Volume of neutron stars compared to living space of cities

[repoman]

Was watching a random video and there was the old neutron star is about 1.4 solar masses crunched into the size of a city. But say there is only an average of 50-100 meters of average height of buildings, wouldn't that mean that a neutron star could hold hundreds of cities?

Is this analogy off by about two orders of magnitude?

 

[Loren Pechtel]

Correct, it can hold hundreds of cities except they would be as crushed as everything else.

 

[rjh01]

If a neutron star hit the earth then it would eat the earth. Their density is very high. A few milliliters would weigh as much as the earth.
In fact all what a neutron star would need to do is go within a few radii of the moon's orbit and it would do serious damage due to tidal forces alone. Like wipe out all satellites. Then the magnetic forces would also do serious damage.

 

[skepticalbip]

^ ^ ^

A neutron star passing a few moon orbit radii away would cause much more than than damaging tidal forces. Such a near pass would throw the Earth out of its orbit.

 

[Loren Pechtel]

If a neutron star hit the earth then it would eat the earth. Their density is very high. A few milliliters would weigh as much as the earth.
In fact all what a neutron star would need to do is go within a few radii of the moon's orbit and it would do serious damage due to tidal forces alone. Like wipe out all satellites. Then the magnetic forces would also do serious damage.

No, a few milliliters are nowhere near as much as the Earth.

^ ^ ^

A neutron star passing a few moon orbit radii away would cause much more than than damaging tidal forces. Such a near pass would throw the Earth out of its orbit.

Ejection would be irrelevant, at that range the tides would have rendered the Earth lifeless anyway. Ejection will happen at a greater range than tidal destruction, though.

Note that if the neutron star passes as close as the moon the Earth is destroyed. (I'm using the fluid Roche limit because against those forces the Earth has no meaningful strength.)

 

[Gun Nut]

will a 340 km rock passing between the Earth and our moon do anything bad? Because that is actually happening pretty soon.

 

[Jokodo]

will a 340 km rock passing between the Earth and our moon do anything bad? Because that is actually happening pretty soon.

Are you talking about this guy: https://en.m.wikipedia.org/wiki/99942_Apophis ?

Off by 3 orders of magnitude - its 370 metres!

 

[Loren Pechtel]

will a 340 km rock passing between the Earth and our moon do anything bad? Because that is actually happening pretty soon.

Well, it certainly would make just about every astronomer on the planet shit their pants and would likely jostle everything in Earth orbit.

Now, the 340 meter rock that's actually going to pass is a close call, nothing more. If it hit it would dwarf Tsar Bomba.

 

[Jokodo]

will a 340 km rock passing between the Earth and our moon do anything bad? Because that is actually happening pretty soon.

Well, it (...) would likely jostle everything in Earth orbit.

That much depends on where exactly it passes - between earth and moon is quite a range. If it effectively grazes the Himalayas, sure that would be very disruptive; if it's more on the moon end if the range, it would be hard to even measure its presence other than visually with the finest instruments mankind has. After all, 340km is less than 1/10 if the moon's diameter, so less than 1/1000 its mass assuming similar densities. The difference between the moon's tidal force when it's close in its elliptical orbit and when it's far is orders of magnitude larger than what such a tiny body could contribute at a similar distance, and lo and behold, the satellites still orbit merrily.

 

[Cycad]

Once a bunch of monks played some ball game in Canterburry . One of them observed a direct hit of a foreign object on the moon. Thought it was the work of Lucifer himself.
It didnt have any effect on earth besides influencing the score of the game. On the moon it dug a nice crater and caused some resonance which can still be measured. Giordano Bruno Crater

I dont see the link with neutron stars butr hey, its weekend

 

[Loren Pechtel]

will a 340 km rock passing between the Earth and our moon do anything bad? Because that is actually happening pretty soon.

Well, it (...) would likely jostle everything in Earth orbit.

That much depends on where exactly it passes - between earth and moon is quite a range. If it effectively grazes the Himalayas, sure that would be very disruptive; if it's more on the moon end if the range, it would be hard to even measure its presence other than visually with the finest instruments mankind has. After all, 340km is less than 1/10 if the moon's diameter, so less than 1/1000 its mass assuming similar densities. The difference between the moon's tidal force when it's close in its elliptical orbit and when it's far is orders of magnitude larger than what such a tiny body could contribute at a similar distance, and lo and behold, the satellites still orbit merrily.

I was picturing something like halfway between. The moon's pull is back and forth, it pretty much neutralizes itself over a month. A passing body won't--no big deal for anything that has thrust, but what is it going to do to all the debris?

 

[Jokodo]

That much depends on where exactly it passes - between earth and moon is quite a range. If it effectively grazes the Himalayas, sure that would be very disruptive; if it's more on the moon end if the range, it would be hard to even measure its presence other than visually with the finest instruments mankind has. After all, 340km is less than 1/10 if the moon's diameter, so less than 1/1000 its mass assuming similar densities. The difference between the moon's tidal force when it's close in its elliptical orbit and when it's far is orders of magnitude larger than what such a tiny body could contribute at a similar distance, and lo and behold, the satellites still orbit merrily.

I was picturing something like halfway between. The moon's pull is back and forth, it pretty much neutralizes itself over a month. A passing body won't--no big deal for anything that has thrust, but what is it going to do to all the debris?

Halfway between and 1/1000 of the mass is still just 1/250 if the gravitational pull, or 1/125 of the tidal effect, the latter being of little significance for small objects like satellites, or space debris. It's not like we have a lot of debris sitting halfway to the moon, it's centred in low earth orbit.

The fact that it would likely pass by at a much higher relative speed than the moon's makes it only more benign since it reduces the time during which it could have any non- negligible influence.

I repeat: it will be hard to even detect other than visually and i add: you didn't really think this through.

 

[Jokodo]

I wrote a little simulator once as a hobby project where I'd shoot stellar sized objects at the inner solar system and found it was hard to throw the inner planets of track even with a body of 1/30 solar masses passing inside of Venus's orbit. In most iterations, they'd at best continue in slightly more elliptical orbits - but only when it chanced to get really close to them. Among hundreds of runs with randomized initial parameters but always passing inside of the orbit of Venus, I succeeded once to to simulate the Earth being ejected, and even then the moon kept orbiting it. Throwing off track something that hugs the Earth as closely as the moon (on solar system scales) or as LEO satellites (at the earth-moon-system scale) is hard.

 

[Jokodo]

OK, this bothered me so I went to Wolfram Alpha. Turns out a 0.001 moon mass object passing at 0.5 moon distances imparts roughly a delta v of about 0.002 m/s on objects in low earth orbit. For simplicitly, I did not integrate its gravitational pull during its entire approach and recline, just pretended that it stays at the given distance for five hours - which is a serious overestimation. Earth takes about 4 hours to cover the Earth-moon distance in its orbit. https://www.wolframalpha.com/input/...+/+1000+/+((0.5+moon+distance)+^2))+*+5+hours

A one-tonne piece of space debris is going to be jostled more by colliding with a 0.1 gram space dust particle than by our planetoid.

As far as I can tell, both are well within the error range of the models used when deploying satellites.

 

[Jokodo]

Those 2.27 mm/s are actually the acceleration at earth's position relative to an external reference frame. The acceleration of a satellite relative to earth will be much lower since the asteroid tugs at both with roughly proportionally equal force. Even for the worst case scenario, a geostationary satellite that happens to be facing the asteroid while it passes, total acceleration will be 3.625mm/s, thus barely over a mm/s relative to earth.: https://wolframalpha.com/input/?i=(...+/+((0.5+*+distance+of+moon)+^2))+)+*+5+hours

For comparison: maintaining a geostationary orbit requires about 50 metres per second per year just to balance the precession caused by the moon's and sun's tug, and unless it's in one of two stable longtitudes, up to another 2 m/s per year to avoid shifting laterally due to the equator being elliptical.https://en.m.wikipedia.org/wiki/Geostationary_orbit

Feel free to redo the calculations with an asteroid of lower relative motion - it will still be hard to measure the tug.

 

[Loren Pechtel]

I wrote a little simulator once as a hobby project where I'd shoot stellar sized objects at the inner solar system and found it was hard to throw the inner planets of track even with a body of 1/30 solar masses passing inside of Venus's orbit. In most iterations, they'd at best continue in slightly more elliptical orbits - but only when it chanced to get really close to them. Among hundreds of runs with randomized initial parameters but always passing inside of the orbit of Venus, I succeeded once to to simulate the Earth being ejected, and even then the moon kept orbiting it. Throwing off track something that hugs the Earth as closely as the moon (on solar system scales) or as LEO satellites (at the earth-moon-system scale) is hard.

Some time back I tried it with neutron stars passing the solar system. All were aimed 10 AU out, 100 km/sec, 2 solar masses. Note that this is not the actual closest approach, but the distance they would have passed had gravity not messed with them.

Any outer planet on that side of the sun got ejected, sometimes outer planets on the other side got ejected. Once the intruder stole Mars and somehow managed to get it in a roughly circular orbit even. Earth was never ejected but that doesn't mean it survived--one run left Jupiter with a periapsis below Mercury.

 

[Jokodo]

I wrote a little simulator once as a hobby project where I'd shoot stellar sized objects at the inner solar system and found it was hard to throw the inner planets of track even with a body of 1/30 solar masses passing inside of Venus's orbit. In most iterations, they'd at best continue in slightly more elliptical orbits - but only when it chanced to get really close to them. Among hundreds of runs with randomized initial parameters but always passing inside of the orbit of Venus, I succeeded once to to simulate the Earth being ejected, and even then the moon kept orbiting it. Throwing off track something that hugs the Earth as closely as the moon (on solar system scales) or as LEO satellites (at the earth-moon-system scale) is hard.

Some time back I tried it with neutron stars passing the solar system. All were aimed 10 AU out, 100 km/sec, 2 solar masses. Note that this is not the actual closest approach, but the distance they would have passed had gravity not messed with them.

Any outer planet on that side of the sun got ejected, sometimes outer planets on the other side got ejected. Once the intruder stole Mars and somehow managed to get it in a roughly circular orbit even. Earth was never ejected but that doesn't mean it survived--one run left Jupiter with a periapsis below Mercury.

At what velocity where you modelling the pass?

And to get back to the planetoid-between-earth-and-moon case: A neutron star passing at 5-10 AUs is closer to Jupiter passing halfway to the moon than to our scenario.

 

[Jokodo]

I started with rogue planets and quickly moved on to brown dwarfs and even small red dwarfs because the results were almost always decidedly unspectacular with smaller objects. You started with something more massive than the sun. And here we're taking about something smaller than Ceres.

 

[Loren Pechtel]

I started with rogue planets and quickly moved on to brown dwarfs and even small red dwarfs because the results were almost always decidedly unspectacular with smaller objects. You started with something more massive than the sun. And here we're taking about something smaller than Ceres.

I was specifically looking for that scenario--addressing a question on StackOverflow.

 

[Jokodo]

I started with rogue planets and quickly moved on to brown dwarfs and even small red dwarfs because the results were almost always decidedly unspectacular with smaller objects. You started with something more massive than the sun. And here we're taking about something smaller than Ceres.

I was specifically looking for that scenario--addressing a question on StackOverflow.

That's all nice, just don't generalise from super-solar top sub-Ceres