Calculating Orbital Period of Satellites

In summary, to calculate the orbital period of an object, such as a satellite, when only the radius of the orbit and the mass of the central object are known, one can use the equation T^2= ((2*pi)^2*r^3)/GM, where r is the radius and M is the mass of the central object. This equation is derived by equating the gravitational force to the centripetal force and assuming the radius of the orbit of the central mass is negligible.
  • #1
Bugsy23
25
0
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?
 
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  • #2
The equations that come to mind are a = 1/r v2 = wr = 2(pi)r/T and mw2r =Mw2R (the two centripetal forces are equal)...M is the big mass, like the Earth with circular radius orbit R..

if the gravitalional force equals the centripetal...F = ma.. so
GMm/(R+r)2 = mw2r and the small m's drop out...

Then just assume R (radius of orbit of the big central mass) is negligible...
and you are right near the answer...
 
  • #3
it comes out to be:

T^2= ((2*pi)^2*r^3)/GM

where r is radius and M is mass of central object. T is time period
 

What is the formula for calculating the orbital period of a satellite?

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.

What is the semi-major axis and how do I measure it?

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.

Do I need to use different units when using the formula to calculate orbital period?

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.

Can the formula for calculating orbital period be used for all types of satellites?

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.

What are some factors that can affect the accuracy of the calculated orbital period?

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.

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