Could Tunnel Construction on the Moon Solve Earth's Practical Problems?

[UrbanXrisis]

I was given the equation for the period of oscillation thought a tunnel:$$T=2 \pi \sqrt{\frac{R_E^3}{GM_E}}$$

then asked how I could transform that into $$T=2 \pi \sqrt{\frac{R_E}{g}}$$

which I did through the idea that $$g=\frac{GM_E}{R_E^2}$$

The the question asked what would be the period if tunnels were made though the moon?

and what practical problem regarding these tunnels on Earth would be removed if they were built on the Moon?

I'm clueless here

 

[UrbanXrisis]

I'm guessing that the equation would be the same equation but just use the radius of the moon and the acceleration of the moon?

The practical problem would be there is no air friction?

 

[BobG]

They gave you the equation for the determining the period of oscillation - all you have to do is find out the radius of the Moon, the gravitational acceleration on the Moon, and plug the numbers into your equation.

Yes, the lack of atmosphere eliminates one practical problem. There's another, though. The Moon, like the Earth, is rotating. What direction will gravity accelerate an object dropped into the tunnel? How long will the tunnel occupy the space that gravity's pulling the object toward? In fact, how much lateral velocity did the object have when it was first dropped? (the object should initially be traveling the same direction and speed as the surface was).

That problem won't exactly be eliminated on the Moon. However, if you calculate the angular velocity of the Earth's rotation and the angular velocity of the Moon's rotation, you'll notice the problem isn't nearly as big on the Moon (in fact, it's about 27.4 times smaller).

Here's a discussion we had about the type of tunnels you're talking about.

tunnel through the centre

 

[OlderDan]

I was given the equation for the period of oscillation thought a tunnel:$$T=2 \pi \sqrt{\frac{R_E^3}{GM_E}}$$

then asked how I could transform that into $$T=2 \pi \sqrt{\frac{R_E}{g}}$$

which I did through the idea that $$g=\frac{GM_E}{R_E^2}$$

The the question asked what would be the period if tunnels were made though the moon?

and what practical problem regarding these tunnels on Earth would be removed if they were built on the Moon?

I'm clueless here

There are no doubt several things one could identify, but most of those could be overcome. Air resistance could be eliminated by evacuating the tunnel. Rotational problems could be eliminated by frictionless magnetic confinement to keep the object in the tunnel. The major practical problem I see is finding a material for the walls of a tunnel that can withstand the environment. What is the composition of the core of the Earth and that of the moon?