Measuring the Diameters of the Moon at Perigee and Apogee

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SUMMARY

The discussion focuses on measuring the diameters of the Moon at perigee and apogee, with specific measurements of 6.00 cm and 13.00 cm provided by a participant. The goal is to determine the ratio of these diameters and calculate the Moon's orbital eccentricity using the formula e = (1 - b²/a²)², where b represents the semi-minor axis. Participants emphasize the need for a formula that directly relates eccentricity to apogee and perigee distances, rather than relying on semi-major and semi-minor axes. The mean orbital eccentricity of the Moon is noted as e = 0.0549 for comparison.

PREREQUISITES
  • Understanding of orbital mechanics and eccentricity
  • Familiarity with measuring techniques for celestial bodies
  • Knowledge of geometric formulas related to ellipses
  • Basic skills in algebra for manipulating equations
NEXT STEPS
  • Research formulas relating eccentricity to apogee and perigee distances
  • Study the properties of elliptical orbits in celestial mechanics
  • Learn about the significance of the semi-major and semi-minor axes in orbital calculations
  • Explore measurement techniques for astronomical observations
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Astronomy students, physics enthusiasts, and educators involved in teaching orbital mechanics and celestial measurements will benefit from this discussion.

crystalplane
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Homework Statement



the image below shows the Moonat perigee and apogee. Measure the diameters for the two, and determine the ratio between perigee and apogee idstance.Based on your result, what is the eccentricity of the Moon'orbit? Compare your value with the Moon' s mean orbital eccentricity(e= 0.0549)

Homework Equations


i have already measured diameters of apogee and perigee, 6.00cm and 13.00 cm(i am not sure about these two numbers.)


The Attempt at a Solution


based on the formula e= (1-b^2/a^2)^0.5,where b is the sei-minor axis...i am very confused about this question.
any help is appreciated.
 
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You need to find a formula that relates eccentricity to apogee and perigee rather than to the semi-major and semiminor axi. (Or find a formula that relates the apogee and perigee to the semi-major and semi minor axi.)

I'd also double check your measurements. (they seem a bit off to me.)
 

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