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        riddles >> medium >> Distant moon
        
(Message started by: towr on Mar 1^st, 2010, 2:30am)

Title: Distant moon
Post by towr on Mar 1^st, 2010, 2:30am

How much further is the earth from the moon than the moon is from the earth? :P

Title: Re: Distant moon
Post by Mike_V on Mar 1^st, 2010, 7:18am

I could see maybe [hide]4640.7 km[/hide]. But I'm probably not quite seeing what you're getting at.

Title: Re: Distant moon
Post by towr on Mar 1^st, 2010, 7:52am

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: [hide]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.[/hide]

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.

Title: Re: Distant moon
Post by rmsgrey on Mar 1^st, 2010, 7:59am

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...

Title: Re: Distant moon
Post by towr on Mar 1^st, 2010, 8:14am

Ah, that explains Mike_V's value, then.

Title: Re: Distant moon
Post by towr on Mar 4^th, 2010, 9:23am

...

Well, anyway, here's what I got.

[hide]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.[/hide]

Title: Re: Distant moon
Post by cobra on Mar 10^th, 2010, 9:31pm

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.

Title: Re: Distant moon
Post by towr on Mar 11^th, 2010, 12:25am

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.