Measuring the Diameters of the Moon at Perigee and Apogee

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To measure the diameters of the Moon at perigee and apogee, the user recorded values of 6.00 cm and 13.00 cm, respectively, but expressed uncertainty about these measurements. The discussion emphasizes the need to find a formula that connects eccentricity directly to apogee and perigee distances, rather than using semi-major and semi-minor axes. A suggested formula for calculating eccentricity is e = (1 - b²/a²)^(0.5), but confusion remains regarding its application. Participants recommend double-checking the diameter measurements, as they appear inconsistent. Accurate measurements and the correct formula are crucial for determining the Moon's orbital eccentricity and comparing it to the known value of 0.0549.
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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.)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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