Mark Shegelski, an associate professor of physics at the University of Northern British Columbia, explains.
The simple answer is, theoretically, yes. First, let us ignore friction, the rotation of the earth, and other complications, and focus on the case of a hole or tunnel entering the earth at one point, going straight through its center, and coming back to the surface at the opposite side of the planet. If we treat the mass distribution in the earth as uniform, one would fall into the tunnel and then come back up to the surface on the other side in a manner much like the motion of a pendulum swinging down and up again. Assuming that the journey began with zero initial speed (simply dropping into the hole), your speed would increase and reach a maximum at the center of the earth, and then decrease until you reached the surface, at which point the speed would again be zero. The gravitational force exerted on the traveler would be proportional to his distance from the center of the earth: it's at a maximum at the surface and zero at the center. The total time required for this trip would be about 42 minutes. The speed of our traveler at the center of the Earth would be 7,900 meters a second. If there were no friction, there would be no energy loss so our traveler could oscillate into and out of the tunnel.
This trip could not take place in the real world for a number of reasons, including the implausibility of building a tunnel 12,756 kilometers long, displacing all of the material in the tunnel's proposed path, and having the tunnel go through both the earth's molten outer core and its inner core, where the temperature is about 6,000 degrees! It would be much easier to build such a tunnel in a small asteroid. Interestingly enough, for a tunnel that reaches from one point to another point on the earth's surface but does not pass through the center of the planet, the travel time would still be about 42 minutes. The reason for this is that although the tunnel is shorter, the gravitational force along its path is also decreased as compared to that of a tunnel that goes through the center of the planet, which means you would travel more slowly. Because the distance and the component of gravity decrease by the same factor, the travel time ends up being the same.
Answer originally posted April 21, 2003.
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17 Comments
Add CommentMark's argument is based on the premise that 'The gravitational force exerted on the traveler would be proportional to his distance from the center of the earth: it's at a maximum at the surface and zero at the center.' Following this logic, an object above the earth's surface would experience an even greater gravitational force and the further away from the surface the greater the force. To me this seems to be counter-intuitive, otherwise all universal objects would be simultaneously attracted to each other in some kind of 'anti big bang' effect. I'm obviously missing something in my reasoning or Mark's basic premise is incorrect (which I doubt!).
Reply | Report Abuse | Link to thisYes, you are "obviously missing something in my reasoning"; namely the difference between [b][i]inside [/i][/b]and [b][i]outside[/i][/b]!
Reply | Report Abuse | Link to thisWhen you are outside of the earth, all of the earth's mass is between you and the center. But when you are inside the earth, you are [b][i]between [/i][/b]some of the mass and the center. So outside, all the gravitational force is toward the center; inside, some is toward the center and some away from the center. At the center of the earth, the inward and outward forces cancel and net gravity is zero.
So the force of gravity from a solid sphere is maximum at the surface and lessens when you move either inward [b][i]OR [/i][/b]outward. Not very intuitive, I agree. Even less intuitive is that the formula for net gravitational force is different for inside and outside. Outward, the force drops off with the square of distance, inside the drop off is linear. Working those formulae out is a college calculus problem.
I believe you would slow in rebounding action until you came to rest and weightless in the center.
Reply | Report Abuse | Link to thisHow does particle physics address this?
Reply | Report Abuse | Link to thisThanks, Don Weaver
Palacios, Texas 77465
The problem is that as you are falling, the mass of Earth above you would be increasing as the mass below would be decreasing. The gravitational attraction from above would soon be much larger than that from below. Just in a quick estimate, you would pass the center on your first trip, but only rise about 1/2 way to the other side, before beginning to fall again, and eventually wind up stuck in the center.
Reply | Report Abuse | Link to thisWouldn't you bounce into the sides of the tunnel, thus decreasing your speed and giving you a lot of bruises?
Reply | Report Abuse | Link to thisIf one evacuated the atmosphere in a tunnel. What would be the impact on speed, other factors being without effect for this issue? If a carrier
Reply | Report Abuse | Link to thiscould be made and a tunnel designed for its use could travel by this method be of any real interest?
A detail: this 42 min period x2, to complete a cycle is the time a zero heigh satellite orbit would take (ignoring air friction, again. Right?
Reply | Report Abuse | Link to thisIn reply to some previous posts:
Reply | Report Abuse | Link to this>>I believe you would slow in rebounding action until you came to rest and weightless in the center.
in reality, you would, because of friction/air resistance. That's why the author said we would ignore those forces.
>>Wouldn't you bounce into the sides of the tunnel, thus decreasing your speed and giving you a lot of bruises?
Not if you do away with all forces except gravity. That's why the author states no friction and the earth isn't spinning.
If gravity is the only force involved, and if the earth is fairly close to spherical and fairly uniform at any given distance from the centre, you will oscillate indefinably, exactly as described.
This is everything that I forgot that I wanted to know, Awesome article, love it!!
Reply | Report Abuse | Link to thisI would fall 1097 kilometers and from that point to the center the travel would be upward due to gravity. The Eath is not a concentric mass. Inner core is compound by solid oxygen (paramagnetic) Outer core y liquid ozygen (paramagnetic).
Reply | Report Abuse | Link to thisThe center of the Earth is the coldest zone of the planet .
A summary of the new theory will be sent if required.
would fall 1097 kilometers and from that point to the center the travel would be upward due to gravity. The Eath is not a concentric mass. Inner core is compound by solid oxygen (paramagnetic) Outer core is liquid oxygen (paramagnetic).
Reply | Report Abuse | Link to thisThe center of the Earth is the coldest zone of the planet .
The Sun and Earth magnetic fields interacts when
earth global warming. Polarity of the Earth magnetic field will reverse soon. It means that due to global warming the North magnetic field will become south and viceversa.
A summary of the new theory will be sent if required.
For the exercise discussed in print (with nice colour diagrams), see:
Reply | Report Abuse | Link to thisJohn Wheeler, "A Journey into Gravity and Spacetime", ISBN 0716760347, Chapter Four, "Boomeranging through the Earth"
What nobody seems to address is that the tunnel should be from the north pole to the south pole, for the idea to more or less work.
Reply | Report Abuse | Link to thisAny other orientation for the tunnel (even if it still passes through the center of the earth), will cause you to have a tangential speed, and you will hit the wall of the tunnel (unless it spirals in an appropriate manner...) because rotational momentum needs to be preserved -- compare this with a skater who enters a spin with his arms extended, then retracts them, causing him to spin faster!
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Edited by Vanfruniken at 01/02/2008 4:48 PM
What happens to electricity that is generated but not used in the grid? (say at night)
Reply | Report Abuse | Link to thisSo here's a corollatry to the question -
Reply | Report Abuse | Link to thisIf you could drill a hole from one end of the Earth to the other, let's say, a meter wide at all points.... What types of interesting things would happen regarding the atmosphere rushing into the tunnel? Would it create a huge vortex much like a tornado? Would the air rushing in from both ends be turning in the same or different directions as it reached the center? What would be the overall force of the air moving at whatever speed it would be moving at; enough to widen the tunnel or wrip apart the Earth?
Just taking the whole question in a ....different direction. :)
love the idea cant get passed the 6K degree core
Reply | Report Abuse | Link to thisyou would not look very good half way up the other side.