Guest lucky Posted March 8, 2005 Report Share Posted March 8, 2005 Okay, so what would happen to the moon if a chunk of its center suddenly vanished? Say 800 cubic km of matter disappeared from its core--would that throw off its orbit or anything? Quote Link to comment Share on other sites More sharing options...
Trebuchet Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question Okay' date=' so what would happen to the moon if a chunk of its center suddenly vanished? Say 800 cubic km of matter disappeared from its core--would that throw off its orbit or anything?[/quote']Absolutely. Since it would then mass less, the Earth's gravity would pull it in closer, and assuming it doesn't crash into the Earth (unlikely) then it would eventually stabilize in a closer and faster orbit. That would affect tides and other things on Earth. Quote Link to comment Share on other sites More sharing options...
Herolover Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question Absolutely. Since it would then mass less' date=' the Earth's gravity would pull it in closer, and assuming it doesn't crash into the Earth (unlikely) then it would eventually stabilize in a closer and faster orbit. That would affect tides and other things on Earth.[/quote'] Possibly not. 1) This would very obviously change the moon's mass. If the moon's mass were to change its major effects would be on the moon's velocity and the moon's gravity. Without the Mass the moon would either do as above or it could possilbly speed off into the universe at large. Either way the earth is screwed. The moon controls many tidal effects in the oceans and the lack of those tidal actions would greatly affect the earth. I think I even read somewhere that the change would effect the heat transfer ability of the oceans which would destroy life on the earth. I suggest you do a google search on this. Quote Link to comment Share on other sites More sharing options...
austenandrews Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question It would change the Earth-Moon binary system, but I doubt it would be noticable. You're talking about removing the middle 6 km radius of a 3,500 km radius sphere - pretty small. The moon's core is around 340km radius and only accounts for 2% of its mass, and the alien ship at the center is going to be far less massive still. (In fact if the ship is mostly open space, that means the current calculations of the moon's core density will be too low.) The ship's mass is comparatively tiny. The loss of this mass will shift the moon slightly farther from the Earth, but probably not reaching significant digits. The change of momentum (however that works with teleportation) would likewise be pretty small. Much more noticable will be the seismic repercussions. The moon's core will suddenly have a 6 km-deep hole in the middle. It will collapse (unless you posit an alien support structure to keep it from collapsing) and even though the crust's compressibility will reduce the surface displacement, you're still going to have some catastrophic moonquakes. Good thing there's no oceans, or last Christmas's tsunami would look like a ripple on a pond. Quote Link to comment Share on other sites More sharing options...
Nadrakas Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question It would change the Earth-Moon binary system' date=' but I doubt it would be noticable. You're talking about removing the middle 6 km radius of a 3,500 km radius sphere - pretty small. The moon's core is around 340km radius and only accounts for 2% of its mass, and the [b']alien ship [/b]at the center is going to be far less massive still. (In fact if the ship is mostly open space, that means the current calculations of the moon's core density will be too low.) The ship's mass is comparatively tiny. The loss of this mass will shift the moon slightly farther from the Earth, but probably not reaching significant digits. The change of momentum (however that works with teleportation) would likewise be pretty small. Much more noticable will be the seismic repercussions. The moon's core will suddenly have a 6 km-deep hole in the middle. It will collapse (unless you posit an alien support structure to keep it from collapsing) and even though the crust's compressibility will reduce the surface displacement, you're still going to have some catastrophic moonquakes. Good thing there's no oceans, or last Christmas's tsunami would look like a ripple on a pond. Huh??? What Alien Ship??? Nadrakas... Quote Link to comment Share on other sites More sharing options...
austenandrews Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question Huh??? What Alien Ship??? Nadrakas... What, you hadn't heard? Quote Link to comment Share on other sites More sharing options...
Nadrakas Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question What' date=' you hadn't heard?[/quote'] The Selenites? Or some other Alien Race??? Nadrakas... Quote Link to comment Share on other sites More sharing options...
Guest lucky Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question the alien ship at the center Huh??? What Alien Ship??? Thanks for referencing my other thread, austenandrews--I should have provided the context myself. I'm working up an idea for a science-fiction-supers game and one of the "kickoff" events is the discovery of a massive alien ship at the center of the moon. The ship is 25km long by 8km wide by 4 km high; truly gargantuan, in other words. Shortly after its discovery, the ship's Faster-Than-Light drive initiates and it vanishes. I want to know what effect this will have and so far I've heard some good answers... Quote Link to comment Share on other sites More sharing options...
keithcurtis Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question I have to second AustenAndrews' assessment, and add that sufficiently violent moonquakes should have minor effects on earth tides, perhaps enough to trigger some "quakes in the waiting". Also, to refute one part of Trebuchet's statement: an object which masses less is not going to be pulled in closer by the earth. If all other things remain constant, it's orbital velocity should cause it to gain a slightly higher orbit. Or maybe just the barycenter of the earth/moon system would change, I'm not sure. But it won't crash into the earth just by missing a tiny portion of its mass. Keith "caveat: I am not a scientist" Curtis Quote Link to comment Share on other sites More sharing options...
austenandrews Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question Though the moon isn't seismically active, I bet you could plausibly arrange for the moonquakes to hurl a big cloud of little rocks at the Earth. You could have a dazzling meteor shower plus a bunch of nasty little impacts. Unfortunately the PCs won't be around to see it, I guess. Quote Link to comment Share on other sites More sharing options...
Trebuchet Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question r some "quakes in the waiting". Also, to refute one part of Trebuchet's statement: an object which masses less is not going to be pulled in closer by the earth. If all other things remain constant, it's orbital velocity should cause it to gain a slightly higher orbit. The orbital trajectory of any moving body is a balance of force between where the orbital velocity of the body's mass in space is equaled by the pull of gravity between the two bodies. If mass "disappears" then the resulting reduction in gravitational attraction will result in an outward shift in the orbit until the forces balance again. (The other method would be to have the body reduce orbital speed, but his scenario does not postulate that variation). Earth's moon has been drifting further away from Earth for eons due to tidal braking slowly reducing it's speed. Some astronomers estimate that hundreds of millions of years ago the moon was only 40% as far away from Earth as it is now. In this particular scenario, with such a small mass removed the effect on the orbit would likely be very small; perhaps undetectable to the naked eye. While there would probably be moonquakes, those probably won't be of much interest except to astronomers. Quote Link to comment Share on other sites More sharing options...
Nadrakas Posted March 8, 2005 Report Share Posted March 8, 2005 Re: Astronomy/Physics question Thanks for referencing my other thread' date=' [b']austenandrews[/b]--I should have provided the context myself. I'm working up an idea for a science-fiction-supers game and one of the "kickoff" events is the discovery of a massive alien ship at the center of the moon. The ship is 25km long by 8km wide by 4 km high; truly gargantuan, in other words. Shortly after its discovery, the ship's Faster-Than-Light drive initiates and it vanishes. I want to know what effect this will have and so far I've heard some good answers... Ok...I'm hearing that the ship is too small to create a problem other than some moon quakes & a couple of depressions in the moons surface. Sooooooo....here is an option. I will assume that for the sake of argument that the FTL drive of the alien ship is a "Hyperspace" or "Jump" style drive. Now...let's say that when the ship goes to FTL that it actually takes a rather large chunk of the moon with it -- say...100 km radius (200 km diameter) from the center of the alien ship. Here is how that would work out: Moon Facts: (http://www.seds.org/nineplanets/nineplanets/luna.html) - Orbit = 384,400 km from Earth - Moon Radius = 1,738 km Radius (3,476 km Diameter) - Volume = 2.199064287e10 km^3 (21,990,642,870 km) - Mass = 7.35e22 kg (73,500,000,000,000,000,000,000 kg) - STR required to lift = 345 Moons Core: - Core Radius = 340 km Radius (2 percent of the Moons total volume) - Core Volume = 164,636,210.2 km^3 - Core Mass = 1.47e21 (1,470,000,000,000,000,000,000 kg) - STR Required to Lift = 330 Results of 100 km Radius/200 km Diameter: - Volume Removed = 4,188,790.205 km^3 (.019 percent of the Moons total volume, & .75 percent of the Cores volume) - Mass Removed = 3.740077346e19 kg (37,400,773,460,000,000,000 kg or .05 percent of the Moons total mass & 2.5 percent of the Cores mass.) - STR Required to Lift = 305 Ships info (25 x 8 x 4): - Dimensions = 25 km long, 8 km wide, 4 km wide - Dimensions in Hexes = 12,500 Hexes long, 4,000 Hexes wide, 2,000 Hexes high - Ship Volume = 800 km^3 (.000003 percent of the Moons total volume or .01 of the Cores Volume - Ship Volume in Hexes = 400,000 Hexes^3 - Ship Real Mass = Unknown - Mass According to Ultimate Vehicle = 64,000,000,000,000 kg (64 million metric tons. This is .00000008 percent of the Moons total mass or .001 of the Cores mass) - STR Required to lift ship = 158 - Volume Removed = 800 ^3 Formula for Volume = (pi x r^3) * 4/3 So...what does this all mean? Well...consider this -- the 100 km radius "Jump" is 5,235.98775625 times the volume & 584,387.0853125 times the mass of the Alien Ship. In other words...a really big difference. Now personally I would eshew the "numbers" game and go for the dramatic effect. Yet...having really "HUGE" numbers to feed to players will allow for them to truly believe that whatever happens to the moon during the game is plausible. Whew...now that the Math Exercise is over I would like to thank my wonderful wife "Isis" (Who does math for fun) for assisting me (a whole lot) in figuring out the above. She's the smart one in the family. Any mistakes in the above are wholly mine. Nadrakas... Quote Link to comment Share on other sites More sharing options...
SirViss Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question I would ,like to point out that the mass of an object has no real bearing on where it would orbit. I had too get my astronomy book out, but the radius of an orbit is calculated thus: r = (GM)/v² r -> Radius of the orbit G -> Gravitational constant M -> Mass of the planet orbited v -> orbital velocity The mass of the "satelite" is not really important to the distance at which it orbits, because the orbital accelaration has to exactly compensate for the accelaration from gravity. So, if the velocity of the moon remains unchanged, there won't be a change in orbit. Now, it up to you to say that the Moon would go faster, slower or stay at the same velocity. I haven't done this kind of math in a long time, so I am going to go lie down. Quote Link to comment Share on other sites More sharing options...
Dave Baum Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question The orbital trajectory of any moving body is a balance of force between where the orbital velocity of the body's mass in space is equaled by the pull of gravity between the two bodies. If mass "disappears" then the resulting reduction in gravitational attraction will result in an outward shift in the orbit until the forces balance again. It has been a long time since I took Physics, but I thought that orbits are when the centripetal force matches the gravitational force. Since both of these forces are proportional to the mass of the orbiting object, mass cancels out and orbital distance is determined by the velocity of the orbiting object and the mass of the center object. Removing mass from the moon therefore should not change its orbit. Am I missing something? Dave p.s. I'm assuming that instantly removing the mass also means instantly removing the kinetic energy associated with that mass. Otherwise, to maintain the same energy, the reduced amount of mass would have to move faster, and that means a larger orbit. Quote Link to comment Share on other sites More sharing options...
austenandrews Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question I was thinking of in terms of conserving momentum while losing mass, which of course would result in higher velocity. I'm not sure why I thought it would work that way, though it's as plausible as not if you're talking about vanishing matter. Quote Link to comment Share on other sites More sharing options...
keithcurtis Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question That was my assumption as well. Keith "But in any case, the moon would not break orbit, leave the solar system and encounter a new planet every week yet stay in the area long enough for multiple vehicle transfers and eventually pick up a hot alien shapeshifter" Curtis Quote Link to comment Share on other sites More sharing options...
Foxiekins Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question Okay, here goes... If that mass vanishes away, there will be no change in the Moon or the Earth's velocity... However... What *will* change slightly is the position of the Center of Mass of the combined Earth/Moon pair, which will suddenly be a bit closer to the center of the Earth than it is now, as well as the gravitational effects of the Moon upon the *Earth*... Earth's mass doesn't change, so the effects of the Earth on the Moon don't change... Earth doesn't curve about as sharply in its orbit of center of system mass as it did before, and Earth's individual center of mass is suddenly closer to the new overall center of mass... Since this is an instant effect, it would introduce an increase in the system's orbital eccentricity... Over time, this would be quite noticable as it will affect orbital periods in the long term, and eventually throw all the Tide Tables off... The length of a Lunar Month will definately increase... The Jewish Calender will be screwed... Dunno offhand what will happen to the Moon's surface itself, though... A slight reshaping possibly, but I don't think there would be anything that would produce escape velocity events... Quote Link to comment Share on other sites More sharing options...
keithcurtis Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question I had mentioned the change in earth-moon Center of Mass in my first post (the barycenter). Also if the length of the Lunar Month increases, then the orbit has to get higher. Keith "The fun part is where did all that lunar material go?" Curtis Quote Link to comment Share on other sites More sharing options...
Dr. Anomaly Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question Since this is an instant effect' date=' it would introduce an increase in the system's orbital eccentricity... Over time, this would be quite noticable as it will affect orbital periods in the long term, and eventually throw all the Tide Tables off... The length of a Lunar Month will definately increase... The Jewish Calender will be screwed...[/quote']Actually, not really...not on a timescale of human civilization, anyway. I don't feel like running the numbers just now (all-day headache I can't shake) but remember the Earth picks up 40,000 metric tons of mass per year on average due to swept-up dust, meteors, and so forth. The moon pics up less (smaller cross section, gravity well is shallower) so this should be shifting things in the Earth's favor bit by bit. I realize the size of the chunk of material you're talking about here is quite a bit larger than the Earth's yearly average increase, but when you look at the time scales involved before you'd notice any changes in the calendar and such, the "normal" addition of mass to the Earth would be a larger impact, orbital mechanics-wise, and it hasn't caused any major destabilizing effects. Remember: just because the period of major planet formation is long past doesn't mean that the accumulation of small fragments onto larger ones has ceased... Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question Okay' date=' so what would happen to the moon if a chunk of its center suddenly vanished? Say 800 cubic km of matter disappeared from its core--would that throw off its orbit or anything?[/quote'] No, definitely not. The force of Earth's gravity on the Moon remnant would diminish only in proportion as the Moon's mass diminished, so the acceleration due to that force (a=F/m) would be unchanged. The velocity and acceleration of the remnant would be unchanged from what they are, and so it would continue in teh same orbit that it is in now. The shell would collapse into the core, releasing an enormous amount of energy as shockwaves. These might raise some material off the surface, but there would definitely not be enough energy to disassemble the moon. The inmost core of the remant would be liquefied as the shockwaves dissipated into heat. Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question Am I missing something? Nothing of the slightest significance. The reduction in the Moons mass will mean infinitesimally smaller lunar gravitation on the Earth, which means an imperceptibly different trajectory for the Earth, which means a slightly different future orbit for the Moon. But the effect is truly tiny. Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question Since this is an instant effect' date=' it would introduce an increase in the system's orbital eccentricity... Over time, this would be quite noticable as it will affect orbital periods in the long term, and eventually throw all the Tide Tables off... The length of a Lunar Month will definately increase... The Jewish Calender will be screwed...[/quote'] Noticeable? I estimate the loss of mass as 4.5 parts per billion in the mass of the moon. The month will get longer by 0.0104 of a second, throwing the time tables out by a minute after 480 years, and the Jewish calendar out by one day after 690,000 years. In both cases, the effect is far smaller than the existing errors in the tables and calendar. Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question But it won't crash into the earth just by missing a tiny portion of its mass. Indeed not. To hit the Earth the Moon would need to lose nearly all of its orbital velocity. Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question The orbital trajectory of any moving body is a balance of force between where the orbital velocity of the body's mass in space is equaled by the pull of gravity between the two bodies. If mass "disappears" then the resulting reduction in gravitational attraction will result in an outward shift in the orbit until the forces balance again. I'm sorry, but that is rubbish. The centripetal force required to keep an object moving along a give curve is proportional to its mass: the formula is f© = m.v^2/r. The force of gravity on the object is also proportional to its mass: the formula is f(g)= GMm/r^2. Since gravity is the centripetal force: f© = f(g) m.v^2/r = G.M.m/r^2 The two 'm's cancel out, as do two of the 'r's. v^2 = G.M/r r = v^2/(G.M) The [instantaneous) radius of curvature of an object's orbit is independent of the object's mass. Don't you remember the thing about the hammer and the feather falling with the same acceleration on the Moon? Quote Link to comment Share on other sites More sharing options...
Agemegos Posted March 9, 2005 Report Share Posted March 9, 2005 Re: Astronomy/Physics question So...what does this all mean? Well...consider this -- the 100 km radius "Jump" is 5,235.98775625 times the volume & 584,387.0853125 times the mass of the Alien Ship. In other words...a really big difference. 584,387 times zero is still zero. The effect will be massive shockwaves in the Moon, liquefying its core and maybe mantle, and a reduction of its radius by 0.018%, or 320 metres. A small amount of material from the Moon's surface may be thrown off. But the Moon remnant will stay right there in the Moon's orbit, except for a very slight discrepancy owing to a tiny change in the Earth's trajectory, which might accumulate to be noticeable after centuries, except that we really don't know any of these orbits precisely enough to notice the difference. If you want the Moon to fly out of its orbit you are going to have to hit it with something of comparable momentum or else ignore physics. If your players remember 10th-grade physics you aren't ever going to pull this off, and if they don't then you don't need to work out the physics. Why not ignore physics? Quote Link to comment Share on other sites More sharing options...
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