Fact of the day : The deepest hole ever drilled by man ...

[BulgarianPride]

So what your saying is if there was a hole right through the earth and you jumped in you would never reach the other side?

No, you reach the other side, and you fall back down.

And is the 42 mins timespan about right?

If golden man says so, then it is. :) Probably. i haven't calculated anything.

 

[1.618034]

So what your saying is if there was a hole right through the earth and you jumped in you would never reach the other side?

No, you reach the other side, and you fall back down.

And is the 42 mins timespan about right?

The Gravity Train

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.
* The time of a trip depends only on the density of the planet and the gravitational constant.
* 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.

Where k=3 you get...


[bigimg]http://upload.wikimedia.org/wikipedia/commons/b/b5/Deltoid2.gif[/bigimg]



If k=4


[bigimg]http://upload.wikimedia.org/wikipedia/commons/0/05/Hypocycloid-4.svg[/bigimg]


Etc....

<a class="postlink" href="http://en.wikipedia.org/wiki/Gravity_train" onclick="window.open(this.href);return false;">http://en.wikipedia.org/wiki/Gravity_train</a>

 

[BulgarianPride]

No, you reach the other side, and you fall back down.

And is the 42 mins timespan about right?

The Gravity Train

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.
* The time of a trip depends only on the density of the planet and the gravitational constant.
* 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.

Where k=3 you get...


[bigimg]http://upload.wikimedia.org/wikipedia/commons/b/b5/Deltoid2.gif[/bigimg]



If k=4


[bigimg]http://upload.wikimedia.org/wikipedia/commons/0/05/Hypocycloid-4.svg[/bigimg]


Etc....

<a class="postlink" href="http://en.wikipedia.org/wiki/Gravity_train" onclick="window.open(this.href);return false;">http://en.wikipedia.org/wiki/Gravity_train</a>

Thats every interesting. Whats the smaller circle (physical interpretation)?

 

[BlueHammer85]

So what your saying is if there was a hole right through the earth and you jumped in you would never reach the other side?

No, you reach the other side, and you fall back down.

And is the 42 mins timespan about right?

 

[1.618034]

And is the 42 mins timespan about right?

The Gravity Train

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.
* The time of a trip depends only on the density of the planet and the gravitational constant.
* 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.

Where k=3 you get...


[bigimg]http://upload.wikimedia.org/wikipedia/commons/b/b5/Deltoid2.gif[/bigimg]



If k=4


[bigimg]http://images.yourdictionary.com/images/main/A4hypcyc.jpg[/bigimg]


Etc....

<a class="postlink" href="http://en.wikipedia.org/wiki/Gravity_train" onclick="window.open(this.href);return false;">http://en.wikipedia.org/wiki/Gravity_train</a>

Thats every interesting. Whats the smaller circle (physical interpretation)?

Not sure what you mean...?

The circle's centre is the focus (of the locus) so exists only as a theoretical centre of movement. I reckon that basically it's saying that straight through the middle isn't necessarily the best/only route. So long as the Train follows one of the possible hypocycloid routes then it should work. In theory.