How Is the Period of a Satellite Calculated?

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SUMMARY

The period of a satellite can be calculated using the formula T = 2πr/v, where r is the distance from the center of the planet and v is the orbital velocity. In this discussion, the gravitational constant G is given as 6.67 x 10^-11 N m²/kg², and the acceleration due to gravity on a planet with a radius of 4910 km is 11.8 m/s². The correct calculation for a satellite at an altitude of 8445.2 km above the surface results in a period T of approximately 6684.425 seconds after correcting the initial miscalculation.

PREREQUISITES
  • Understanding of gravitational force and Newton's law of universal gravitation
  • Familiarity with circular motion and centripetal acceleration
  • Knowledge of basic trigonometric functions and π (pi)
  • Ability to perform unit conversions (e.g., km to m)
NEXT STEPS
  • Study the derivation of the orbital period formula T = 2πr/v
  • Learn about the implications of Kepler's laws of planetary motion
  • Explore the effects of altitude on satellite velocity and period
  • Investigate the applications of satellite period calculations in real-world scenarios
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in satellite dynamics and orbital mechanics will benefit from this discussion.

KDizzle
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[SOLVED] Period of a satellite

1. Given: G = 6.67 x 10^-11 N m^2/ kg^2
The acceleration of gravity on the surface of a planet of radius R = 4910 km is 11.8 m/s^2. What is the period T of a satellite in circular h = 8445.2 km above the surface? Answer in units of s.



2. F = GMm/r^2
F = ma = mv^2/r
v = sqrt(GM/r)
T = 2pi*r/v



3. i got r = 13355200 m; a = 11.8 m/s^2; that gave me the velocity = 12553.54m/s. i plugged it into the period equation and got T = 6684.425s but its wrong
 
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