Astronomy/cosmology questions...

[Buster's Uncle]

Lori, how long has it been since a lunar month was 27 days?

How close is it to 28 days exactly, now?  Surely not EXACTLY 28 days, right?  The would be one heck of a coincidence...

[Lorizael]

Well, so, what do you mean exactly by the lunar month? If you're talking about the time it takes for the moon to complete one orbit around the Earth (relative to the fixed stars), that's about 27.3 days. If you're talking about the time it takes to go through a full set of lunar phases, from one new moon to another, that's roughly 29.5 days.

Over the last few hundred million years, the distance between the Earth and moon has increased by an average of slightly more than 2 cm per year. From that, and using Kepler's laws, you can do a little math and find that the orbital period (called the sidereal month) would have been exactly 27 days about 140 million years ago.

If you're talking about when the lunar phases took 27 days (called the synodic month), that would have been when the orbital period was just over 25 days long. Doing the same math as above, and assuming the recession rate maintains that average even further back, then that would have been about 950 million years ago.

[Buster's Uncle]

Interesting.  Thanks.

[Lorizael]

No problem. And of course, that all ties into eclipses. About a billion years ago, the apparent size of the moon was maybe 5% larger, so the moon would always cover up the sun if it passed between the earth and it. In another billion years, as the moon gets farther away, it will never be able to totally eclipse the sun. We're so special.

[Geo]

No problem. And of course, that all ties into eclipses. About a billion years ago, the apparent size of the moon was maybe 5% larger, so the moon would always cover up the sun if it passed between the earth and it. In another billion years, as the moon gets farther away, it will never be able to totally eclipse the sun. We're so special.

So were the dinosaurs, if any species of it was intelligent enough to admire the show.
There was an article in one of our news sites writing about the end of full totality eclipses as well. IIRC they came up with 650 million years before the Moon is too far out to cover the Sun completely.

[Buster's Uncle]

Lori, come straighten us out, please...
http://alphacentauri2.info/index.php?topic=19956.msg107971#msg107971

[Geo]

A couple of questions about Haumea because of a recently released article.

https://www.sciencedaily.com/releases/2017/10/171012093350.htm

I'll post the excerpt and my question(s) below it.

Haumea is an interesting object: it rotates around the Sun in an elliptic orbit which takes it 284 years to complete (it presently lies fifty times further from the Sun than the Earth),
and it takes 3.9 hours to rotate around its axis, much less than any other body measuring more than a hundred kilometers long in the entire Solar System. This rotational speed causes it
to flatten out, giving it an ellipsoid shape similar to a rugby ball. The recently published data reveal that Haumea measures 2,320 kilometers in its largest axis -- almost the same as Pluto --
but lacks the global atmosphere that Pluto has.

Is there a likelihood that Haumea, instead of being a single body, is two 'lobes' connected somewhat like 216 Kleopatra, but closer?
It's just that I find it odd Haumea pulls a Jinx-like object on us like in Larry Niven's Known Space novels.

First Trans-Neptunian Object With a Ring

According to the data obtained from the stellar occultation, the ring lies on the equatorial plane of the dwarf planet, just like its biggest satellite, Hi´iaka, and it displays a 3:1 resonance
with respect to the rotation of Haumea, which means that the frozen particles which compose the ring rotate three times slower around the planet than it rotates around its own axis.

Assuming that the longest axis of Haumea also lies in its equatorial plane, I wonder if this ring would orbit the dwarf planet in an ellipsoid shape as well instead of the usual circular one.
I mean, the orbital velocities needed to stay at a given distance of the surface are not 'circular' in respect to this world's equator.

[Lorizael]

Ack. I was going to show you a figure from the paper to help answer your question, but I just realized I only have access to the paper when I'm at work. I mean I could probably finagle something, but I'm lazy and can make do.

Is there a likelihood that Haumea, instead of being a single body, is two 'lobes' connected somewhat like 216 Kleopatra, but closer?
It's just that I find it odd Haumea pulls a Jinx-like object on us like in Larry Niven's Known Space novels.

So before this set of observations, the shape of Haumea was known only through its lightcurve. That is, it would periodically get bright and dim, and we can infer from that (after taking into account its distance, angle with the sun, etc.) that it's dim when we're seeing a narrow profile and bright when we're seeing a wide profile. And yeah, there are a bunch of assumptions baked into that kind of observation, so it's possible to get the shape wrong. But the occultation done here mostly rules all that out.

This set of observations was done at the same time from a dozen telescopes at different latitudes on Earth, which means we see the occulted star at different angles. This means you can trace different lines across Haumea representing the star's path as seen from different points on Earth. For however long the star is invisible (because it's behind Haumea) from that angle, you get Haumea's width at that line. At no point did the star disappear, blink back, and disappear again, which is what you'd expect for lobes. Instead, it remains completely occulted for some period and is then visible again.

Assuming that the longest axis of Haumea also lies in its equatorial plane, I wonder if this ring would orbit the dwarf planet in an ellipsoid shape as well instead of the usual circular one.
I mean, the orbital velocities needed to stay at a given distance of the surface are not 'circular' in respect to this world's equator.

This is a difficult question to answer. I know the paper concludes that the ring is circular, and they do this by identifying points on the ring via the occultation and then connecting the dots to get the projection of the ring from our angle. If you tilt the projection to line up with the equator, you get a circle.

Whether or not the ring should be circular is something else to consider. The question is whether Haumea's shape "excites" the orbit of the ring particles. Circular orbits have the lowest energy for an orbit of a given semi-major axis. If you pump energy into the orbit, it becomes more eccentric (elliptical) until eventually particles are able to escape. But there's no simple answer for whether or not a particular configuration of stuff is going to excite an orbit; it involves a lot of perturbation analysis and numerical integration. (This answer is somewhat of a cop out because my knowledge of complicated orbital mechanics is sketchy.) That said, general features which could excite an orbit include resonances. The article mentions the ring's orbit being very close to a 3:1 resonance with Haumea's own rotation. That is the kind of orbital parameter that could spice things up. /me shrugs.

[Geo]

Thanks a ton, Lorizael. 

[Rusty Edge]

Obviously I'm out of my depth in this discussion, but for purposes of an orbit, isn't it the point of center mass what matters rather than the distance between the two surfaces, or the density of the planet? A moon circling a gas giant or a round rock, or a rugby shaped rock of the same mass would have the same orbit based on the speed of the moon and distance between the centers of mass, wouldn't it?

A Moon crossing the Andes of Earth or the seams of Rugby shouldn't have a measureable effect on it's orbit, should it?

No hurry on this one, not like it's haunting my thoughts or anything.

[Geo]

You're of course right, Rusty. And to bring the punch home, Haumea's biggest moon (Hiʻiaka) has a similar excentricity as the Moon shows in respect to Earth.
But I keep finding it odd that Haumea has such a weird shape, with two huge protusions along its equator. Something must have caused it so that not the whole equator is more or less evenly 'flattened out', as to have more the shape of a disc. A more spread out distribution of the core mass? In any case, to me if felt like the ring system could have behaved differently then it appearantly does (circular orbit around Haumea as well).

[Lorizael]

A Moon crossing the Andes of Earth or the seams of Rugby shouldn't have a measureable effect on it's orbit, should it?

It absolutely does, which is how we're able to produce maps like this:



This is the "geoid" and is sometimes referred to as the true figure of the Earth, gravitationally speaking. We measure this with satellites by very carefully tracking deviations from the orbit we expect. The thing to remember about gravity is that the "real" way to calculate the gravitational force on an object is to add up the mass and distance of every single particle that could attract the object. So if you have more particles closer to you, there's more gravity.

Thankfully, we don't actually have to do this because Newton proved a theorem (shell theorem) which says that you can treat a perfectly symmetric sphere of uniform density as if it were just a single point of mass at the center. If you're very far away from something that's roughly a sphere, you can pretend the shell theorem applies and everything works out pretty well. The closer you get/the more deformed the object is, the less you can get away with it.

A final note is that even with satellites measuring orbital deviations, we're basically still just pretending the Earth is a sphere. But we're pretending it's like a couple thousand slightly different spheres stacked on top of each other (a mathematical trick known as spherical harmonics). Doing that is still way, way easier than counting all the grains of sand and measuring their gravity...

[Geo]

Guess that shows we have different ideas about 'measurable', Lori.
I'm definitely a layman in these matters.

[Rusty Edge]

That is so cool....especially since I'm not in school and don't have to solve those kinds of story problems! Thanks, Lorizael! I should have known, the interconnectedness of all things. Gravity as Zen.

I imagined the actual earth shape was relatively smoother, but with more of an apparent belly bulge than that. A little less spherical.
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So this has me wondering, what factors create a rugby planetoid, rather than the more familiar spherical ones?

For example, is this more likely to happen when the denser core of a moon/planet does an amoeba style complete separation while still travelling in the same orbit, resulting in a faster and slower Rugby? Or is it the lack of rotation, or rotation perpendicular to the axis of orbit that is the key factor?   Or is it something else, more like a ball of playdough in orbit, collecting gravel and dust in it's path? Or maybe more of a giant teardrop of liquid gas gathering droplets of other gasses on it's leading bulbous end?

Again, no hurry on this one.

[Lorizael]

I imagined the actual earth shape was relatively smoother, but with more of an apparent belly bulge than that. A little less spherical.

Oh, I mean, the real physical shape of the Earth is nearly a perfect sphere. The radius of the Earth is ~6400 km and Everest is 8.8 km high. That map is just a map of the relative strength of gravity from one location to the next. Buttttt, if you pretend the Earth is a perfect fluid with the current density distribution, then the "fluid" of the Earth would flow so that the Earth's shape resembled that geoid. (Although that map is an exaggeration of the true geoid, I think.)

So this has me wondering, what factors create a rugby planetoid, rather than the more familiar spherical ones?

For example, is this more likely to happen when the denser core of a moon/planet does an amoeba style complete separation while still travelling in the same orbit, resulting in a faster and slower Rugby? Or is it the lack of rotation, or rotation perpendicular to the axis of orbit that is the key factor?   Or is it something else, more like a ball of playdough in orbit, collecting gravel and dust in it's path? Or maybe more of a giant teardrop of liquid gas gathering droplets of other gasses on it's leading bulbous end?

Again, no hurry on this one.

The answer is mostly rotation. Absent any other forces, a gravitating mass will coalesce into a sphere. If the mass is made up of rocks and other hard, pointy objects and is small enough, gravity can't reshape it into a sphere and it retains whatever clumps originated from the collisions that formed it. If it's rotating, then the faster it rotates, the more of an equatorial bulge it will have, as you pointed out. Direction relative to orbit shouldn't matter in general, although that does come up with the YORP effect, where pressure from solar radiation can mess with an asteroid's spin and shape.