On Monday, October 5,2015, the Moon will be in its Third (or Last) Quarter phase

Question

On Monday, October 5,2015, the Moon will be in its Third (or Last) Quarter phase. In this position, the Moon is crossing the Earth's orbital path around the Sun, ahead of the Earth. If it's clear that day, take a look at the Moon sometime in the morning. And think about it That's where we're headed! In some amount of time, the Earth will be in the place where the Moon is (when you're looking at it)! In how much time will that be? (Look up any necessary astronomical data; it can be found inside the back cover of your textbook for example.)

Explanation / Answer

First calculate the orbital speed of earth around sun.

for that using circular motion conecept,

gravitational force = centripetal force

GMm / r^2   = mv^2 / r

GM /r =v^2

6.67 x 10^-11 x 1.99 x10^30 / (1.50 x 10^11) = v^2

v = 29747.04 m/s

when moon is ahead of earth.

moon will at a distance ahead of earth equal to orbital radius of moon about earth.

that is d = 3.84 x 10^8 m

time taken to earth to go 3.84 x 10^8 m to come to moon's place,

t = d/v = 12908.85 sec

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