on causes of moon fragmentation

[bwanaaa]

how much more massive would the earth have to be to cause tidal forces on the moon sufficiently strong to turn it into an asteroid belt?

Initially, i thought that depended on the cohesiveness of the moons core. But then thinking about the fact that the moon's surface is dust, that component should be trivial.

the process of fragmentation would begin when the force at the near side of the moon and the far side of the moon are sufficiently different to cause different orbital velocities of the dirt on the different sides of the moon. - the same forces that cause a satellite in a lower orbit to travel faster than one in a higher orbit. when this force difference exceeds the gravitational force of the moon on itself, then the moon spreads out- like lumpy peanut butter on bread.

do you agree?

 

[Matt1970]

It would have to be quite massive. Think of the gravitational pull the sun has on Murcury.

 

[bwanaaa]

D= distance to moon=~380 km
R=radius of moon=~2 km
Grav force on near side of moon- Grav force on far side=
G=m1m2/r^2
DeltaG=m1m2/382^2 -m1m2/378^2
DeltaG=(145924-142884)m1m2/2.085x10^10
DeltaG=3.04 m1m2/2.085x10^7
DeltaG~1.5 m1m2 x 10^-7

Grav force on the moon is 1/6 earth=0.15G= 1.5x10^-1

The earth would have to be a million times more massive to have tidal forces at the moon's opposite sides differing about the same as moon's gravity. yes?

 

[Evadman]

D= distance to moon=~380 km
R=radius of moon=~2 km
Grav force on near side of moon- Grav force on far side=
G=m1m2/r^2
DeltaG=m1m2/382^2 -m1m2/378^2
DeltaG=(145924-142884)m1m2/2.085x10^10
DeltaG=3.04 m1m2/2.085x10^7
DeltaG~1.5 m1m2 x 10^-7

Grav force on the moon is 1/6 earth=0.15G= 1.5x10^-1

The earth would have to be a million times more massive to have tidal forces at the moon's opposite sides differing about the same as moon's gravity. yes?

The moon as a radius of 2 km and is 380 km away? Radius of the moon is 1737 km, and is ~350000 to ~400000 km away depending on apogee and perigee IRC.

The limit the OP is looking for is the Roche limit I believe. If we assume the moon had no tensile strength at all (was a liquid basically), then the roche limit is about 18000 km or so. The moon is probably in the 9500 km range, or 1.5 times the earth radius.

 

[Lemon law]

Maybe the thing to point out is, that the earth's moon used to have an orbit much closer to earth than it does now. Meaning the inverse square laws of gravity translates into saying, if the earth itself had insufficient gravitational attraction mass to tear its moon apart billions of years ago, our planet Earth certainly has a greatly diminished gravitation attraction to tear our moon apart now.

As I recall the Moon's orbital distance increase about 1.5 inches per year. Its then possible to calculate
that the Moon had a zero orbital distance some 10 billion years ago. Of course three flaws in that reasoning, I am not 100% sure on my 1.5 inch/yr figure, I am not sure that that 1.5 inch rate of recession is a constant over time, and oops, our solar system is supposed to be about 4.4 billion years old or so. Figures do not lie, but fools figure.

 

[bwanaaa]

The moon as a radius of 2 km and is 380 km away? Radius of the moon is 1737 km, and is ~350000 to ~400000 km away depending on apogee and perigee IRC.

The limit the OP is looking for is the Roche limit I believe. If we assume the moon had no tensile strength at all (was a liquid basically), then the roche limit is about 18000 km or so. The moon is probably in the 9500 km range, or 1.5 times the earth radius.

oops!
off by factors of 10^3
assume distance is 380000 km, radius 1800
DeltaG=G(nearside)-G(farside)
DeltaG=m1m2/378200 ^2 -m1m2/381800^2
DeltaG=(1.45771*10^11-1.43035*10^11)m1m2/2.085x10^22
DeltaG=2.736m1m2/2.085x10^10
DeltaG~1.312 m1m2 x 10^-10
so the earth would have to be a billion times more massive to disintegrate the moon at its current orbit.

but yes, i wiki'd the roche limit and it is another way to measure what i ask. that formula is
d=R * (2 * primarydensity/secondarydensity)^ 1/3

d=6739km (2 * 5.52 g/cm3/3.346 g/cm3) ^ 1/3
which gives the result evadman kindly posted.

I came across this thought after reading preston's book, Impact. In that novel, a miniature black hole is shot at earth. An interesting explanation for the survival of the planet is that the black hole absorbs the mass of what it passes through and therefore there is no shockwave. Of course, i imagine that the transient increase in gravity would squash everything flat at the surface (but that is not addressed). And of course the thought about the moon being ripped apart is not mentioned either.



btw, tnx evadman. i also like your blog about hashes crypto etc. check this out
https://www.pwdhash.com/

 

[Evadman]

Its then possible to calculate
that the Moon had a zero orbital distance some 10 billion years ago.

Actually, the math breaks down when the moon gets to within ~150km of the surface, and the moon is spinning around earth every few days or so. That is the big gap in the 'earth spins so fast the moon is flung off the surface' theory of moon formation. The current best fit theory is that a mars size object collided with earth, and the debris formed the moon.

 

[Lemon law]

Actually, the math breaks down when the moon gets to within ~150km of the surface, and the moon is spinning around earth every few days or so. That is the big gap in the 'earth spins so fast the moon is flung off the surface' theory of moon formation. The current best fit theory is that a mars size object collided with earth, and the debris formed the moon.

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Actually the math breaks down far before that, because our whole solar system, the earth , and the moon are less than 5 Billion years old.

But if we accept the current best fit theory of earth's moon being created when a mars sized object collided with earth early in the history of our solar system, as I recall that best fit theory predicted two things. (1) That our protomoon, after being sheared off when a Mars object impacted earth did not consist as a single coherent object, and instead consisted as a large debris field that resembled an asteroid belt that orbited earth. (2) Over a fairly short time period, gravitational attraction consolidated the debris field into a single object we know as the moon. And at the time of consolidation of the moon, the moon was at a hot enough temperature to melt rock. Since that time of moon formation, both the earth and moon have cooled significantly. But the moon's crust now is sufficiently thick to prevent tectonic process's, while earth is still geologically active.

But either way, it refutes the thread OP's conjecture that the earth's gravity will ever be strong enough to bust our moon into the asteroid belt it may have been.

 

[The Boston Dangler]

how much more massive would the earth have to be to cause tidal forces on the moon sufficiently strong to turn it into an asteroid belt?

Initially, i thought that depended on the cohesiveness of the moons core. But then thinking about the fact that the moon's surface is dust, that component should be trivial.

the process of fragmentation would begin when the force at the near side of the moon and the far side of the moon are sufficiently different to cause different orbital velocities of the dirt on the different sides of the moon. - the same forces that cause a satellite in a lower orbit to travel faster than one in a higher orbit. when this force difference exceeds the gravitational force of the moon on itself, then the moon spreads out- like lumpy peanut butter on bread.

do you agree?

no, i don't.
http://en.wikipedia.org/wiki/Jupiter#Moons

 

[William Gaatjes]

no, i don't.
http://en.wikipedia.org/wiki/Jupiter#Moons

Always fun to become aware of more interesting items ^_^ :

The orbits of Io, Europa, and Ganymede, some of the largest satellites in the Solar System, form a pattern known as a Laplace resonance; for every four orbits that Io makes around Jupiter, Europa makes exactly two orbits and Ganymede makes exactly one. This resonance causes the gravitational effects of the three large moons to distort their orbits into elliptical shapes, since each moon receives an extra tug from its neighbors at the same point in every orbit it makes. The tidal force from Jupiter, on the other hand, works to circularize their orbits.[104]

The eccentricity of their orbits causes regular flexing of the three moons' shapes, with Jupiter's gravity stretching them out as they approach it and allowing them to spring back to more spherical shapes as they swing away. This tidal flexing heats the moons' interiors by friction. This is seen most dramatically in the extraordinary volcanic activity of innermost Io (which is subject to the strongest tidal forces), and to a lesser degree in the geological youth of Europa's surface (indicating recent resurfacing of the moon's exterior).

Along with the Sun, the gravitational influence of Jupiter has helped shape the Solar System. The orbits of most of the system's planets lie closer to Jupiter's orbital plane than the Sun's equatorial plane (Mercury is the only planet that is closer to the Sun's equator in orbital tilt), the Kirkwood gaps in the asteroid belt are mostly caused by Jupiter, and the planet may have been responsible for the Late Heavy Bombardment of the inner Solar System's history.[108]

http://en.wikipedia.org/wiki/Laplace_resonance

 

[Evadman]

Always fun to become aware of more interesting itemshttp://en.wikipedia.org/wiki/Laplace_resonance

You should check out the Greek, Trojan and Hilda asteroids at the L3, L4 and L5 positions in the Jupiter-Sun orbit. Also, watch this.

 

[William Gaatjes]

You should check out the Greek, Trojan and Hilda asteroids at the L3, L4 and L5 positions in the Jupiter-Sun orbit. Also, watch this.

The video gets more beautiful as time passes.
But the flashes of clustered white dots are i assume new found asteroids ?

EDIT:

Never mind. I just now read the text below the video.

 

[bwanaaa]

omg! all those red dots are so close!

 

[JTsyo]

OP your goal of creating a ring for the earth is bound to fail since the earth doesn't have any other moons to be shepherd moons.

 

[bwanaaa]

OP your goal of creating a ring for the earth is bound to fail since the earth doesn't have any other moons to be shepherd moons.

I guess the pieces would eventually fall to earth. But could you imagine if we could do it?! create a belt of millions of pieces, polish the surface of each piece that faces the earth with a laser-make sure that the pieces focus at the narrow belt on the moon's ecliptic projected on the earth. Put solar collectors around the earth to generate limitless supplies of power.

larry niven would be intrigued.
electricity would be free , like the air.


OTOH, looking at some of those beautiful graphs above, we better be prepared for some nasty bits fallin in toward the earth - not to worry, we'll make the pieces small enough so that they burn up as they hit the atmosphere.

or we can wait until chinese nuclear reactors start to fail. you think they dont have earthquakes too?