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.
Read more about this topic: Gravity Train
Famous quotes containing the word mathematical:
“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
—Blaise Pascal (1623–1662)