A Question of Gravity

[russellhq]

Interesting thought, 2 options I would guess:

You jump and at t=0 you have G=0 so off you go apparently forever.

As you get higher there is steadily more mass "below" you then above so you begin to slow down, in effect as gravity gets greater you get dragged back.

A slight difference to leaping off the earths surface as the higher you go the less the pull of gravity is.

The mathematics of your jump at the centre of the earth is likely to be dependant on r² not r^-2.

The other option is at any distance from the centre then you are no longer in a zero gravity environment, and lets leave it at that. :grin:

I figured it would be along the lines of the second option, though I was curious as to how high I could jump. For instance, if we assume I have a mass of 75kg and can jump 0.5m while standing on the surface of the earth (g=9.81m/s2), how high could I jump at the centre of the earth? I think it could be quite high...

[Tiki]

Taking the question one step further: if after jumping into our tunnel and all the oscillating, we are now at rest at the centre of the earth. If I steady myself and have a small platform to stand on. How high could I jump in this "zero gravity" environment?

If you could jump 0.8m on the earths surface then a similar jump at the earth's centre would take you about 1600m (assuming the earth has a constant density and I have the units right).

As Acey says, if you jump down a shaft which passes through the centre of the earth you will not touch the sides. Imagine you are at the centre of the earth looking up the shaft and someone  drops in a stone. The stone will hit you at about 7900m/sec unless you move. The coriolis force is a pseudo force and will not save you. If you are able to watch this sequence events from afar then the angular momentum of the stone will appear to change (and the coriolis force is invoked to explain matters).

If you jump into a shaft that doesn't go straight down then the force of gravity is that which might propel you into the walls.

Idealized gravity trains (no friction and constant density) are pretty cool and illustrate quite nicely the deep relationship between inertial and gravitational mass.

Edit: 3200m not 1600m

[russellhq]

That's an impressive jump, almost half way in one go!

[Tiki]

That's an impressive jump, almost half way in one go!

3200m not 3200km....