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Why the motion of the Moon looks very slow in the sky? Doesn't it need the high speed in order to escape the earth's gravity?

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Did you try to calculate what it's velocity should be approximately? –  Bernhard Feb 28 '13 at 7:22
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No. I just meant the apparent motion. –  richard Feb 28 '13 at 7:27
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The moon hasn't escaped Earth's gravity, or it wouldn't be revolving around the earth. The moon is gravitationally bound to the Earth. –  Kitchi Feb 28 '13 at 9:50
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Your profile says you're a postdoc in physics, so this question seems a bit strange. –  Mike Dunlavey Mar 19 '13 at 22:02
    
Thanks Mike.... –  richard Mar 25 '13 at 9:33

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The Moon moves at about a thousand metres per second, but it's a long way away so it only appears to move slowly. Most of the apparent movement of the Moon is actually due to the rotation of the Earth. We see it appearing to go round the Earth once a day, but it actually takes about 28 days to complete an orbit.

The Wikipedia article on the Moon's orbit has these and many other stats about the Moon.

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The moon is in orbit of the earth, an ellipse. A circle is a good approximation for the orbit, due to the low eccentricity. It's potential energy in radial direction is at a minimum. The speed is $$v_{\text{moon}}=1022\,\frac{\text{m}}{\text{s}}$$. Thats triple speed of sound. An airplane travelling at this speed would take not much time to appear oit of sight. The moon however appears slower. Due to its distance to the viewer it appears to travel slowly at the sky: low angular velocity $\omega=\frac{v_{\text{moon}}}{r_{\text{moon}}}=\frac{1}{T}$.

Estimating the speed of the moon

Earth also rotates and the period of a moon cycle is longer. One cycle takes $T=27.32$ days to complete. Assuming a circular orbit with mean distance $r_{\text{moon}}=385\,000$ km allows calculation of the speed of the moon. This calculation yields the velocity of about one kilometer per second.

Fun fact

The motion of the moon has a fun fact: Due to tidal locking one side of the moon always faces towards the earth.

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1022 m/s or km/s? –  richard Mar 4 '13 at 17:44
    
Thanks. Updated answer. Provided data for calculation of the speed of the moon. –  Stefan Bischof Mar 4 '13 at 18:26

When we stand on the side of a street and watch a car zooming at 100 Km/H we feel that the car is moving fast. But when you look at the same car from a distance of 10 Km, it appears slower because of the car and the observer. This is because when you are standing 10 Km away, the span of perpendicular view of your eyes has increased while the speed of the car remained at 100 Km/H. So the car has to spend more time to travel across your span of view so it appears slower. When you are standing on the same street as the car, you span of perpendicular view is very small and so the car car appears to zoom past it. Same with the moon.

The Moon orbits the Earth at a mean distance of 384,400 Km with a mean orbital velocity of 1.023 Km/S which is thrice the speed of sound. But it is at a distance of 384,400 Km so your the span of view is the entire sky due to which it appears to move slowly to us.

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