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Instructions
Determine the length of the orbit's semi-major axis and cube it. The satellite will orbit a larger, central body (such as a planet) in an elliptical orbit. You will need to know the length from the center of the orbit to its farthest reaches.
After you've cubed the length of the orbit's semi-major axis, divide by μ.
Next, take the square root of the number you've calculated.
Multiply by 2 times π, also known as pi. Pi is approximately equal to 3.14159265. Use the π function on your calculator when calculating; alternatively, use the appropriate number of significant figures if rounding. Pi is a mathematical constant whose value is the ratio of any circle's circumference to its diameter.
What you have just calculated is the orbital period, or "T," of the satellite. You now know the time, in seconds, it takes for the satellite to make one full trip around the central body.
In an ellipse, the major axis is the longest diameter possible, running through the center of the circle and foci. The ends are at the widest parts of the ellipse. To get the "a," divide the length of the major axis by two. In a circle, the semi-major axis is equal to the radius of the circle.
"μ," also known as mu, is equal to the universal gravitational (G) constant times the mass of the central body (M). You will need to know the mass of the central body. (Note: this is not the mass of the satellite.) The value of the universal gravitational constant is 6.67300 --- 10^(-11) m^3 kg^(-1) s^(-2). Be sure to multiply the constant times the mass first, before dividing.
If you want to know how many minutes, hours or days it will take for the satellite to orbit, you will need to convert T. For example, if you wanted to convert into minutes, you would have to divide by 60.