Orbit of Earth&Moon around Sun

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We all know that the moon orbits the earth. (Well actually they both orbit about their common center of mass (barycenter), which for the earth-moon system lies about 1500km inside the Earths center, so the center of mass of the Earth-Moon system is actually inside the Earth due to the Earth being much much more massive, so we can approximate and say that the moon is orbiting about the Earth). Anyway, just imagining that the Moon orbits about the Earth and then the fact that (similar mass argument for the Earth-Sun system) the Earth orbits about the Sun, what do you think the Earth-Moon orbit around the sun would look like? This is actually a very interesting and hard to visualize question. Just try it.

Will the Moon ever be going backwards around the Sun, relative to Earth, considering that it is going around the Earth, as the Earth goes around the Sun. The answer is no.
Not like this: https://haplofromnexus.files.wordpress.com/2012/11/moon_sun_wrong.jpg
Like this: https://haplofromnexus.files.wordpress.com/2012/11/moonorbitdiagram.jpg
Or even better like this: https://haplofromnexus.files.wordpress.com/2012/11/moon_synodic_cycle.jpg

There are no rearward loops in the Moons solar orbit, due the fact that the orbital velocity of the Moon about the Earth (1km/s) is small compared to the orbital velocity of the Earth about the sun (30km/s). Also because the suns gravitational pull on the moon is over twice as great as the Earths pull on it, the Moons orbit around the Sun is always convex.
Have an orbital day,
Mete.

You can read more about this topic here:
http://www.math.nus.edu.sg/aslaksen/teaching/convex.html
http://en.wikipedia.org/wiki/Orbit_of_the_Moon

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