Surface gravities and Density dostribution

karov · 2008-01-09 15:03:57

Re: Terraforming Mercury, where it was discussed the idea deeper = higher gravity.

Strange, but it is true! If you have serious difference in the density of the gravito-chemically differentiated interriors, the maximum gravity equipotential closed surface, deosn`t coincides with the outer solid ( or liquid ) surface.

Proof #1: http://www.worlddreambank.org/W/WITCHCOR.HTM

Proof #2: The surface gravity of Mercury is ~0.38 gees, now strip 30% of its mass to reach 1/4 less radius / only the metal core PARADOXALLY at the core the "surface" gravity is 0.49 gees.
In no case the mass over the core , could outpull the core beneath. It is too spread, thin and distant.

RickSmith · 2008-01-10 00:16:08

Hi Karov, everyone.
I am wondering if we should have a multiplying of new thread or if replies to existing threads are better within them?

Warm regards, Rick.

karov · 2008-01-10 05:19:35

Hi RickSmith,
I concluded that new thread is better for that theme, cause it is not limited to Mercury alone, first, and second sometimes the threads become way too long to follow and interesting generalizations like that are lost in the big volume.

Could you help me with the maths ( pointing sources, etc. ) for such density distribution vs. surface gravity problems. Cause gravity INSIDE mathers and the Newtonian approximation doesn`t applies.

Chart of the Earth gravity from the surface DOWN to the center?

karov · 2008-01-10 13:10:38

the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

noosfractal · 2008-01-10 23:54:48

http://www.math.harvard.edu/~knill//tea … a/hell.pdf

The force due to gravity drops linearly from the surface to zero at the center (assuming constant density).

F(r) = G*(4/3)*pi*rho*r

where G is the gravitational constant
r is the distance from the center
and rho is the density of the mass in the sphere defined by r

** Edit to add gravitational constant.

noosfractal · 2008-01-11 00:16:51

variation%20of%20g.png

http://www.splung.com/content/sid/2/page/gravitation

The green line shows Earth internal gravity taking into account density variation - it actually goes up before dropping linearly.

Terraformer · 2008-01-11 11:39:45

I've been looking for that site! Wikipedia said I had incorrect phyics because I said that gravity increases as you move towards the center of a body of mass that has an iron core.

Wait for it, someone will be along with a wikipedia link to say it can't be done. Although you can't trust wikipedia.

JoshNH4H · 2008-01-11 13:41:33

to say that what can't be done? If you have a dense core, and a not-so-dense mantle, you could do it, but it would be hot down there. Of course the mantle above you does have gravity.

Just to be funny, http://www.en.wikipedia.org/wiki/gravity

Where did you try to post this on wikipedia? You are aware, though, that they don't accept new ideas, right?

Terraformer · 2008-01-11 14:01:24

In an article I made, 'Terraforming Mercury'. They deleted it citing Incorect physics, semi-nonsense etc. Anything I did was deleted lol.

JoshNH4H · 2008-01-11 15:01:48

Just put it on the NM wiki, it would get accessed about as much there.

karov · 2008-01-12 04:24:28

ONLY the mass bellow pulls you down, any mass above the radius between your feet and the center, cancells itself to zero. Draw two concentric circles. Try to figure the vectors of gravity pull for a point onto the inner circle.

Depth
km Layer Density
g/cm³
0–60 Lithosphere (locally varies between 5 and 200 km) —
0–35 ... Crust (locally varies between 5 and 70 km) 2.2–2.9
35–60 ... Uppermost part of mantle 3.4–4.4
35–2890 Mantle 3.4–5.6
100–700 ... Asthenosphere —
2890–5100 Outer core 9.9–12.2
5100–6378 Inner core 12.8–13.1

Radius of the Outer core = ~ 3500km = 3 500 000 m
Volume = 170x10exp18 m3 x density of ~10exp4 kg/m3 =
Mass = 17x10exp23 kg. = 0.28 the earth`s mass
Radius = 0.55 earths radius.

The Outer earth`s core gravity is only slightly smaller than surface one.

qraal · 2008-01-16 05:36:00

Hi All

To see what gravity does, according to a venerable Earth model, deep down check this one out...

http://geophysics.ou.edu/solid_earth/prem.html

...which has, interestingly, multiple high points for the gravity at certain depths. Bottom of the Upper Mantle is one peak (radius = 5701 km), and the other is at the top of the Outer Core (radius = 3480 km). Gravity peaks at 10.6823 m/s^2.

The PERM is from 1981 and a new ERM is in the works, but things haven't changed too much in a bulk sense. The PERM is pretty PERManent for an ostensibly "soon to be superseded" model. A lot of our detailed knowledge has changed and the Mantle/Core boundary is known in much greater detail, but for the purposes of our discussions I think we should refer back to the PERM when discussing Earth's insides.

Terraformer · 2008-01-19 08:36:24

This could affect the terraforming of the moon (the moon has an iron core).

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#1 2008-01-09 15:03:57

Re: Surface gravities and Density dostribution

#2 2008-01-10 00:16:08

Re: Surface gravities and Density dostribution

#3 2008-01-10 05:19:35

Re: Surface gravities and Density dostribution

#4 2008-01-10 13:10:38

Re: Surface gravities and Density dostribution

#5 2008-01-10 23:54:48

Re: Surface gravities and Density dostribution

#6 2008-01-11 00:16:51

Re: Surface gravities and Density dostribution

#7 2008-01-11 11:39:45

Re: Surface gravities and Density dostribution

#8 2008-01-11 13:41:33

Re: Surface gravities and Density dostribution

#9 2008-01-11 14:01:24

Re: Surface gravities and Density dostribution

#10 2008-01-11 15:01:48

Re: Surface gravities and Density dostribution

#11 2008-01-12 04:24:28

Re: Surface gravities and Density dostribution

#12 2008-01-16 05:36:00

Re: Surface gravities and Density dostribution

#13 2008-01-19 08:36:24

Re: Surface gravities and Density dostribution

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