# The Naked Scientists Forum

### Author Topic: How big is Earth when compressed  (Read 4130 times)

#### engrByDayPianstByNight

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##### How big is Earth when compressed
« on: 09/08/2007 05:37:31 »
I'm curious to know: If the whole of Earth were compressed as tightly as possible (i.e., no spacing between molecules), how big would it be? Assume that we exclude all living things on earth, but include water.

Anyone can offer a reasonable guesstimate? Thanks.

#### lightarrow

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##### How big is Earth when compressed
« Reply #1 on: 09/08/2007 19:11:06 »
I'm curious to know: If the whole of Earth were compressed as tightly as possible (i.e., no spacing between molecules), how big would it be? Assume that we exclude all living things on earth, but include water.

Anyone can offer a reasonable guesstimate? Thanks.

1. Not considering the athmosphere, it would be as it is now. There's no space between molecules in matter at condensed state.
2. As tightly as possible is not "with no spacing between molecules". If it were made of neutrons only, as in the most dense neutron stars (density ≈ 2*1015 g/cm3), it would have a diametre ≈ 67 metres.
If it were a black hole, it would measure ≈ 3 millimetres (I don't remember if in diametre or in radius).

#### engrByDayPianstByNight

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##### How big is Earth when compressed
« Reply #2 on: 09/08/2007 19:31:58 »

#### Soul Surfer

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• keep banging the rocks together
##### How big is Earth when compressed
« Reply #3 on: 11/08/2007 22:53:56 »
http://xaonon.dyndns.org/hawking/

gives the radius of an earth mass black hole as about 9 mm

#### lightarrow

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##### How big is Earth when compressed
« Reply #4 on: 11/08/2007 23:10:22 »
http://xaonon.dyndns.org/hawking/

gives the radius of an earth mass black hole as about 9 mm

#### syhprum

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##### How big is Earth when compressed
« Reply #5 on: 12/08/2007 16:05:58 »
My arithmetic makes the diameter of the compressed Earth as 180 meters.
« Last Edit: 12/08/2007 21:09:26 by syhprum »

#### lightarrow

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##### How big is Earth when compressed
« Reply #6 on: 13/08/2007 17:27:27 »
My arithmetic makes the diameter of the compressed Earth as 180 meters.
Yes. I have made the computation another time and I have to say your result is correct (I can't understand where I made the mistake last time.) [B)]

#### syhprum

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##### How big is Earth when compressed
« Reply #7 on: 13/08/2007 19:23:52 »
Lightarrow

I think that what you did was make a computation for the radius and neglected to allow for the 5.5 gm/cm^3 density of the uncompressed Earth

#### Soul Surfer

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##### How big is Earth when compressed
« Reply #8 on: 13/08/2007 22:35:54 »
That's very interesting.  There is quite a big difference between the size of the earth as neutron star material and its size as a black hole.  By the time you get to the size of a real neutron star which has between one and two solar masses of material the black hole is only slightly smaller  (ie less than a factor of 2) than the neutron star.

It is also interesting to think that the radius of a blackhole with the mass of a galaxy is a sizable fraction of a light year and one with a radius of about the distance light has travelled since the big bang is about equal to the mass of all the galaxies in that volume.

This is because the radius of a black hole is a linear function of the mass while volume and mass vary as the cube of the radius.

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##### How big is Earth when compressed
« Reply #8 on: 13/08/2007 22:35:54 »