Calculating Orbital Period of Satellites

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SUMMARY

The orbital period of a satellite can be calculated using the formula T^2 = (4π^2r^3) / (GM), where T is the orbital period, r is the radius of the orbit, and M is the mass of the central object. This equation derives from equating gravitational force to centripetal force, simplifying the relationship between the radius and mass. The gravitational constant G is essential for these calculations, and the mass of the satellite is negligible compared to the central mass, such as Earth.

PREREQUISITES
  • Understanding of gravitational force and centripetal force concepts
  • Familiarity with the gravitational constant (G)
  • Basic knowledge of circular motion equations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of Kepler's Third Law of Planetary Motion
  • Learn about the implications of orbital mechanics in satellite design
  • Explore the effects of varying mass and radius on orbital periods
  • Investigate the applications of the gravitational constant in astrophysics
USEFUL FOR

Aerospace engineers, astrophysicists, students studying orbital mechanics, and anyone involved in satellite technology will benefit from this discussion.

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?
 
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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...
 
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
 

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