PDA

View Full Version : The Football Planet



Roger E. Moore
2019-Jan-31, 01:19 PM
I anticipate that this discovery will make a good bit of news given the timing of the Super Bowl. However, finding a planet shaped like a gigantic iron football is pretty wild no matter what. Reminds me of Larry Niven's planet Jinx. Very relevant to studies of Mercury.


https://arxiv.org/abs/1901.10666

Tidally-Distorted, Iron-Enhanced Exoplanets Closely Orbiting Their Stars

Ellen M. Price, Leslie A. Rogers (Submitted on 30 Jan 2019)

The origin of Mercury's enhanced iron content is a matter of ongoing debate. The characterization of rocky exoplanets promises to provide new, independent insights on this topic by constraining the occurrence rate and physical and orbital properties of iron-enhanced planets orbiting distant stars. The transiting planet candidate KOI 1843.03 (0.6 Earth radius, 4.245 hour orbital period, 0.46 solar mass host star) has the shortest orbital period of any planet yet discovered. Here we show, using the first three-dimensional interior structure simulations of ultra-short-period tidally distorted rocky exoplanets, that KOI 1843.03 may be shaped like an American football, elongated along the planet-star axis with an aspect ratio of up to 1.79. Furthermore, for KOI 1843.03 to have avoided tidal disruption (wherein the planet is pulled apart by the tidal gravity of its host star) on such a close-in orbit, KOI 1843.03 must be as iron-rich as Mercury (about 66% by mass iron compared to Mercury's 70% by mass iron). Of the ultra-short-period (P < 1 day) planets with physically-meaningful constraints on their densities characterized to date, just under half (4 out of 9) are iron-enhanced. As more are discovered, we will better understand the origin of the planet Mercury in our Solar System.

Roger E. Moore
2019-Jan-31, 01:31 PM
Then again, we already have Haumea, shaped more like an Australian-rules football ball, or a rugby ball.

George
2019-Jan-31, 06:38 PM
A near-realistic artistic depiction would be interesting. Would basins and older craters look stretched? If it is spiraling along its major axis, then an American football should be favored. ;)

Roger E. Moore
2019-Jan-31, 06:46 PM
A near-realistic artistic depiction would be interesting. Would basins and older craters look stretched? If it is spiraling along its major axis, then an American football should be favored. ;)

I would guess most of the visible impact damage would be recent, overlapping the earliest (stretched-looking) craters and basins, so impacts would look circular.

The American football ball has points on the end which I am not sure would work. Internal gravity might pull the points inward and round them.

I was kind of going with a Haumea / rugby ball shape (see image, with Wikipedia image of Haumea and a rugby ball). I prefer that sort of "ellipsoid", but I'm not versed in astrophysics. :)

Roger E. Moore
2019-Jan-31, 06:57 PM
D'OH! Forgot the illustration of KOI 1843.03 in the article! It IS a rugby ball!

Given the article's estimation of this planet being .32 to 1.06 Earth's mass, and .61 times Earth's diameter, that is one darn hefty rugby ball.

.

George
2019-Jan-31, 08:15 PM
D'OH! Forgot the illustration of KOI 1843.03 in the article! It IS a rugby ball!

Given the article's estimation of this planet being .32 to 1.06 Earth's mass, and .61 times Earth's diameter, that is one darn hefty rugby ball.

.
The aspect ratio of ~ 1.79 (max) actually favors the American football (~ 1.65) compared to the rugby ball of ~ 1.5, per my napkin calculations. My curiosity is more about possible surface stretch marks from tidal stress but that wouldn't be easy to determine unless the chronological history was known, I suppose.

Roger E. Moore
2019-Jan-31, 08:17 PM
The aspect ratio of ~ 1.79 (max) actually favors the American football (~ 1.65) compared to the rugby ball of ~ 1.5, per my napkin calculations. My curiosity is more about possible surface stretch marks from tidal stress but that wouldn't be easy to determine unless the chronological history was known, I suppose.

I always yield in favor of the better math. :)

Roger E. Moore
2019-Jan-31, 08:42 PM
Had a side thought that those ultra-short-period planets suspected of disintegrating must not have a high percentage of iron or other ductile metal. If they are primarily rocky or have heavy rocky mantles/crusts, it would explain the disintegration.

Conversely, whatever crust this Football Planet had could have well been pulled away by now, perhaps crashing back into it to form craters.

KaiYeves
2019-Feb-01, 01:01 AM
If you’re willing to be sufficiently loose about sphere-osity, I guess many planets are fairly close to the shape of a football/soccer ball.

DaveC426913
2019-Feb-01, 02:10 AM
I would guess most of the visible impact damage would be recent, overlapping the earliest (stretched-looking) craters and basins, so impacts would look circular.

I doubt craters would be stretched. It implies the whole asteroid stretched uniformly like putty.

More likely, I'd think, is that the body is loosely held together, and any small debris would be flung off the equator to settle near the poles where the centrifugal velocity is lower. i.e. the asteroid is not so much being deformed as being redistributed, pebble-by-pebble.

grapes
2019-Feb-01, 04:02 PM
More likely, I'd think, is that the body is loosely held together, and any small debris would be flung off the equator to settle near the poles where the centrifugal velocity is lower. i.e. the asteroid is not so much being deformed as being redistributed, pebble-by-pebble.
Centrifugal velocity? Is the center the center of the star? Centrifugal velocity would be smallest at the "far" end of the planet, no?

George
2019-Feb-01, 06:49 PM
I doubt craters would be stretched. It implies the whole asteroid stretched uniformly like putty.

More likely, I'd think, is that the body is loosely held together, and any small debris would be flung off the equator to settle near the poles where the centrifugal velocity is lower. i.e. the asteroid is not so much being deformed as being redistributed, pebble-by-pebble. Is that likely given that it's about the size of Mars and more like Mercury in heavier metal composition. It looks to be close to their tweaked Roche limit for such objects. I wonder if such a large aspect ratio wouldn't be indicative of where such objects are to their Roche limit?

DaveC426913
2019-Feb-02, 11:56 PM
Centrifugal velocity? Is the center the center of the star? Centrifugal velocity would be smallest at the "far" end of the planet, no?
OK, that was sloppy terminology.

But yes, escape velocity is largest at the poles, where it is not assisted by the body's rotation. So particles and bodies ejected from the equator will tend to accumulate at the poles.

Not sure what "star" has to do with it.

agingjb
2019-Feb-03, 08:13 AM
I understand how a rapidly spinning body could be an oblate spheroid, but how does a substantial prolate spheroid form? The tidal stress must be enormous.

DaveC426913
2019-Feb-03, 05:16 PM
I understand how a rapidly spinning body could be an oblate spheroid, but how does a substantial prolate spheroid form? The tidal stress must be enormous.

By not assuming the shape is entirely defined by its spin and not assuming it's distorting elastically.

DaveC426913
2019-Feb-03, 05:29 PM
This is what I'm suggesting.

Roger E. Moore
2019-Feb-04, 03:37 PM
As I get it, the football planet has one end pointing at its sun, always, and the other end always pointing away. The long axis goes through the star. The far end is always in shadow.

Would torque prevent the planet from rotating around its long axis?

DaveC426913
2019-Feb-05, 12:17 AM
As I get it, the football planet has one end pointing at its sun, always, and the other end always pointing away. The long axis goes through the star. The far end is always in shadow.

Would torque prevent the planet from rotating around its long axis?

All bodies in orbit (including artificial Earth satellites) will tend to point their long axes at the central mass. The stronger the tidal forces between the two ends, the more it will tend to stay that way.

Hornblower
2019-Feb-05, 12:57 AM
As I get it, the football planet has one end pointing at its sun, always, and the other end always pointing away. The long axis goes through the star. The far end is always in shadow.

Would torque prevent the planet from rotating around its long axis?My bold. Perhaps we should turn that around and ask if any conceivable torque would get the body to rotate around its long axis. I don't envision something analogous to the rifling of a gun barrel acting on a bullet, or a quarterback's hand acting on a football.

Roger E. Moore
2019-Feb-05, 01:32 PM
I was wondering if an early rotational period, from the Football Planet's creation, would have survived when the planet migrated inward toward its sun and became severely deformed. It does not seem likely to me, but only on an intuitive level. The world would not rotate around any short axis, but would it do so around its long axis? The sunward side would see the stars around the sun rotate in the sky (if sun was blocked from view), nightside the same but without the sun.

grapes
2019-Feb-06, 09:14 PM
Centrifugal velocity? Is the center the center of the star? Centrifugal velocity would be smallest at the "far" end of the planet, no?
OK, that was sloppy terminology.

But yes, escape velocity is largest at the poles, where it is not assisted by the body's rotation. So particles and bodies ejected from the equator will tend to accumulate at the poles.

Not sure what "star" has to do with it.
I wasn't sure what you were considering the "center" for the centrifugal velocity. If you follow each point of the planet, it describes a circle around the star (or at least the star/planet barycenter).




I was wondering if an early rotational period, from the Football Planet's creation, would have survived when the planet migrated inward toward its sun and became severely deformed. It does not seem likely to me, but only on an intuitive level. The world would not rotate around any short axis, but would it do so around its long axis? The sunward side would see the stars around the sun rotate in the sky (if sun was blocked from view), nightside the same but without the sun.
That would be a very complicated motion, since the planet is rotating around its short axis once per revolution. The long axis would have to precess one whole rotation per revolution.

Hornblower
2019-Feb-06, 10:38 PM
I was wondering if an early rotational period, from the Football Planet's creation, would have survived when the planet migrated inward toward its sun and became severely deformed. It does not seem likely to me, but only on an intuitive level. The world would not rotate around any short axis, but would it do so around its long axis? The sunward side would see the stars around the sun rotate in the sky (if sun was blocked from view), nightside the same but without the sun.

It is possible for an elongated body to rotate around its long axis while also rotating end over end. I can make a hammer do that, and divers or gymnasts doing twisting somersaults in the air are doing similar motion. However I don't think the spin around a long axis will last long for a deformable planet in near its Roche limit. I am pretty certain that such spin will damp out under the tidal stresses, leaving the body as a triaxial ellipsoid rotating end over end in unison with its orbital motion. I expect it to be triaxial because the centrifugal effect of the rotation will flatten it at the poles, while the tidal stress will elongate it along a perpendicular axis.

21st Century Schizoid Man
2019-Feb-07, 10:03 AM
So, should the inhabitants of this planet use latitude/longitude to describe their location, or would some other system work better?

Hornblower
2019-Feb-07, 12:15 PM
So, should the inhabitants of this planet use latitude/longitude to describe their location, or would some other system work better?

They should use whatever fits their needs.

Roger E. Moore
2019-Feb-07, 04:16 PM
When NASA or anyone else gets around to mapping this world, I would bet the subsolar point on one end of the football is "north", the antisolar point is "south", the equator is the circumference between the two, and it all goes together from there.

Hornblower
2019-Feb-07, 11:15 PM
I would say that Roger's idea is a good one, with the permanent subsolar point as the origin of these polar coordinates. This planet is an interesting beast to envision. It is so close to its sun that the sun will have an angular radius on the order of 30 degrees, so there will be a broad penumbral zone straddling the equator. The reputed prolate elongation means that the linear distance to each pole will be about 2/3 of the way to the pole. I estimated that by plotting a suitable ellipse and using a protractor to find where the slope was 30 degrees. That's not mathematically elegant but was easier for this quickie purpose than differentiating the equation for the ellipse with my rusty calculus. Only a relatively small portion of the total surface would be dark.

An interesting geometric curiosity is that the celestial poles will be directly over the equator as defined here.

Roger E. Moore
2019-Feb-08, 12:14 AM
That was very cool, thank you! :)

21st Century Schizoid Man
2019-Feb-12, 12:36 PM
They should use whatever fits their needs.

Well that's the question now, isn't it? What fits their needs?

DaveC426913
2019-Feb-12, 06:43 PM
Well that's the question now, isn't it? What fits their needs?
Well, this is the Astronomy Forum, so there's no "they" to speak of.

If we were going to go on discuss hypothetical denizens, maybe we should move this to a fiction forum?

Roger E. Moore
2019-Feb-12, 08:22 PM
Well, this is the Astronomy Forum, so there's no "they" to speak of.

If we were going to go on discuss hypothetical denizens, maybe we should move this to a fiction forum?

I think by "they", it really means "we". We will need to map the world. Even if humans never get to the stellar system, our robots might, and mapping a football-shaped planet will be a priority for someone's Ph.D.