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Topic: Distant moon (Read 792 times) |
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towr
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Distant moon
« on: Mar 1st, 2010, 2:30am » |
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How much further is the earth from the moon than the moon is from the earth? 
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Mike_V
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Re: Distant moon
« Reply #1 on: Mar 1st, 2010, 7:18am » |
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I could see maybe 4640.7 km. But I'm probably not quite seeing what you're getting at.
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towr
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Re: Distant moon
« Reply #2 on: Mar 1st, 2010, 7:52am » |
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Well, that's several orders of magnitude over what I got. I'd be interested to see what you're reasoning is, but I think it's safe to say it is not in the direction I was thinking of.
Hint: There is a physical difference between what an observer on the moon would measure, from what an observer on the earth would measure, between the same two points on the earth and moon.
Well.. assuming they could measure distance sufficiently accurately in the first place.
The real problem for me lies in finding the right formulas to use. I'm not sure I've got the right value myself, although I'm pretty sure I'm close.
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| « Last Edit: Mar 1st, 2010, 7:56am by towr » |
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rmsgrey
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Re: Distant moon
« Reply #3 on: Mar 1st, 2010, 7:59am » |
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If you look at distance to the other's centre when standing on the one's surface, the moon's centre is closer to the closest point on the Earth's surface than the Earth's centre is from the closest point on the moon's surface. Of course, if you go from the furthest point, the Earth is closer to the moon than the moon to the Earth...
Another possible point of difference is looking at how much energy you have to expend to get a standard mass from one to the other...
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towr
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Re: Distant moon
« Reply #5 on: Mar 4th, 2010, 9:23am » |
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...
Well, anyway, here's what I got.
The matter at hand is time dilation, which means that if you measure the same distance, you'll get a different result dependent on how fast clocks run in your location.
There is time dilation both as result of velocity, and as a result of gravity. In a gravity well (or when accelerating) and at greater velocity clocks run slower. Gravitational time dilation is conveniently equal to a velocity time dilation at escape velocity (as far as I can tell).
So together this gives about 1/2*(11.1862 - 1.0222 - 2.382)/2997922 * 384.5*106 = 0.25m difference. The earth is therefore almost a foot further from the moon than the moon is from the earth.
Feel free to check by seeing how long it takes for a laser pulse to bounce back, from both locations.
We can measure the distance to an accuracy of about 3cm, so it should actually be noticeable.
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| « Last Edit: Mar 4th, 2010, 9:28am by towr » |
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cobra
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Re: Distant moon
« Reply #6 on: Mar 10th, 2010, 9:31pm » |
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I think distance of moon from earth implies the distance from earth's circumference (b'coz that is the place from where an observer will calculate the distance) to moon's center and vice-versa. So,
Let distance b/w their centers = x.
D of Earth from Moon = x - Rm.
D of Moon from Earth = x - Re.
Hence, Earth is further by d = Re - Rm.
where Re = Radius of Earth.
Rm = Radius of Moon.
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towr
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Re: Distant moon
« Reply #7 on: Mar 11th, 2010, 12:25am » |
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But if you measure the distance from the circumference of the earth to the circumference of the moon, that difference cancels out. In both case you'd get x-Re-Rm. But there's a difference even if you measure between the same two points, simply depending on which of the two places you measure from. The earth-sun distance is also different depending on whether you measure it from earth or the moon.
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| « Last Edit: Mar 11th, 2010, 1:06am by towr » |
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