What-if 0067: "Expanding Earth"

What if there was a forum for discussing these?

Moderators: Moderators General, Prelates, Magistrates

jozwa
Posts: 141
Joined: Fri Sep 11, 2009 3:16 pm UTC
Location: Finland

What-if 0067: "Expanding Earth"

Postby jozwa » Tue Oct 15, 2013 2:43 pm UTC

Expanding Earth

Image

These doomsday speculations are my favorites.

kurukkan
Posts: 13
Joined: Tue Nov 20, 2012 2:40 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby kurukkan » Tue Oct 15, 2013 2:45 pm UTC

Sooner or later this will happen to Phobos.
The Roche limit part i mean.

User avatar
cellocgw
Posts: 1956
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby cellocgw » Tue Oct 15, 2013 2:54 pm UTC

Just jumping in to remind everyone that

a) we don't strictly speaking "weigh" N kg.

b) If we're foolish enough to use a balance scale instead of a spring scale, our weight will never increase!
https://app.box.com/witthoftresume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

Barstro
Posts: 103
Joined: Mon Aug 13, 2012 2:34 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Barstro » Tue Oct 15, 2013 3:39 pm UTC

... Mt. Everest would ...would be taller—climbing would be more work.


Why would Mt. Everest be taller? Wouldn't it be the same height relative to the new sea level, since the earth is expanding at a constant rate?

enigmadan
Posts: 1
Joined: Tue Oct 15, 2013 3:39 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby enigmadan » Tue Oct 15, 2013 3:45 pm UTC

Is there a specific reason that citation 12 comes before citation 11?
Am I missing something clever?
Or is it just weird that I noticed it because I love reading every single one of the citations?

User avatar
keithl
Posts: 643
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby keithl » Tue Oct 15, 2013 3:55 pm UTC

Gaping hole in this What-If. The atmosphere would become very hot.

Compress air and it heats up (some other gasses cool). Whatever air there is (thinned, or increasing) gets compressed and heated by the increased gravity. Won't the heat just radiate out into space, returning to radiative equilibrium? Eventually the infrared returns to around 240W/m2, but the temperature lapse rate ( change in temperature with altitude) increases; it gets colder faster as you go up, or hotter faster as you go down.

The infrared temperature of the earth, as viewed from space, is NOT the surface temperature. At many wavelengths, it is the temperature of the CO2 at very high altitudes, where it becomes thin enough to become transparent, and at the rest of the wavelengths, the temperature at the altitudes where water vapor condenses. The latter altitude is at constant temperature, around freezing, but CO2 stays a gas, IR opaque in its absorption bands. The temperature at which the CO2 emission produces equilibrium is roughly constant, but if the height of the atmosphere column underneath increases, or the lapse rate (driven by gravity) increases, then the temperature rise down the column to the surface increases also. Venus has more air, the column is higher, so it is an inferno at the surface.

The "CO2 radiates at high altitude" phenomena is why atmospheric scientists postulate global warming; double the CO2 and the altitude where it becomes effectively transparent rises, increasing as the logarithm of the CO2 density in our well mixed, exponentially-thinning-with-altitude atmosphere. A big part of our current problem is the replacement of forest and grassland with farms and cattle; we ate the feedback control mechanisms, and combustion emissions aren't the only warming threat. Until we return (somehow) to deep-rooted, high biomass/acre plant cover, and restore deserts and scrub to the grasslands they once were, CO2 will continue to increase even if we reduce combustion emissions to zero.

In the expanding earth scenario, the trees and plants fall down and rot. Bacteria and non-flying insects aren't much affected by gravity. They will rapidly turn most of that biomass into CO2, and wildfires will consume the rest. The earth won't turn into Venus right away, nor will all life vanish, but most of the multicellular life will.
Last edited by keithl on Tue Oct 15, 2013 3:56 pm UTC, edited 1 time in total.

User avatar
PolakoVoador
Posts: 1028
Joined: Fri Jun 10, 2011 11:11 pm UTC
Location: Brazil

Re: What-if 0067: "Expanding Earth"

Postby PolakoVoador » Tue Oct 15, 2013 3:55 pm UTC

Hey, we discussed this "huge rocky planet" stuff around here recently, with similar conclusions.

notmartin
Posts: 1
Joined: Tue Oct 15, 2013 3:49 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby notmartin » Tue Oct 15, 2013 3:57 pm UTC

In the essay he says circumference is proportional to radius, which is incorrect. The increase of 2pi units is due to the 2 unit increase of diameter (one on each side).

User avatar
rhomboidal
Posts: 791
Joined: Wed Jun 15, 2011 5:25 pm UTC
Contact:

Re: What-if 0067: "Expanding Earth"

Postby rhomboidal » Tue Oct 15, 2013 3:58 pm UTC

Man, the equatorial region gets EVERYTHING.

Solid_Kalium
Posts: 2
Joined: Wed Mar 20, 2013 5:05 am UTC

Re: What-if 0067: "Expanding Earth"

Postby Solid_Kalium » Tue Oct 15, 2013 4:28 pm UTC

notmartin wrote:In the essay he says circumference is proportional to radius, which is incorrect. The increase of 2pi units is due to the 2 unit increase of diameter (one on each side).

Circumference is proportional to both radius and diameter.

what-if wrote:Circumference is proportional to radius, so if you increase diameter by 1 unit, you increase circumference by 2π units.

The only wrong part is that a 1 unit change in the diameter is actually a 1π unit change in circumference.

Ryeinn
Posts: 5
Joined: Tue Oct 15, 2013 4:38 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Ryeinn » Tue Oct 15, 2013 4:41 pm UTC

I'm surprised no one has yet brought up the conservation of angular momentum. As Earth gets bigger, it must slow down. What would that then do to the atmosphere? I would believe that the inertia of the atmosphere is only loosely coupled with Earth's motion.so would we be beset by huge gale force winds?

rmsgrey
Posts: 3485
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby rmsgrey » Tue Oct 15, 2013 4:51 pm UTC

Barstro wrote:
... Mt. Everest would ...would be taller—climbing would be more work.


Why would Mt. Everest be taller? Wouldn't it be the same height relative to the new sea level, since the earth is expanding at a constant rate?

If you doubled the radius of the Earth, then the new top of Mount Everest would presumably end up twice as far from the center as the old one, and similarly for sea level - so 2(r+h)-2r = 2h - the peak's height above sea level would also double.

Of course, that assumes that the new Earth is similar to the old one in shape - if you expand in a non-uniform way, then other outcomes are possible.

User avatar
cellocgw
Posts: 1956
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby cellocgw » Tue Oct 15, 2013 4:59 pm UTC

notmartin wrote:In the essay he says circumference is proportional to radius, which is incorrect. The increase of 2pi units is due to the 2 unit increase of diameter (one on each side).


Ummmm.... you got any idea at all what the word "proportional" means?
https://app.box.com/witthoftresume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

syrinxsean
Posts: 7
Joined: Tue Nov 27, 2012 2:34 pm UTC

GPS messed up?

Postby syrinxsean » Tue Oct 15, 2013 5:25 pm UTC

So I don't get why GPS would be all messed up right off the bat. Yes, GPS is dependent upon very precise timing. But that's presumably timing for the satellites, not anything on the earth's surface. As GPS works in 3D (reporting altitude in addition to latitude and longitude), including in flight above the earth, presumably an increase of the earth's radius wouldn't affect the GPS satellites until they fell out of orbit due to increased gravity. What am I missing here?

bleus
Posts: 4
Joined: Sat Aug 03, 2013 10:37 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby bleus » Tue Oct 15, 2013 5:49 pm UTC

Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase diameter by 1 unit, you increase circumference by 2π units.


I think he either meant radius...

Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase radius by 1 unit, you increase circumference by 2π units.


...or he meant two units...

Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase diameter by 2 units, you increase circumference by 2π units.


Mixing/mashing them up is slightly confusing...

jotun
Posts: 14
Joined: Tue Oct 15, 2013 6:34 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby jotun » Tue Oct 15, 2013 6:40 pm UTC

Black hole?
When would the Earth eventually become a black hole?
It's hard to answer that, because the premise of the question is that the radius is steadily expanding while the density stays the same—whereas a black hole, the density increases.


So let's say it is expanding while the average density remains the same (some magical force preventing gravitational collapse).

How big WOULD it get before becoming a black hole? At some point the planet's radius would exceed the Schwartzchild radius for its mass, right?

Jragonlord
Posts: 10
Joined: Sat Jul 14, 2012 8:33 am UTC

Re: What-if 0067: "Expanding Earth"

Postby Jragonlord » Tue Oct 15, 2013 6:42 pm UTC

Also missing: If you increase the mass of the Earth, you increase the gravitational pull between the Earth and Sun. We're not adding to the velocity of the Earth in this scenario, so our planet would not have enough velocity to maintain orbit around the Sun, resulting in it gradually spiraling toward our star. Assuming we don't run into Venus or Mercury on the way, we may not get the chance to observe the lovely Roche Limit effect - we'll become a lump of charcoal* in the Sun.
*I am aware the entirety of Earth is not made of carbon, and that the core of the Earth is iron. "A lump of charcoal" just sounds better.

arhalts
Posts: 1
Joined: Tue Oct 15, 2013 8:14 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby arhalts » Tue Oct 15, 2013 8:18 pm UTC

If you weighed 70 kg when the expansion started, you'd weigh 88 kg now.
For shame you magnificent man. for shame. you know why and I am disappointed.

User avatar
eran_rathan
Mostly Wrong
Posts: 1822
Joined: Fri Apr 09, 2010 2:36 pm UTC
Location: in your ceiling, judging you

Re: GPS messed up?

Postby eran_rathan » Tue Oct 15, 2013 8:20 pm UTC

syrinxsean wrote:So I don't get why GPS would be all messed up right off the bat. Yes, GPS is dependent upon very precise timing. But that's presumably timing for the satellites, not anything on the earth's surface. As GPS works in 3D (reporting altitude in addition to latitude and longitude), including in flight above the earth, presumably an increase of the earth's radius wouldn't affect the GPS satellites until they fell out of orbit due to increased gravity. What am I missing here?



Because GPS works by measuring distance to multiple satellites concurrently, and having precise ephemerides for each SV, thereby calculating position by solving the n-dimensional matrix for distance of each satellite. If the ephemerides are borked, so is GPS.
"Does this smell like chloroform to you?"
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ

jotun
Posts: 14
Joined: Tue Oct 15, 2013 6:34 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby jotun » Tue Oct 15, 2013 8:42 pm UTC

jotun wrote:
Black hole?
When would the Earth eventually become a black hole?
It's hard to answer that, because the premise of the question is that the radius is steadily expanding while the density stays the same—whereas a black hole, the density increases.


So let's say it is expanding while the average density remains the same (some magical force preventing gravitational collapse).

How big WOULD it get before becoming a black hole? At some point the planet's radius would exceed the Schwartzchild radius for its mass, right?


Alright, I think I managed to answer my own question, assuming my math was right

After about 541858 years, the Earth would grow to a radius of 1.71x1011m, or 1.143 AU. Given an average density of 5515 kg/m3, that would give it a mass of 1.155x1038kg, or 58 million solar masses. At this point it would be within its own Schwarzchild radius as a supermassive black hole.

Also at this point, an extra cm of radius adds 2.027x1025kg of mass - an extra solar mass every 1.136 days and accelerating
Last edited by jotun on Tue Oct 15, 2013 8:53 pm UTC, edited 1 time in total.

Nicias
Posts: 162
Joined: Tue Aug 13, 2013 4:22 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Nicias » Tue Oct 15, 2013 8:43 pm UTC

It's worse than that. The GPS signals also adjust for GR & SR time dilation effects. As the mass of the earth changed these would change too.

JeffR23
Posts: 14
Joined: Tue Jul 30, 2013 10:16 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby JeffR23 » Tue Oct 15, 2013 9:16 pm UTC

What kind of mayhem should we expect from the Solar System as the Earth keeps growing? (Which planets are likely to be captured away from the sun, and which ones expelled entirely? Does the asteroid belt relocate, and is that bad news for any of the planets in the way?)

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26547
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0067: "Expanding Earth"

Postby gmalivuk » Tue Oct 15, 2013 9:47 pm UTC

kurukkan wrote:Sooner or later this will happen to Phobos.
The Roche limit part i mean.

Isn't the Roche limit for Mars within the planet itself?

Jragonlord wrote:Also missing: If you increase the mass of the Earth, you increase the gravitational pull between the Earth and Sun. We're not adding to the velocity of the Earth in this scenario, so our planet would not have enough velocity to maintain orbit around the Sun, resulting in it gradually spiraling toward our star. Assuming we don't run into Venus or Mercury on the way, we may not get the chance to observe the lovely Roche Limit effect - we'll become a lump of charcoal* in the Sun.
*I am aware the entirety of Earth is not made of carbon, and that the core of the Earth is iron. "A lump of charcoal" just sounds better.
If the new mass is moving at the same velocity as Earth already is moving, Earth's orbit wouldn't change significantly until it becomes a significant fraction of the mass of the Sun.

Increasing a central body's mass has a much greater orbital impact than increasing the mass of a relatively much smaller orbiting body.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
keithl
Posts: 643
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby keithl » Tue Oct 15, 2013 10:01 pm UTC

Ryeinn wrote:I'm surprised no one has yet brought up the conservation of angular momentum. As Earth gets bigger, it must slow down. What would that then do to the atmosphere? I would believe that the inertia of the atmosphere is only loosely coupled with Earth's motion.so would we be beset by huge gale force winds?
Interesting thought ... but the atmosphere is not that uncoupled.

The angular velocity of the earth (sidereal, relative to the stars) is (2π/86164 sec) ≅ 7.292e-5 radians/sec . The rotation velocity at the equator (6378km radius) is 465 m/s . If the angular velocity stayed the same, and the radius increased by 864 meters per day at the equator, the surface would speed up by 0.063 meters per second over the course of a day. a gale force wind is 17 meters per second, 270 times faster. We can expect air and surface to couple with a time scale of a week or less, about as fast as hurricanes dissipate, so expect a gentle breeze but not a storm.

If angular momentum is conserved, the angular inertia of a constant density sphere goes up as the 5th power of the radius. So the angular velocity is proportional to the inverse of R5, and if the radius is increasing at 150ppm per day, the angular velocity is decreasing at around 750ppm per day. With the radius increase, the surface velocity goes down at 0.25m/s/day . A bit more of a breeze!

But think through the implications. If the extra material is being added (somewhere!) without angular velocity, it is colliding with the moving earth, as fast as 465 m/s near the equatorial surface. We are talking a LOT of mass per day, colliding at very high speeds, vastly more energy than is contained in a drifting continental plate. The continents will probably shatter, then melt. That would be vastly friskier than anything a mere 100 tons of air per square meter can do.

So, we can assume that whatever magic process violates conservation of mass, is also violating the conservation of energy and momentum and a whole bunch of other stuff. The Flying Spagetti Monster doesn't do such things to us because the accounting is too much work.

Edit: M = (4/3)πρR3 for a sphere with constant density ρ, so I = (2/5)MR2 = (2/5)(4/3)πρR3R2 = (8/15)πρR5 . When I was in high school, I tended to lose points on tests for not showing my work, or lose points for "sarcasm" for showing way too much of it. I found it difficult (and still do) gauging the knowledge (or conversely, the ignorance) of "experts".
Last edited by keithl on Wed Oct 16, 2013 4:45 pm UTC, edited 1 time in total.

Ryeinn
Posts: 5
Joined: Tue Oct 15, 2013 4:38 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Ryeinn » Tue Oct 15, 2013 10:03 pm UTC

Jragonlord wrote:Also missing: If you increase the mass of the Earth, you increase the gravitational pull between the Earth and Sun. We're not adding to the velocity of the Earth in this scenario, so our planet would not have enough velocity to maintain orbit around the Sun, resulting in it gradually spiraling toward our star.


Someone correct me if I'm off here, being a simple High School Physics teacher, but I'm pretty sure that, at least for point masses, orbital speed requirements don't depend on the mass of the object orbiting. In simplified circular orbits, centripetal force can be set equal to the gravitational forces and the mass of the orbiting object cancels from the equation.

The only things I can imagine leading to this being off is the difference between point and extant masses, the non-circularity of Earth's orbit, or something where GR contradicts Newton. I have a feeling that that my assumptions work, but personally I would love to be proved wrong, gives me something to talk about when we get to orbits in my classes.

Mikeski
Posts: 1045
Joined: Sun Jan 13, 2008 7:24 am UTC
Location: Minnesota, USA

Re: What-if 0067: "Expanding Earth"

Postby Mikeski » Tue Oct 15, 2013 10:06 pm UTC

gmalivuk wrote:
kurukkan wrote:Sooner or later this will happen to Phobos.
The Roche limit part i mean.

Isn't the Roche limit for Mars within the planet itself?

No, although Phobos is already within its Roche limit. Roche is an approximation that only uses density and size, nothing about material strength.

(radius of Mars 3390km, Roche Limit of Mars-Phobos 10800km, orbit of Phobos 9380km)

Ryeinn
Posts: 5
Joined: Tue Oct 15, 2013 4:38 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Ryeinn » Tue Oct 15, 2013 10:17 pm UTC

keithl wrote:Interesting thought ... but the atmosphere is not that uncoupled.


Thanks! That was something I was curious about. I like the way of looking at hurricanes being evidence of coupling. Neat.

keithl wrote:If angular momentum is conserved, the angular inertia of a constant density sphere goes up as the 5th power of the radius. So the angular velocity is proportional to the inverse of R5, and if the radius is increasing at 150ppm per day, the angular velocity is decreasing at around 750ppm per day. With the radius increase, the surface velocity goes down at 0.25m/s/day . A bit more of a breeze!


Now, this confuses me. I've always been teaching to my high school students the Moment of (Rotational) Inertia for a sphere is 2/5*MR2. Where's the 5th power come in? Am I leading them astray or is there some complication I'm skipping over unawares?

Also, as I play with L=(moment of inertia)*(angular velocity)...I get a differential equation for angular velocity.

keithl wrote:But think through the implications. If the extra material is being added (somewhere!) without angular velocity, it is colliding with the moving earth, as fast as 465 m/s near the equatorial surface. We are talking a LOT of mass per day, colliding at very high speeds, vastly more energy than is contained in a drifting continental plate. The continents will probably shatter, then melt. That would be vastly friskier than anything a mere 100 tons of air per square meter can do.


This is truly frightening. Maybe it is coming up from the center and pushing out.

brenok
Needs Directions
Posts: 507
Joined: Mon Oct 17, 2011 5:35 pm UTC
Location: Brazil

Re: What-if 0067: "Expanding Earth"

Postby brenok » Tue Oct 15, 2013 10:23 pm UTC

Ryeinn wrote:
keithl wrote:If angular momentum is conserved, the angular inertia of a constant density sphere goes up as the 5th power of the radius. So the angular velocity is proportional to the inverse of R5, and if the radius is increasing at 150ppm per day, the angular velocity is decreasing at around 750ppm per day. With the radius increase, the surface velocity goes down at 0.25m/s/day . A bit more of a breeze!

Now, this confuses me. I've always been teaching to my high school students the Moment of (Rotational) Inertia for a sphere is 2/5*MR2. Where's the 5th power come in? Am I leading them astray or is there some complication I'm skipping over unawares?

Mass is proportional to volume, which is proportional to R3

Ryeinn
Posts: 5
Joined: Tue Oct 15, 2013 4:38 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Ryeinn » Tue Oct 15, 2013 10:31 pm UTC

brenok wrote:
Ryeinn wrote:
keithl wrote:If angular momentum is conserved, the angular inertia of a constant density sphere goes up as the 5th power of the radius. So the angular velocity is proportional to the inverse of R5, and if the radius is increasing at 150ppm per day, the angular velocity is decreasing at around 750ppm per day. With the radius increase, the surface velocity goes down at 0.25m/s/day . A bit more of a breeze!

Now, this confuses me. I've always been teaching to my high school students the Moment of (Rotational) Inertia for a sphere is 2/5*MR2. Where's the 5th power come in? Am I leading them astray or is there some complication I'm skipping over unawares?

Mass is proportional to volume, which is proportional to R3


Well now I feel dumb. Should have made that jump. Thanks!

rmsgrey
Posts: 3485
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby rmsgrey » Tue Oct 15, 2013 10:34 pm UTC

Ryeinn wrote:
Jragonlord wrote:Also missing: If you increase the mass of the Earth, you increase the gravitational pull between the Earth and Sun. We're not adding to the velocity of the Earth in this scenario, so our planet would not have enough velocity to maintain orbit around the Sun, resulting in it gradually spiraling toward our star.


Someone correct me if I'm off here, being a simple High School Physics teacher, but I'm pretty sure that, at least for point masses, orbital speed requirements don't depend on the mass of the object orbiting. In simplified circular orbits, centripetal force can be set equal to the gravitational forces and the mass of the orbiting object cancels from the equation.

The only things I can imagine leading to this being off is the difference between point and extant masses, the non-circularity of Earth's orbit, or something where GR contradicts Newton. I have a feeling that that my assumptions work, but personally I would love to be proved wrong, gives me something to talk about when we get to orbits in my classes.


Newton and point masses will do just fine - consider what happens as the "orbiting" mass approaches the same magnitude as the "orbited" mass - if the "central" mass stayed still, the orbit would be unchanged, but you can't ignore the motion of the central mass once the two are sufficiently close in mass...

Mikeski
Posts: 1045
Joined: Sun Jan 13, 2008 7:24 am UTC
Location: Minnesota, USA

Re: What-if 0067: "Expanding Earth"

Postby Mikeski » Tue Oct 15, 2013 10:34 pm UTC

Ryeinn wrote:
Jragonlord wrote:Also missing: If you increase the mass of the Earth, you increase the gravitational pull between the Earth and Sun. We're not adding to the velocity of the Earth in this scenario, so our planet would not have enough velocity to maintain orbit around the Sun, resulting in it gradually spiraling toward our star.


Someone correct me if I'm off here, being a simple High School Physics teacher, but I'm pretty sure that, at least for point masses, orbital speed requirements don't depend on the mass of the object orbiting. In simplified circular orbits, centripetal force can be set equal to the gravitational forces and the mass of the orbiting object cancels from the equation.

The only things I can imagine leading to this being off is the difference between point and extant masses, the non-circularity of Earth's orbit, or something where GR contradicts Newton. I have a feeling that that my assumptions work, but personally I would love to be proved wrong, gives me something to talk about when we get to orbits in my classes.

You're correct for orbits where the orbiting body is much less massive.

You're also missing that the sun isn't tacked down in the center of the solar system; even it is in "orbit" around the solar system's center of mass, and that "center" keeps moving. Making the Earth much much heavier will affect the barycenter quite a bit... when we start approaching the Sun's mass, we'll orbit each other (that is, orbit our common barycenter) like a binary star.

If you want something to share with your high school class, you can tell them that when they were in middle school, we were actually orbiting a point outside the sun...

User avatar
Himself
Posts: 156
Joined: Sat Aug 27, 2011 4:17 am UTC

Re: What-if 0067: "Expanding Earth"

Postby Himself » Wed Oct 16, 2013 1:00 am UTC

Ryeinn wrote:I'm surprised no one has yet brought up the conservation of angular momentum. As Earth gets bigger, it must slow down. What would that then do to the atmosphere? I would believe that the inertia of the atmosphere is only loosely coupled with Earth's motion.so would we be beset by huge gale force winds?

The atmosphere is very much affected by drag. So, extreme winds would likely be an issue if earth's rotation slowed suddenly, but not in this scenario where the the rate of expansion is comparable to the movement of a glacier. The winds in the main wind belts of Earth as well as the rotation of large-scale weather systems depend on Earth's rotation. So we'd actually see a decrease in winds as the prevailing winds slow and cyclones fail to organize.
"Looking me am a civilization person"
-Ratio Tile

User avatar
edo
Posts: 432
Joined: Thu Mar 28, 2013 7:05 pm UTC
Location: ~TrApPeD iN mY PhOnE~

Re: What-if 0067: "Expanding Earth"

Postby edo » Wed Oct 16, 2013 2:16 am UTC

Mikeski wrote:If you want something to share with your high school class, you can tell them that when they were in middle school, we were actually orbiting a point outside the sun...
Execpt this year that point appears to be pretty deep in the sun...

Randall, in the title text of the last image wrote:If you liked it then you should have moved a mass inside its Roche limit.

Am I the only one to get this?
Spoiler:
"move a mass inside its Roche limit." = "Put a ring on it"
Co-proprietor of a Mome and Pope Shope

Mikeski
Posts: 1045
Joined: Sun Jan 13, 2008 7:24 am UTC
Location: Minnesota, USA

Re: What-if 0067: "Expanding Earth"

Postby Mikeski » Wed Oct 16, 2013 3:22 am UTC

edo wrote:
Mikeski wrote:If you want something to share with your high school class, you can tell them that when they were in middle school, we were actually orbiting a point outside the sun...
Execpt this year that point appears to be pretty deep in the sun...

"high school class" = now.
"when they were in middle school" = 3 or so years ago.

(Next year, he'll have to say "when they were in grade school", I guess.)

User avatar
runetrantor
Posts: 12
Joined: Tue Jul 09, 2013 10:03 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby runetrantor » Wed Oct 16, 2013 5:52 am UTC

Does anyone know at what point would the buildings collapse due to the gravity? I kind of need to know, I had this story about a weapon that increased the planet's gravity tenfold for a few minutes, and I expected it to kill all humans in the affected area, AND collapse towers too.

How much do I have to up that thing? (Yes, I am aware this bomb is weird, and lacking much real science behind it)

shockburner
Posts: 2
Joined: Fri Nov 30, 2012 4:01 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby shockburner » Wed Oct 16, 2013 5:53 am UTC

jotun wrote:
jotun wrote:
Black hole?
When would the Earth eventually become a black hole?
It's hard to answer that, because the premise of the question is that the radius is steadily expanding while the density stays the same—whereas a black hole, the density increases.


So let's say it is expanding while the average density remains the same (some magical force preventing gravitational collapse).

How big WOULD it get before becoming a black hole? At some point the planet's radius would exceed the Schwartzchild radius for its mass, right?


Alright, I think I managed to answer my own question, assuming my math was right

After about 541858 years, the Earth would grow to a radius of 1.71x1011m, or 1.143 AU. Given an average density of 5515 kg/m3, that would give it a mass of 1.155x1038kg, or 58 million solar masses. At this point it would be within its own Schwarzchild radius as a supermassive black hole.

Also at this point, an extra cm of radius adds 2.027x1025kg of mass - an extra solar mass every 1.136 days and accelerating


Shoot, you totally beat me to this. I did this independently before seeing it here and got the same numbers.

What I have to add is that this mass is about 13 times that of Sagittarius A* (the super massive black hole at the center of our galaxy).
Thus the Earth would become the new center of the Milky Way!

jotun
Posts: 14
Joined: Tue Oct 15, 2013 6:34 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby jotun » Wed Oct 16, 2013 8:49 am UTC

shockburner wrote:
jotun wrote:After about 541858 years, the Earth would grow to a radius of 1.71x1011m, or 1.143 AU. Given an average density of 5515 kg/m3, that would give it a mass of 1.155x1038kg, or 58 million solar masses. At this point it would be within its own Schwarzchild radius as a supermassive black hole.

Also at this point, an extra cm of radius adds 2.027x1025kg of mass - an extra solar mass every 1.136 days and accelerating


Shoot, you totally beat me to this. I did this independently before seeing it here and got the same numbers.

What I have to add is that this mass is about 13 times that of Sagittarius A* (the super massive black hole at the center of our galaxy).
Thus the Earth would become the new center of the Milky Way!


That mass is still about a factor of 105 below the total mass of the galaxy. It would probably cause a lot of havoc locally, but I don't imagine it would have much immediate effect on the galaxy as a whole - the galactic core would still dwarf it in mass. Of course, the Earth's expansion adds mass at an accelerating rate, so in about 15 million years its mass would match the mass of the rest of the galaxy. It would take ~52 billion years to match the mass of the rest of the universe (1053kg)

Barstro
Posts: 103
Joined: Mon Aug 13, 2012 2:34 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby Barstro » Wed Oct 16, 2013 12:03 pm UTC

rmsgrey wrote:
Barstro wrote:
... Mt. Everest would ...would be taller—climbing would be more work.


Why would Mt. Everest be taller? Wouldn't it be the same height relative to the new sea level, since the earth is expanding at a constant rate?

If you doubled the radius of the Earth, then the new top of Mount Everest would presumably end up twice as far from the center as the old one, and similarly for sea level - so 2(r+h)-2r = 2h - the peak's height above sea level would also double.

Of course, that assumes that the new Earth is similar to the old one in shape - if you expand in a non-uniform way, then other outcomes are possible.


Ah, you and Randall read "mean radius of the world expanded by 1cm every second" differently than I. I take it to mean that we add 1/2cm of homogeneous soil over every aspect of the earth every second. You take it as increasing a certain percentage that averages the same amount, with valleys getting less and mountains getting more.

User avatar
eran_rathan
Mostly Wrong
Posts: 1822
Joined: Fri Apr 09, 2010 2:36 pm UTC
Location: in your ceiling, judging you

Re: What-if 0067: "Expanding Earth"

Postby eran_rathan » Wed Oct 16, 2013 12:21 pm UTC

Nicias wrote:It's worse than that. The GPS signals also adjust for GR & SR time dilation effects. As the mass of the earth changed these would change too.



I know that (I'm a surveyor :mrgreen: ). The differences in the ephemerides, however, would overwhelm the SR and GR errors by an order of magnitude within a few hours.

Seriously. The SR and GR errors work out to about 5 milliseconds a day, which adds approx. 1-2 m error. The ephemeris being off would add 10-30 m errors in the same span of time. Look at the early years of GPS when the military would turn off the L2C band so that civilians couldn't get precise locations without multiple receivers and long occupations.
"Does this smell like chloroform to you?"
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ

rmsgrey
Posts: 3485
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: What-if 0067: "Expanding Earth"

Postby rmsgrey » Wed Oct 16, 2013 2:49 pm UTC

Barstro wrote:
rmsgrey wrote:
Barstro wrote:
... Mt. Everest would ...would be taller—climbing would be more work.


Why would Mt. Everest be taller? Wouldn't it be the same height relative to the new sea level, since the earth is expanding at a constant rate?

If you doubled the radius of the Earth, then the new top of Mount Everest would presumably end up twice as far from the center as the old one, and similarly for sea level - so 2(r+h)-2r = 2h - the peak's height above sea level would also double.

Of course, that assumes that the new Earth is similar to the old one in shape - if you expand in a non-uniform way, then other outcomes are possible.


Ah, you and Randall read "mean radius of the world expanded by 1cm every second" differently than I. I take it to mean that we add 1/2cm of homogeneous soil over every aspect of the earth every second. You take it as increasing a certain percentage that averages the same amount, with valleys getting less and mountains getting more.


From the article:

let's imagine all the matter in the Earth, from the crust to the core, starts expanding uniformly.


For 1cm/s, that's very roughly 1 atom added to a chunk of material for every 100 moles of that atom there were before, every second - so a kilogram of coal would get about one extra carbon atom per second - technically, this is compounded, but it'll take a while for that to make a difference...

Anyway, yeah, the top of Everest has more matter under it than any other bit of the Earth's surface, so it rises marginally faster (roughly 0.1% faster) under this model - growing roughly a millimeter taller above sea-level for every meter sea-level rises.


Return to “What If?”

Who is online

Users browsing this forum: No registered users and 6 guests