In a certain binary star system, each star has the same mass as our sun, and they revolve about their center of mass. The distance between them is the same as the distance between the EArth and sun. Wha tis their period of revolution in years?
You know the force of gravity, you know the radius of rotation.
GMsMs/r^2=Ms v^2/r
but v=2PI r/Period
solve for period.
To determine the period of revolution for the binary star system, we can use Kepler's third law of planetary motion. This law states that the square of the period of revolution of any two objects is proportional to the cube of the average distance between them.
In this case, we have two stars with the same mass as our sun, and they are revolving around their center of mass. The distance between the two stars is the same as the distance between the Earth and the sun, which is approximately 149.6 million kilometers (or about 93 million miles).
So, let's calculate the period of revolution for the binary star system:
1. Calculate the average distance between the stars:
The distance between the Earth and the sun is 149.6 million kilometers.
2. Cube the average distance:
Cube the distance calculated in step 1 to get the value of the average distance cubed.
3. Calculate the period of revolution squared:
The period of revolution squared is equal to the average distance cubed.
4. Take the square root and convert to years:
Finally, take the square root of the period of revolution squared to get the period of revolution in years.
Note: Kepler's third law assumes that the masses involved are much smaller than the central mass (in this case, the combined mass of the two stars is much smaller than the mass of the center of mass). So, it should work well for stars with masses comparable to our sun, as in this scenario.
By following these steps, you should be able to calculate the period of revolution for the binary star system.