What Are the Formulas for Calculating Height in Synchronous Orbit?

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SUMMARY

The discussion focuses on calculating the height required for a synchronous orbit above Mars, specifically for the fictional starship Enterprise. Key formulas mentioned include Newton's law of universal gravitation (Fg = Gm1m2/r^2) and the orbital period formula (T = sqrt(4π^2r^3/Gm)). The period of Mars is given as T = 8.85 x 10^4 seconds, with Mars' mass specified as m = 6.37 x 10^23 kg. The relationship between the radius of the orbit and the orbital period is crucial for determining the necessary height for synchronous orbit.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Familiarity with orbital mechanics and period calculations
  • Knowledge of basic physics formulas related to circular motion
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of the orbital period formula T = 2π√(r^3/Gm)
  • Learn how to apply Newton's law of gravitation to calculate forces in orbital mechanics
  • Research the specific radius of Mars to accurately compute synchronous orbit height
  • Explore the concept of geostationary orbits and their applications
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Astronomy students, physics enthusiasts, and anyone interested in orbital mechanics and satellite positioning will benefit from this discussion.

Shelilla
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Homework Statement


In order for the enterprise to use its transporter it must be in synchronous orbit over the beam-down point. What heigh above the planet Mars must the enterprise be for a synchronous orbit?

Homework Equations


Please, can someone tell me for future reference what I should use in the formulas for this sort of equation? For every solution I've tried on this, all of them require some radius, so should I use the radius of mars?? And please don't just tell me 'combine Newton's something law and something something law' because frankly that doesn't mean anything to me and confuses me extremely, because I find it very hard and incomprehensible to combine formulas.

Fg= Gm1m2/r^2
ac=4pi^2r/T^2
F=ma?
g=Fg/m?
T=sqrt4pi^2r^3/Gm?
v=sqrtGm/r?

The Attempt at a Solution


I've tried several, but I'm just not sure where to start. Should I get the Fg? The ac? I was told that since it's in a synchronous orbit the period of rotation will be the same as the planet, so all I know for sure so far is that T=8.85*10^4 s and m=6.37*10^23 kg
 
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Shelilla said:
I was told that since it's in a synchronous orbit the period of rotation will be the same as the planet, so all I know for sure so far is that T=8.85*10^4 s and m=6.37*10^23 kg
So how do you accomplish this. What is the relation between the radius and the period?
 
Orodruin said:
So how do you accomplish this. What is the relation between the radius and the period?
Velocity?
 

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