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Transit Time in a Tunnel Through the Moon

12/31/2013 9:56 PM

If one could make a tunnel thru the Moon (I know, it has a creamy center of molten iron, but just forget that) and step in one end, how long would it take to reach the other end? And what max speed would one achieve?

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#1

Re: Transit time in a tunnel thru the Moon

12/31/2013 10:26 PM

Molten iron huh?

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#2

Re: Transit time in a tunnel thru the Moon

12/31/2013 10:27 PM

1/6 of whatever it would be on earth.

The problem is that as soon as you dive in, the gravitational attraction begins to decrease.

It's neutral at the center. I don't know how to figure this out.

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#5
In reply to #2

Re: Transit time in a tunnel thru the Moon

01/01/2014 12:43 AM

No, it's actually quicker to go through the earth in a vacuum- about 54 minutes at a peak velocity of around 7,900 m/second.

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#3

Re: Transit time in a tunnel thru the Moon

12/31/2013 10:48 PM

I seem to recall that the length of time to fall all the way through and come back to the starting point is identical to the time it would take to orbit the moon just above the lunar surface. Right now, it's too late where I am to even think about doing the math. Feel free to try it on your own.

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#4

Re: Transit time in a tunnel thru the Moon

12/31/2013 11:58 PM

68 minutes and 59 seconds, maximum velocity of 1,678.365 metres per second achieved at the core.

Bathroom breaks are additional and may only be taken on the first, third and 49th oscillations through the passage. Please note this is subject to seat sale restrictions and oversized luggage may cause difficulty exiting the tunnel........

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#6

Re: Transit time in a tunnel thru the Moon

01/01/2014 7:49 AM

extra dumb question,stop smoking

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#17
In reply to #6

Re: Transit time in a tunnel thru the Moon

01/02/2014 1:57 PM

doesn't that mean the people responding were smoking as well? and smoking what exactly?

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#7

Re: Transit time in a tunnel thru the Moon

01/01/2014 11:51 AM

We had a CR4 challenge question a while ago, with the Earth being the subject rather than the moon as in your question here.

The solution there was a thought problem called a Gravity Train. The great thing about the solution to the Gravity train is, the math works for all celestial bodies.

Change the gravitational constant and density to those of the selected celestial body in any Gravity Train solution, and you will have your answers.

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#8
In reply to #7

Re: Transit time in a tunnel thru the Moon

01/01/2014 11:56 AM

What a memory.

Happy New Year!

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#9
In reply to #8

Re: Transit time in a tunnel thru the Moon

01/01/2014 12:40 PM

Lyn, one thing is about being forgetful is....... You meet new friends every day.....:P

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#10
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Re: Transit time in a tunnel thru the Moon

01/01/2014 1:56 PM

And the jokes never get old.

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#11
In reply to #10

Re: Transit time in a tunnel thru the Moon

01/01/2014 2:08 PM

"And the jokes never get old."

And that's why an occasional henway still gets a laugh. Rats! If I had remembered I woulda tossed one of them, or maybe a duckdo, into the first comment.

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#12
In reply to #11

Re: Transit time in a tunnel thru the Moon

01/01/2014 2:21 PM

What's a duckdo again?

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#13
In reply to #12

Re: Transit time in a tunnel thru the Moon

01/01/2014 3:05 PM

He goes "Quack-Quack"!

You're still the best straight man in the business!

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#18
In reply to #10

Re: Transit time in a tunnel thru the Moon

01/03/2014 10:52 AM

Did anyone hear the one about the lonely scientist?

I will save you from it, unless you require the joke to be told. As to falling through the moon, same joke, different constants, It probably means the answer is precisely 258 minutes, since the mass of the moon is about 1/6 of the earth, but both are made of "green cheese" leftover from proto-planetary collision over 3 billion years ago.

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#14
In reply to #7

Re: Transit time in a tunnel thru the Moon

01/01/2014 6:15 PM

"Change the gravitational constant" - eh?

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#20
In reply to #14

Re: Transit time in a tunnel thru the Moon

01/08/2014 5:10 PM

Well. At least here locally, the gravitational acceleration is a constant, up to so many decimal places. However, smart physicists will always be quick to point out that pendulum experiments are available to constantly monitor the acceleration of gravity, and to this experiment, it is anything but constant. Short term and long term measurements are taken, and it changes depending on where you are on the earth's surface (or above or below). Obviously at the moon, you still use the newtonian gravitational constant, but you must substitute in the M mass for the moon rather than earth, etc, etc.

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#21
In reply to #20

Re: Transit time in a tunnel thru the Moon

01/09/2014 4:11 AM

Are you sure you're not confusing "g", the (local) acceleration due to gravity, with "G", the universal gravitational constant?

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#15

Re: Transit Time in a Tunnel Through the Moon

01/01/2014 6:54 PM

"We had a CR4 challenge question a while ago, with the Earth being the subject rather than the moon as in your question here.

The solution there was a thought problem called a Gravity Train. The great thing about the solution to the Gravity train is, the math works for all celestial bodies.

Change the gravitational constant and density to those of the selected celestial body in any Gravity Train solution, and you will have your answers."

Thanks, Doorman, you get a GA. The Gravity Train led me to this http://www.math.purdue.edu/~eremenko/dvi/gravsol.pdf by a Purdue prof that gives the math. I'll post again when I've got the numbers for the moon.

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#16

Re: Transit Time in a Tunnel Through the Moon

01/01/2014 8:14 PM

OK, I get a transit time of 54 minutes and a max speed of 1700m/s (3800 mph).

Sounds counterintuitive that it would take longer since the moon is only 1/4 the radius of the Earth. But it seems that transit time is only dependent on density of the body; the size doesn't matter! Transit time is inversely proportional to sq rt of density. Denser and you get there quicker. But max speed is directly proportional to radius of body and sq rt of density: bigger and denser means faster.

That would be an E ticket ride for sure. Think I'd take the moon shuttle craft instead.

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#19

Re: Transit Time in a Tunnel Through the Moon

01/08/2014 11:01 AM

Assuming a perfect sphere in shape with a gravitational field that is only a function of distance from the centre then one would never reach the other end, as the tiny amount of atmosphere that the Moon has would introduce sufficient drag to prevent arrival.

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