Measuring the Diameters of the Moon at Perigee and Apogee

[crystalplane]

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.

 

[Janus]

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.)

 

[Moetasim]

I would first clarify the measurements provided in the problem statement. Are the measurements in centimeters or another unit? Are the measurements accurate and precise? It is important to have accurate and precise measurements in order to calculate the eccentricity of the Moon's orbit.

Assuming the measurements are in centimeters, the ratio between the diameters at perigee and apogee would be 13.00cm/6.00cm, or approximately 2.17. However, this ratio alone does not provide enough information to determine the eccentricity of the Moon's orbit.

To calculate the eccentricity, we need to know the semi-major axis (a) and semi-minor axis (b) of the Moon's orbit. These values can be calculated using the measured diameters and the formula for the eccentricity of an ellipse (e= c/a, where c is the distance from the center of the ellipse to one of its foci).

Without knowing the values for a and b, it is not possible to accurately determine the eccentricity of the Moon's orbit. However, we can compare the calculated eccentricity with the Moon's mean orbital eccentricity (e= 0.0549). If the calculated eccentricity is significantly different from the mean value, it could indicate that the measurements were not precise or that there are other factors affecting the Moon's orbit. Further analysis and data collection would be needed to accurately determine the eccentricity of the Moon's orbit.