How Long Will It Take the Aimless Wanderer to Orbit Planet Mongo?

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SUMMARY

The discussion focuses on calculating the orbital period of a starship, the Aimless Wanderer, around the planet Mongo. Given the mass of Mongo as 3.71×10^25 kg and the radius at the surface, the user seeks to determine the time required for a circular orbit at an altitude of 3.00×10^4 meters. Key equations utilized include gravitational force F_g = (GM1M2)/R^2 and the relationship T^2 = R^3. The user attempts to apply the proportions rule for orbital periods but requires further assistance in calculating the necessary parameters.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F_g = (GM1M2)/R^2
  • Familiarity with circular motion concepts, including centripetal force Fc = mw^2(R+h)
  • Knowledge of orbital mechanics, particularly the relationship T^2 = R^3
  • Basic kinematics to solve for acceleration and velocity
NEXT STEPS
  • Study the derivation and application of Kepler's Third Law for orbital periods
  • Learn how to calculate gravitational acceleration on celestial bodies using g = GM/R^2
  • Explore the concept of angular velocity and its relation to orbital motion
  • Investigate the implications of altitude on orbital mechanics and period calculations
USEFUL FOR

Astronomy students, physics enthusiasts, and anyone interested in orbital mechanics and gravitational calculations will benefit from this discussion.

anthonym44
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Homework Statement

Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 11.0 returns to the ground in 9.00 ; the circumference of Mongo at the equator is 2.00×10^5 ; and there is no appreciable atmosphere on Mongo. I found the mass to be 3.71*10^25, now part B asks me for..."If the Aimless Wanderer goes into a circular orbit 3.00×104 above the surface of Mongo, how many hours will it take the ship to complete one orbit?"




Homework Equations

F_g = (GM1M2)/R^2, g= GM/R^2, T^2=R^3, V=(2piR)/T



The Attempt at a Solution

I attempt to use the propotions rule where (T1^2/R1^3) = (T2^2/R^3) using this i have to calculate the period of the planet some how. I figured in order to do this i must need velocity of the planet. if the mass of the ship was given i would also be able to solve the problem so i attempted to use the equation F_g=(GM1M2)/R^2 but do not know F_g, I thought maybe this was F=ma therefore F=(3.71*10^25)(2.44) (2.44 was solved for a using kinematics.) Any help would be appreciated thanks.
 
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At the given altitude,

Fc = GMm/(R+h)^2, where Fc = mw^2(R+h). Find w and hence T directly.
 

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