Gravity train Wikipedia entry
Geege Schuman stashed this in Physics
Origin of the concept In the 17th century, British scientist Robert Hooke presented the idea of an object accelerating inside a planet in a letter to Isaac Newton. A gravity train project was seriously presented to the Paris Academy of Sciences in the 19th century. The same idea was proposed, without calculation, by Lewis Carroll in 1893 in Sylvie and Bruno Concluded. The idea was rediscovered in the 1960s when physicist Paul Cooper published a paper in the American Journal of Physics suggesting that gravity trains be considered for a future transportation project.
Mathematical considerations The gravity train has several curious properties.
- All straight-line gravity trains on a given planet take exactly the same amount of time to complete a journey (that is, no matter where on the surface the two endpoints of its trajectory are located). For Earth, this time would equal 2530.30 seconds (nearly 42.2 minutes) if it were a perfect sphere and of uniform density.
- The time of a trip depends only on the density of the planet and the gravitational constant (except when travelling at a significant proportion of the speed of light).
- The maximum speed is reached at the middle point of the trajectory. For a train that goes directly through the center of the Earth, this maximum speed is about 7,900 metres per second (28440 km/h).
The derivation assumes that the mass is distributed homogeneously throughout the earth. The shortest time tunnel through a homogeneous earth is a Hypocycloid.
Two thoughts: 1) won't work, and 2) remove just two letters and you have "gravy train", something I *would* like to ride.
It looks like fun! But how do you get off it?