Calculating Mass of the Moon with Apollo 11 Data

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SUMMARY

The discussion focuses on calculating the mass of the Moon using data from the Apollo 11 mission. The mass of the Apollo 11 vehicle is 9979 kg, with an orbital period of 119 minutes and distances from the Moon's center ranging from 1861 km to 1838 km. Participants confirm that the semi-major axis, calculated as the average of the maximum and minimum distances (1849.5 km), is essential for applying Newton's version of Kepler's Third Law to derive the Moon's mass. The correct application of gravitational equations and Kepler's laws is emphasized as crucial for solving the problem.

PREREQUISITES
  • Newton's Law of Universal Gravitation
  • Kepler's Third Law of Planetary Motion
  • Understanding of semi-major axis in orbital mechanics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study Newton's Law of Universal Gravitation in detail
  • Learn how to apply Kepler's Third Law to different celestial bodies
  • Explore the concept of semi-major axis and its significance in orbital calculations
  • Practice solving problems involving gravitational forces and orbital mechanics
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Students in physics or astronomy, educators teaching orbital mechanics, and anyone interested in celestial calculations using historical space mission data.

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Homework Statement



Before landing men on the moon, Apollo 11 space vehicle was put into orbit about the moon. The mass of the vehicle was 9979kg and the period of the orbit was 119 min. The maximum and minimum distances from the center of the moon were 1861 km and 1838km . Assuming the moon to be a uniform spherical body, what is the mass of the moon according to these data?


Homework Equations



GMm/R^2
elliptic equation?


The Attempt at a Solution



I tried using the kepler's law and Gravitational equation.. It seems I can't get the mass of the moon. Anyone can help me through?

thankx
 
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Period, distance and mass will suggest Newton's version of Keplers's third law. You will have to work out what the semi major axis is though.
 
is the semi major axis the radius for the r^3 in the kepler's thrid law? I use the (1861+1838)/2 is correct that this is the value for r? 1849.5?

thank for replying..
 
Last edited:
Yes Kepler's 3rd is based on the semi major axis. You have correctly worked it out.
 
thanks then I think I got of correct d.. Thanks..
 

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