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Bugsy23
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How do you calculate the orbital period of an object, eg. a satellite, if the only known values are the radius of the orbit and the mass of the central object?
The formula for calculating the orbital period of a satellite is T = 2π√(a^3/GM), where T is the orbital period in seconds, a is the semi-major axis in meters, G is the gravitational constant (6.67 x 10^-11 m^3/kg s^2), and M is the mass of the central body in kilograms.
The semi-major axis is the half of the longest diameter of the elliptical orbit of a satellite. It can be measured using the distance between the center of the central body (such as Earth) and the center of the satellite's orbit at its farthest point.
Yes, the units used in the formula for calculating orbital period are meters for distance (a) and kilograms for mass (M). The resulting orbital period will be in seconds.
The formula can be used for all types of satellites as long as they follow an elliptical orbit around a central body. However, it may not be accurate for satellites in highly eccentric orbits or those affected by external forces such as atmospheric drag.
Factors that can affect the accuracy of the calculated orbital period include external forces (such as atmospheric drag), changes in the mass of the central body, and deviations from a perfectly circular or elliptical orbit. Additionally, using inaccurate or imprecise measurements of the semi-major axis or mass can also affect the accuracy of the calculated orbital period.