Planetary Motion, calculation of orbital period

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SUMMARY

The discussion centers on calculating the orbital period of a space shuttle orbiting Earth at a distance of 6720 km from its center, using the gravitational field strength of 8.9 N/kg. The correct formula to use is g = 4π²R/T², which relates gravitational acceleration to orbital radius and period. The confusion arises from the misconception that the equation r³/T² can be used interchangeably with g, despite the latter having different dimensions and constants. Understanding the distinction between these equations is crucial for accurate calculations in orbital mechanics.

PREREQUISITES
  • Understanding of gravitational field strength and its units (N/kg)
  • Familiarity with orbital mechanics and Kepler's laws
  • Knowledge of the formula g = 4π²R/T²
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of Kepler's Third Law of Planetary Motion
  • Learn about the implications of gravitational constants in orbital calculations
  • Explore the differences between gravitational acceleration and centripetal acceleration
  • Practice solving problems involving orbital periods using various distances and gravitational strengths
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and orbital dynamics, as well as educators looking for clarification on gravitational equations.

Stevo_evo_22
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Hi everyone,



I'm really confused with a particular question:

Homework Statement






A space shuttle orbits the Earth at 6720 km from its centre. The gravitational field strength is 8.9N/kg. Calculate the shuttle's orbital period in minutes...

Homework Equations



g=4pi^2 x R /T^2

The Attempt at a Solution


The thing is, I know how to solve it using g=4pi^2 x R /T^2, but I want to know why I can't just use g=r^3/T^2 (the constant for all objects orbiting a particular mass)...if I have r and g, why can't i just use this equation?

Thanks!

Steve
 
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Because r^3/T^2 is a constant. But that constant isn't the same as g. It doesn't even have the right dimensions.
 
Dick said:
Because r^3/T^2 is a constant. But that constant isn't the same as g. It doesn't even have the right dimensions.

ahh ok...thanks :)
 

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