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This is just a reality that I have stumbled upon that I'm sure was well-known, but I still found it interesting. I apologize if this is second-nature to physics experts.

I was responding to a post on a different thread that claimed you could make a tunnel around the Earth and if you sent a train or something around that tunnel at 11.2 km/s, the people inside would feel weightless. Of course, this isn't the case; they only need to be traveling at what the orbital velocity would be at the surface of the Earth. I corrected him, and also wanted to be able to tell him what would happen if the train WERE going 11.2 km/s, and I calculated it, and as it turns out, the people on that train would experience 1G, but toward the top of the train. I though maybe this was a coincidence, so I actually did the math and it turns out that it is EXACTLY 1G. Like I said, I'm sure this is well-known, but I though it was a cool fact. At escape velocity, you would experience exactly 1G toward the roof. It would feel as though you were still on Earth, but the ceiling of the train would become the floor. I further delved into the equations and came up with why this was the case.

The acceleration due to gravity is GM/r². Centripetal acceleration can be calculated as v²/r. Escape velocity is √(2GM/r), and if we plug in the escape velocity into the centripetal acceleration equation, we get 2GM/r². I found that to be very cool. Acceleration due to gravity is GM/r² while centripetal acceleration with a radial velocity equal to escape velocity would be 2GM/r². Gotta love physics.

I was responding to a post on a different thread that claimed you could make a tunnel around the Earth and if you sent a train or something around that tunnel at 11.2 km/s, the people inside would feel weightless. Of course, this isn't the case; they only need to be traveling at what the orbital velocity would be at the surface of the Earth. I corrected him, and also wanted to be able to tell him what would happen if the train WERE going 11.2 km/s, and I calculated it, and as it turns out, the people on that train would experience 1G, but toward the top of the train. I though maybe this was a coincidence, so I actually did the math and it turns out that it is EXACTLY 1G. Like I said, I'm sure this is well-known, but I though it was a cool fact. At escape velocity, you would experience exactly 1G toward the roof. It would feel as though you were still on Earth, but the ceiling of the train would become the floor. I further delved into the equations and came up with why this was the case.

The acceleration due to gravity is GM/r². Centripetal acceleration can be calculated as v²/r. Escape velocity is √(2GM/r), and if we plug in the escape velocity into the centripetal acceleration equation, we get 2GM/r². I found that to be very cool. Acceleration due to gravity is GM/r² while centripetal acceleration with a radial velocity equal to escape velocity would be 2GM/r². Gotta love physics.

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