The paper doesn’t calculate the radius of the star’s Roche limit, instead opting to calculate the orbital period of the Roche limit. I’ve never done a Roche limit calculation for stars, but I have for planets/moons, and I’m not seeing anything that suggests it’s different than for planets. So, I think I did this correctly (excepting typos):
The star’s Roche limit is about 1.5 million km from its centre (~1 million km above its surface), and the planet’s orbit is about 2 million km from the star’s centre. Assuming a circular orbit, which should be the case at these distances, the orbit has a circumference of about 12.7 million km, and the planet is whipping around at a speed of about 2.3 million km/h, or 0.2% the speed of light.
So much math here that my head is already overheating. I need to find the time to learn all this math. Kudos to you internet stranger on your examplary calculations.
The numbers are big, so it can be intimidating, but the math isn’t too bad. It’s a little bit of multiplication and division. The most daunting bit is a cube-root, which you can find on most scientific calculators these days.
It’s hunting down the numbers you need to use that’s the trick, and making sure they’re all in the right units.
The equation for the Roche limit is the most complex math, but that’s just something you look up:
Roche Limit = 2.44 x {the radius of the star} x cube-root(( {the mass of the planet} / {the radius of the planet}^3 ) / ( {the mass of the star} / {the radius of the star}^3 ))
All of the things in the braces are also just values you look up.
The article mentions the star being a dwarf. Are dwarf stars older and in a degrading state. Would the star have had less gravitational force when younger.
How would a plant form that close if the gravitational pull from the star was this strong.
Dwarf stars are technically any star that is in its core phase of life. They are dwarves in comparison to giant stars. The sun is a G-type dwarf star, for instance.
The star is a K-type dwarf, which means it is cooler and smaller than the sun (stars are labelled froom hottest/most massive coolest least hot/least massive: O, B, A, F, G, K, and M for historical reasons).
Planet formation is a complicated and still somewhat young field of study. Planets being close to their stars was a real shock 20 years ago when we stared finding them. The best models we have for this is planetary migration, where the planets form farther aewy from the star, but friction/drag forces from the nebula from which they formed causes them to slow down and fall into smaller orbits.
This planet continues to see its orbit degrade for even more complex reasons, related to both drag – it is interacting with the star’s atmosphere, which is causing it to slow – and tidal effects. When you’re close enough to a massive, rotating body that the differences in gravitational pull strength due to things like variations in density become significant, the rotating body will force you into an orbit that matches its rotation length. If you’re already orbiting faster than it is spinning, that means it will slow you down. But slowing down will cause your orbit to shrink, which shortens the time it takes you to complete an orbit, which will make the central body slow you down more, which will shrink your orbit, which…
Not in the same way, no. None of our planets are touching the Sun’s atmosphere in the same way this planet is, and none of them are orbiting at rates that are faster than the Sun’s rotation. If anything, tidal interactions would want to speed up the planet’s orbits, and push them into higher orbits.
But eventually the Sun will become a red giant star, which will change some of these relationships. We will see competing effects then: The Sun will begin shedding its outer layers, which will create a higher drag environment for the planets (that were not swallowed during the Sun’s expansion) which would tend towards inward migration, but this will also lower the Sun’s mass, which will lend itself toward an outward migration.
Jupiter is not currently migrating inward, nor are any of the other planets. If inward migration happens after the Sun becomes a red giant, those other outer planets will not get anywhere close to it. As a red giant, the Sun will approximately fill Earth’s orbit. Jupiter’s orbit is 5x larger than this; Saturn’s is 10x larger, and by the time the Sun actually grows this large, all of the planets’ orbits will be even larger than they are today, thanks to gradual mass loss.
None of the outer planets are expected to fall into the Sun at any point in time.
When we hit the floor you just watch them move aside
We will take them for a ride of rides
They all love your miniature ways
You know what they say about small boys
They were never considered stranded, except maybe for the few days between Starliner’s empty return and the Crew-9 Dragon’s arrival. Certainly not for 9 months.
Unfortunately we’ll never get to visit them in person if Prostetnic Vogon Jeltz has anything to say about it:
We are about to jump into hyperspace for the journey to Barnard’s Star. On arrival we will stay in dock for a seventy-two-hour refit, and no one’s to leave the ship during that time. I repeat, all planet leave is canceled. I’ve just had an unhappy love affair, so I don’t see why anybody else should have a good time.
Gonna hijack this post to ask a somewhat related but possibly stupid question, would it be possible that instead of a singularity there happened to be a region of space with non-negligible size (ie, not a point sized region) that acted like a well instead? Things could “fall” into that well and not be able to escape, but it’s not like everything in the well is at a single point.
I may be misunderstanding your question, but black holes are regions of space that have non-negligible size; the boundary between what can escape and what can’t is called the event horizon. The singularity is what happens at the center.
I guess what I mean to say is, would a non-negligible sized “singularity” (I know I’m messing with that term quite a bit, I’ll stray from the mathematical definition) be consistent with our current theories?
Basically, what makes sense logically isn’t backed up by what data and math we have. Logically, we would assume as enough stuff is pulled together that the density hits a point where gravity is stronger than the bonds that hold matter together, that those bonds would break and the individual elements, initially atoms, but as gravity gets stronger and stronger the bonds between the components of atoms and so on and so forth also break down.
At some point, there is a limit to how much matter can break back down into further and further smaller components. What specifically happens when that limit is reached? That is a huge part of what could be throwing the math off. We don’t really know, but we have some guesses. Could be at the end, one of the components is weightless, and unaffected by the gravity, we do see some energy radiating out of some black holes in a straight line or “jet”. Hard to say for sure. Logic doesn’t always get us there when we don’t have enough data and need to make a leap. It might eventually, as we can slowly tie more and more stuff together with more data. Could be whatever energy starts that jet either immediately or already on the way out, mixes/mixed with other components and particles to become what we end up detecting it as. But if we could see it earlier, it maybe would be completely different before that.
Depends what you mean by “our current theories”. In classical General Relatively the answer is pretty conclusively no but many people think that a quantum theory of gravity should be able to remove the singularities. In fact, this article is about an attempt to do just that with a fairly natural extension to GR (albeit one that is only mathematically tractable in 5 or more dimensions) and seems to have succeeded for the static spherically symmetric case at least.
Nobody really thinks singularities exist. It’s only what comes out from our math. That’s also how we know our math is wrong, we’re just not sure yet how to do it better.
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