| From: anthony johnstone | 23/07/00
22:17:58 |
| Subject: gravity | post id:
103728 |
| Why are all planetary bodies
spherical, if in fact they are? | |
| From: DV (Avatar) | 23/07/00
22:59:44 |
| Subject: re: gravity | post id:
103739 |
| Spherical planets: Speaking crudely, gravity makes mass want to get together. If I have two pieces of mass, they will be attracted to each other by gravity. They will be able to get to a low potential energy state by getting closer together. Suppose we have a non-spherical planet: say, a cubic planet. Over time, bits of the planet will be broken off, by impact events, or regular erosion. Furthermore, even solid materials have a tendency to change shape over time, if a force is applied. Now, for a cube, if I break a piece off a vertex (corner), it will be able to be closer to the centre of mass by being placed at the centre of a face rather than at a vertex. So, having been broken off, it will tend to roll down towards the centre of a face. Basically, any piece that is further than necessary from the centre will tend to be relocated (by impact, folding, erosion, mass wasting etc) to a place that is nearer to the centre of mass, so that the total potential energy is as low as possible. So, even if you started with a large planet that was significantly non-spherical, over time it would tend towards a shape where everything was packed as closely as possible towards the centre (ie a sphere). Complications: the rotation of a planet will change the potential energy situation, so that the minimum energy shape will be an oblate (squashed) spheroid (as the earth is). Furthermore, gravity is not the only force at play. Electrostatic forces tend to hold solid objects together against the force of gravity, so we can have local variations from a perfect spheroid (mountains, valleys etc.) Speaking very generally, the smaller an object, the more likely it is that forces other than gravity will appear dominant. For a moon or asteroid about 1000km across, the irregularities tend to be striking. As you start looking at moons and asteroids smaller than about 500km across, the shapes start tending to be very irregular (again, speaking very generally). Satellites and asteroids about 50km tend to be any old shape they want. | |
| From: Cam ® | 23/07/00
23:08:38 |
| Subject: re: gravity | post id:
103740 |
| Excluding impact craters (they
never happened, this is hypothetical), would there be a planet somewhere
that has a flat surface? One that, of course, conforms to the oblate
spheroid (hehe I love New Words) shape that our own planet does. I imagine
such a place would not have experienced any volcanic activity. Does my
planet exist, or is its existence indeed
possible? :o) | |
| From: Chris W (Avatar) | 23/07/00
23:15:16 |
| Subject: re: gravity | post id:
103741 |
If the object is small enough
then gravitational forces are insufficient to force the near spherical
shape. The asteroid Eros is a prime example. | |
| From: DV (Avatar) | 23/07/00
23:26:11 |
| Subject: re: gravity | post id:
103742 |
| Okay, well, how flat do you want
it? The Jovian planets (Jupiter, Saturn, Uranus and Neptune) have quite flat "surfaces", because the only surface we know about is the top layer of translucent cloud. Europa has a fairly flat surface (ie the amount of variation in topography is relatively low) due to the icy surface (which may have solidified relatively recently, on a geological time scale). (On a small scale, however, it is quite chunky.) There are a few other icy bodies out there that are probably similar flat. However, if you are talking about a planet with a solid, rocky surface that is smooth/flat, I don't think so. Any solid object will have copped meteor impacts over time. I guess the only way that could work would be if the planet was heated so much, so suddenly that the crust melted. This would have to be followed by a period of cooling, so you might get a fairly flat surface of andesite or basalt type material. (This would have to have happened after the early period of intense bombardment.) It would also need to be volcanically and tectonically dead. I don't think any body in the solar system fits this description, but there are rocky-surface bodies (including our moon) that have some areas here and there that are kind of flat. Ish. These will mostly be volcanic flood planes, (or in the case of Mars, sedimented basins of erstwhile seas, ???) | |
| From: Cam ® | 23/07/00
23:29:39 |
| Subject: re: gravity | post id:
103743 |
| Ahh, those erstwhile seas. They
will lap the shores of Ares once more, mark my words. I was imagining an object that might not exist, DV, but WRT the 'sudden heating'; could this happen? What mechanism would be at play here? :o) | |
| From: DV (Avatar) | 23/07/00
23:48:10 |
| Subject: re: gravity | post id:
103746 |
| As I say, it would need to happen
after the early intense impact phase, which makes me think that it is
geologically unlikely that the planet would suddenly heat up so much
because of internal activity. Hmmm.... Unless for some whacky reason the planet was not properly solidified until after the period of intense bombardment... There should be a variety of tomfoolery in the early period, before things settle down. A near collision between two large bodies sends one of them out of the stellar system (still too hot to have a thick solid crust). The next part would be the dodgy part: it would need to be "caught" by a mature system, where the bombardment rate had eased off (like ours). The nature of celestial mechanics means you can't just whirl a planet into a solar system and expect it to stick: if you do that, it will just come whirling straight out again on a hyperbolic path. For a planet to be captured by a star, you would need an unlikely event involving the planet, the star and at least one other body. Not impossible, but you'd call it a "freak occurence". Since this planet wasn't formed like the rest of the planets in this solar system, there would be no reason to expect its orbit to be on the same plane as the other planets. A related idea: it could have been a far outer solar system body that formed in the absense of intense bombardment. Later on, a similarly unlikely sequence of events could bring it closer in. (cf Pluto being "captured" into a solar orbit by Neptune.) Completely different idea: the sun goes through a number of fluctuations in its output, on a scale of billions of years. The mature star goes large (to use Donald Trump's phrase), singes the planet, then enters a quiescent period, leaving a fairly smooth planet. (Then again, a severe cooking might trigger shallow volcanism...can't tell you which effect would dominate.) Probably some more outlandish scenarios I haven't mentioned. | |
| From: Martin B | 24/07/00
11:04:23 |
| Subject: re: gravity | post id:
103855 |
| Hi Darth I never replied to your riposte to my modelling exercise in which I suggested that gravity would not be able to make a solid planet of modest proportions spherical unless that planet had at some stage been able to respond in a fluid manner, or had some atmospheric erosion happening. You responded that the Moon has indeed changed its shape as its rotational period has changed. What I never responded was that that case involves essentially an elastic deformation from one ellipsoid into another. I was referring to a situation where a non-ellipsoid shape was changed into an ellipsoid. This would involve a more catastrophic yield limit, and hence require higher gravitational forces. In that time I have read some sources that suggest that internal melting is a crucial stage in the formation of a terrestrial planet, and some which suggest that gravity is sufficient to spherise a planet regardless of melting as you suggest. Any further thoughts or references on this issue? | |
| From: DV (Avatar) | 24/07/00
22:19:49 |
| Subject: re: gravity | post id:
104265 |
| Okay, good call, Martin
B. Obviously, in would heavily depend on the nature of the material of which the object was composed. The earth's mantle, which is technically solid, is quite plastic. If we had a cube of that... I think the most popular theory at the moment for moon formation is the idea that protoearth collided with another large body. A chunk was swiped out of the protoearth. This chunk became the moon. After this incident, one would have to guess that the earth would have been significantly nonspherical, but wound up being a spheroid in the fullness of time. I guess I would really need to sit down and do the engineering. If we had a planet made of the same stuff as the earth, but cubic (same volume), we would basically have a cube about 10 000 km on a side. This is basically the same as a sphere with 5000km radius, on which are placed eight pyramids with trianguloid base (and mutually perpendicular edges) with and a height of 3660km. The crust would be too thin to provide much structural support, so we are basically talking about mantle mountains. Have I done the math? No. However, my "gut feeling" is that there is no way these semiplastic mantle mountains are going to be able to support their own weight. On earth, when a mountain range is pushed up (by tectonic collision for instance), the extra potential causes the continental mass to sink somewhat. The idea of mountains 3660km high holding themselves up just doesn't seem right. | |
| From: Martin | 25/07/00
10:23:38 |
| Subject: re: gravity | post id:
104375 |
| Hi DV Thanks for replying. I agree with your gut feeling. I am just trying to clarify in my own mind what it is that 'gives' and it seems to me that it is the fluid or semi-fluid parts of the planet that allow a deformation into spherical shape. | |
| From: DV (Avatar) | 25/07/00
12:57:57 |
| Subject: re: gravity | post id:
104508 |
| I did a "back of the envelope"
calculation. The shear stresses experienced at the base of these
"pyramids" would be in the tens of
gigapascals. Crunch! | |