 x (2.28 x 10^20 m) / (7.94 x 10^15 s)
Now, calculate this expression to find the speed of the sun around the galactic cluster:
v ≈ 1.81 x 10^5 m/s
Therefore, the sun is traveling at approximately 181,000 m/s around the galactic cluster.