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zompist bboard :: View topic - Effects of higher gravity
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Effects of higher gravity
http://www.incatena.org/viewtopic.php?f=15&t=36835
Page 2 of 2

Author:  Torco [ Sat Jan 22, 2011 3:33 pm ]
Post subject:  Re: Effects of higher gravity


Author:  su_liam [ Sat Jan 22, 2011 4:32 pm ]
Post subject:  Re: Effects of higher gravity


Author:  su_liam [ Sat Jan 22, 2011 4:34 pm ]
Post subject:  Re: Effects of higher gravity


Author:  finlay [ Sat Jan 22, 2011 5:08 pm ]
Post subject:  Re: Effects of higher gravity


Author:  su_liam [ Sat Jan 22, 2011 8:12 pm ]
Post subject:  Re: Effects of higher gravity

Word Press is generally easy and looks good, but every so often it does weird things you can't fix without a PhD in Scary Mindbendy Computer-science.

Maybe I should go back to using Mathematica and posting everything as PDFs...

Author:  Dothraki_physicist [ Tue Jan 25, 2011 1:16 am ]
Post subject:  Re: Effects of higher gravity

Moving out of biological questions now and into the geophysical realm.

I read somewhere that because of earth's gravity, mountains here can never be more than 9 miles high. Does this mean that in 1.5 gees, they can't be higher than 6 miles? I just figured something like that would have a straightforward proportionality.

Author:  su_liam [ Wed Jan 26, 2011 9:31 pm ]
Post subject:  Re: Effects of higher gravity

Let's see. The heat output of radioactive materials should be, assuming the planet has an earthlike composition, proportional to volume(treat that as g^3). The surface area through which that heat must pass is proportional g^2. So the heat throughput per unit area would be proportional to g^(3/2). This is the energy driving mountain-building.

Erosion rates should be proportional to boundary shear stress.

tau-0=rho*g*R*s, where rho is the density of water(essentially a constant), g is gravity, R is the hydraulic radius(lets ignore that for now, I can't see why it would vary with gravity), and s is the slope over which the water is falling.

Thus, erosion is proportional to gravity.

Given all that, mountain heights should be an equilibrium between driving energy and erosion. So I figure mountain height would vary roughly as the square root of gravity.

1.25g -> mountains 1.12 times as high.
1.50g -> mountains 1.22 times as high.

Hmm... Not the result I was expecting.

Author:  bulbaquil [ Thu Jan 27, 2011 10:55 pm ]
Post subject:  Re: Effects of higher gravity

If it helps, assuming no difference in density, gravity will be proportional to the radius:

V = 4/3 * pi * r^3 for a sphere
F = G * m1 * m2 / r^2; dividing by m2 (which we assume to be 1 kg) to get g, we have

g = G * M / r^2 (M=mass of the planet). Letting M = rho * V = rho * 4/3 * pi * r^3, we get
g = G * 4/3 * pi * rho * r

Units check: < N*m^2/kg^2)*(kg/m^3)*(m) = N/kg = m/s^2 > which checks out,

I guess that makes sense then that you could treat surface area as proportional to g^2, then, if the density of your planet's fixed.

Author:  su_liam [ Fri Jan 28, 2011 2:39 am ]
Post subject:  Re: Effects of higher gravity

Yeah, I'm assuming constant density, which is not altogether reasonable given my assumption of similar composition and taking compression effects into account. I'll stick to the constant density assumption unless someone can give me a reasonable formula for compression effects on planetary density.

Did I miss a non-linearity in the relationship between energy and height?

Energy required to lift a mass against gravity:
W=E=fD ... force is weight: w=mg
W=mgD ... I'll assume the mass moved doesn't vary with gravity, so we can neglect that part
W:=gD ... so

h=D:=W/g

From before
W:=g^(3/2) ... so
h:=g^(1/2)

I'm clearly where I started.

I was expecting something like h:=g^-(1/2) as opposed to h:=g^-1, what I got was...
Yuck.
I obviously have something seriously wrong here, but I'm too effing stupid to figure it out.

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