A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 6.2 x 1020 m, and the angular speed of the star is 4.3 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center?
T=2π/ω
To find the time it takes for the star to make one revolution around the center of its galaxy, we can use the formula:
Period (T) = 2π / angular speed (ω)
where ω represents the angular speed.
Substituting the given values:
T = 2π / (4.3 x 10^-15 rad/s)
Calculating this gives:
T ≈ 1.47 x 10^15 s
To convert this time to years, we divide by the number of seconds in a year:
T (in years) ≈ (1.47 x 10^15 s) / (60s * 60min * 24hr * 365 days)
T (in years) ≈ 4.66 x 10^7 years
Therefore, it takes approximately 4.66 x 10^7 years for the star to make one revolution around the center of its galaxy.
To find the time it takes for the star to make one revolution around the center of its galaxy, we can use the formula for the period of revolution of an object in a circular orbit.
The formula for the period of revolution (T) is given by:
T = (2π) / ω
Where ω represents the angular speed of the star.
Given:
Radius of the orbit (r) = 6.2 x 10^20 m
Angular speed (ω) = 4.3 x 10^-15 rad/s
First, we need to convert the angular speed from radians per second to revolutions per second. Since there are 2π radians in one revolution, we can use the following conversion:
ω (rev/s) = ω (rad/s) / (2π)
Substituting the given values:
ω (rev/s) = (4.3 x 10^-15 rad/s) / (2π)
Next, we can calculate the period of revolution (T) using the formula mentioned earlier:
T = (2π) / ω (rev/s)
Substituting the value of ω (rev/s):
T = (2π) / [(4.3 x 10^-15 rad/s) / (2π)]
Simplifying the expression:
T = [(2π) * (2π)] / (4.3 x 10^-15)
Now, we have obtained the period of revolution in seconds. To convert it to years, we need to divide it by the number of seconds in a year.
1 year = 365 days * 24 hours * 60 minutes * 60 seconds
Substituting the values:
1 year = 365 * 24 * 60 * 60 seconds
Now, we can calculate the time it takes for the star to make one revolution around the center in years:
T (years) = T (seconds) / (365 * 24 * 60 * 60)
Substituting the value of T (seconds):
T (years) = [(2π) * (2π)] / (4.3 x 10^-15) / (365 * 24 * 60 * 60)
Calculating the final result will give you the answer in years.