Determining Gravitic Pull

[Steve Long]

OK, Science Wizards, let's talk about gravity!

 

As you know, I'm working on The Ultimate Metamorph, which covers (among many other things) Density Increase and Growth. For purposes of dealing with ultra-heavy characters (including macroscopic characters), it would be nice to include some short, simple information/rules on the sort of gravitic effects a truly heavy/large character could exert.

 

Before I start delving into all this astrophysical stuff myself, I figured I'd find out if any of you out there have already considered the issue. For example:

 

--At what amount of weight would a character begin exerting a noticeable (i.e., game effective) gravitic pull on other characters and objects? How would that go up as the character's weight/size increase?

 

--Does the character's shape or composition effect this?

 

 

If anyone has any thoughts or formulae they'd like to provide, feel free. Otherwise I'll just break out the ol' slide rule and gee up something myself.

[Super Squirrel]

Re: Determining Gravitic Pull

 

I'm pretty sure this is the answer but I'm still trying to comprehend it.

http://en.wikipedia.org/wiki/Gravity#Gravitational_potential

[Doc Democracy]

Re: Determining Gravitic Pull

 

OK, Science Wizards, let's talk about gravity!

 

As you know, I'm working on The Ultimate Metamorph, which covers (among many other things) Density Increase and Growth. For purposes of dealing with ultra-heavy characters (including macroscopic characters), it would be nice to include some short, simple information/rules on the sort of gravitic effects a truly heavy/large character could exert.

 

Before I start delving into all this astrophysical stuff myself, I figured I'd find out if any of you out there have already considered the issue. For example:

 

--At what amount of weight would a character begin exerting a noticeable (i.e., game effective) gravitic pull on other characters and objects? How would that go up as the character's weight/size increase?

 

--Does the character's shape or composition effect this?

 

 

If anyone has any thoughts or formulae they'd like to provide, feel free. Otherwise I'll just break out the ol' slide rule and gee up something myself.

 

 

Oooh gravity.

 

Well, the simple part I'll jump in and answer first. Gravity is a question of mass and thus shape and composition do not affect this.

 

Given sensitive enough equipment then any mass will have a noticeable effect on any other mass - the earth pulls you toward it and we pull the earth towards us - its reciprocal but the earth wins out on a massive scale!

 

We have no real handle on gravity and how it works (haven't discovered gravitons or anything like that yet) so all our stuff is based on measurements which are all distorted by the presence of other gravity inducing masses around the experiment.

 

The equation used to describe the attraction between two bodies of matter is

 

F = G(Mm/r^2)

 

Where F is the force of attraction [measured in Newtons (N)], the mass of one body is M and the other is m, the distance between them is r and the gravitational constant is G [6.67 x 10^-11 N(m^2/kg^2)].

 

That's the equation. I'm not sure what force we begin to sense with our skin but I'd suspect that in a gravity well it may have to be within orders of magnitude of the gravity well (tenth or a hundredth at least).

 

 

Doc

[Cancer]

Re: Determining Gravitic Pull

 

AAAARRRRRRRRRRGGGGGGGGGGGHHHHHHHH

 

Here I was ready to get lots of productive work done this morning and then you post this.... sigh. Some general comments here, and quantitative ones later.

 

General comment: on a human scale, the effects of self-gravity are extremely negligible and differential gravity (tides) are smaller than that.

 

Standard solid matter ... rock, ice, metal ... does not deform under the force of its own gravity until you have a chunk of it on the order of a couple of hundred kilometers in diameter.

 

A standard freshman physics homework problem is to determine how large an asteroid you can jump off strictly with leg strength. That depends on density, obviously, but solids (and liquids) have a pretty narrow range of densities, mostly in the range 1 to 10 (grams/cm^3 == metric tons/m^3).

[keithcurtis]

Re: Determining Gravitic Pull

 

Well' date=' the simple part I'll jump in and answer first. Gravity is a question of mass and thus shape and composition do not affect this.[/quote']

 

Actual shape is extremely important. I can stand on the surface of the earth. If I tried to stand on a hunk of neutronium with the same mass as earth, I would be paste. Shape and size determine surface gravity and tidal forces. I would post a lot more, but I would defer to our actual astronomers.

Doc Anomaly?

Other than that, I think a good fraction of gravity that makes a difference to game play would be 1/32 g. 1/16 g would be detectable, I imagine, but 1/32 would pull you back down so slowly that it shouldn't have any effect on game movement.

 

Keith "Any other ideas?" Curtis

[Super Squirrel]

Re: Determining Gravitic Pull

 

Earth's ~M = 7 x 10^24kg

Moon's ~M = 6 x 10^22kg

Sun's ~M = 2 x 10^30kg

 

Earth and the Moon are off by a magnitude of 10^2

They are at +1 1/2 MegaScale

 

Earth and the Sun are off by a magnitude of 10^6

They are at +2 MegaScale

 

I would say you need at least 10^6 difference in Mass the Mass of your Location to begin showing signs of influencing the effect the course of gravity for an object and that for every 10^1 difference in Mass, you extend your range of influence from a base +0 Megascale by +1/4.

[Doc Democracy]

Re: Determining Gravitic Pull

 

Actual shape is extremely important.

 

Hmmm.

 

Perhaps I was hasty!

 

The r in the equation would measure from the 'centre' of one mass to the 'centre' of the other.

 

As Force will increase inversely with the square of that distance then you get the Force quadrupling as the distance of r halves (correct?).

 

It wouldn't matter whether the shape of the substance was a sphere or a square or humanoid. Just the distance from the 'centre' of the mass.

 

Composition therefore matters while shape does not - the more dense the material is then the smaller it is with regard to similar masses and thus the smaller the distance of r and thus the much greater increase in F.

 

I think that puts us on the same page a la neutronium Keith, yes?

 

 

Doc

[Cancer]

Re: Determining Gravitic Pull

 

Actual shape is extremely important.

 

Err ... sorry, that's exactly wrong, as long as you're far enough away. Shape doesn't matter at all. I refer you to Gauss's Law.

 

It could matter if (for example) you had a standard spaceship trying to escape the grasp of a humanoid 1 AU tall. If you (the ship) are nearly in its grasp, then you have to use the integral of the mass distribution, because you're "inside" the gravitating mass, sort of.

 

But if you are safely outside the gravitating mass, it can be formally shown that shape does not matter.

[Cancer]

Re: Determining Gravitic Pull

 

Your life will be simpler if you use scaling relations rather than the raw equations.

 

for example, instead of going back to G = G m1 m2 / r^2, use

 

a = g * (m / m0) / (r / r0)^2

 

where a is the acceleration of the "target" caused by gravity of the "caster",

g is 1 Earth gravity (9.8 meters second^-2),

m is the mass of the "caster",

m0 is the mass of the Earth (6.0e+24 kg),

r is the distance from the center of the "target" to the center of the "caster",

r0 is the radius of the Earth (6,400 km).

 

Another form, the logarithmic one, is

 

log( a / g ) = log( m / m0 ) - 2 * log( r / r0 )

or

log a = 1.0 - log( m / m0 ) - 2 * log( r / r0 )

Where in that last one, a is meters second^-2. As long as you are consistent, it does not matter which flavor of logs you use, of course.

 

It turns out that for astronomical objects (stars, black holes, etc.) you will more commonly find things listed in solar units or centimeter-gram-second units. (These are the units I keep in my head, actually; it turns out in cgs units, the mass of the sun and the luminosity of the sun have the same exponent, 33 ... solar mass is 2e+33 grams, solar luminosity is 4e+33 ergs/second.) Then you can use

 

log a = 4.44 + log( M ) - 2 log R

where a now is in centimeters second^-2

M is the mass of the "caster" in solar masses,

R is the distance from the center of the "target" to the center of the "caster" in units of the solar radius (7e+5 km).

(The surface gravity of the Sun is 28 times the surface gravity of the Earth.)

 

1 AU = 215 solar radii. 1 parsec = 206265 AU. Do not soil yourself by trying to use light-years.

[Phil]

Re: Determining Gravitic Pull

 

Actual shape is extremely important. I can stand on the surface of the earth. If I tried to stand on a hunk of neutronium with the same mass as earth' date=' I would be paste. Shape and size determine surface gravity and tidal forces. I would post a lot more, but I would defer to our actual astronomers.[/quote']

 

But it sounds to me like you're actually saying not that shape is important, but density. It doesnt matter whether the Earth is cuboid or spherical (unless it's purely cuboid and you're straddling the edge - *ouch*), and it doesnt matter whether that hunk of neutronium is cuboid or spherical, you're still squished.

 

Phil

[Phil]

Re: Determining Gravitic Pull

 

Also, in terms of the gravity effect of a Mass Increased character on other characters, I think you're treading dodgy ground invoking science. Because if you invoke science on gravity between two PCs, you cant just ignore other aspects of mass and gravity...

 

Such as the effect of having an object of only 2sq m with sufficient mass to exert 1/32G standing on the average street!

[garou]

Re: Determining Gravitic Pull

 

If I did my math correctly (which is suspect with an 18-month-old pulling at my arm as I type), and using a = GM2/r^2, I came up with some random values:

 

If you weigh a mere 3,200,000 kilos, you start exhibiting noticable gravitational effects if r is a mere 0.02 meters. (In this case, noticable is a half g of acceleration). If you want to have an effect at 10 meters, a mere 819,200,000,000 kilos will suffice.

 

You might be better off expressing everything in terms of levels of growth that are required to affect someone at 0 hexes, 1 hex, 2 hex, etc - but I suspect that beyond 1 hex, the levels of growth or density increase needed to get .5 g (or 1g).

 

(Again, if my math is correct, you need about 145 points of density increase in order to have .5g of pull on everything within 2 meters.)

[Steve Long]

Re: Determining Gravitic Pull

 

You might be better off expressing everything in terms of levels of growth that are required to affect someone

 

That's exactly what I intend to do... assuming I can boil down all this information in a way that I'm satisfied is reasonable. (Though actually I believe it should depend on mass, not on size, so what you'd look at is the character's mass from DI, Growth, and/or Shrinking.) Fortunately, at the root level of things I only have to satisfy dramatic reality, not real reality.

 

Thanx for the info so far, folx! Please feel free to post more if you like.

[Cancer]

Re: Determining Gravitic Pull

 

You might be better off expressing everything in terms of levels of growth that are required to affect someone at 0 hexes, 1 hex, 2 hex, etc - but I suspect that beyond 1 hex, the levels of growth or density increase needed to get .5 g (or 1g).

 

(Again, if my math is correct, you need about 145 points of density increase in order to have .5g of pull on everything within 2 meters.)

 

(I didn't check your math; it doesn't feel terribly off, though.)

 

You may be able to relate that to STR equivalent via the Lifting rules, too. Assuming that the weight that a given STR can lift corresponds to inducing a 0.1 gee acceleration upon the lifted weight, and now you can try relating the passive effects of gravity in that way.

 

Use the scaling law for how acceleration changes with distance, and at that point you have fully defined the passive gravitational effect of the gravity field in the same terms as Telekinesis: its STR equivalent, with the direction always directed toward the gravity source.

 

[That could lead to some serious inconsistencies, though. By no means have I thought this through, trying to mesh HERO with real physics.]

 

There's gonna be some "collateral damage" things that are harder to figure ... atmospheric pressure is one. Another is damage to structures. A lot of structures are strong enough to stand up against gravity ONLY if gravity is directed in what the building thinks of as "down". Even very minor changes to that could cause structural failures.

[ajackson]

Re: Determining Gravitic Pull

 

Ok, the force of gravity is GMm/r^2. The acceleration is GM/r^2.

 

To produce 1G at 1 hex, GM/(4m^2) = 10 m/s^2

GM = 40

M = 40/G = 40/6.67x10^-11 = 6x10^11kg

 

33 levels of increased mass gives a mass between 4x10^11kg and 8x10^11 kg, which we can call 1g at 1 hex.

 

As a more general rule, if (DI1) is the first character's levels of increased mass (both density increase and growth), and (DI2) is the second character's level, and ® is the range modifier (treat 1 hex range as a range modifier of +2), the total strength is (DI1 + DI2 + R - 33) * 5.

 

More random points: a white dwarf has a typical density of up to 100T/cc, or around 26 levels of density increase. A neutron star has a typical density of up to 100MT/cc, or around 46 levels of density increase. The schwarzchild radius for a black hole is 7.4x10^-28m/kg, so a character has an event horizon equal to his size if (density increase + 2/3 growth + shrinking) >= 90.

[Rapier]

Re: Determining Gravitic Pull

 

Actual shape is extremely important.

 

Actually, thats not the case at all. Gravity, in its pure definition, is about the attraction of two objects of mass. Period. The equation for determing gravity contains values for the force of gravity, the mass of the objects, their distance apart and the universal gravitational constant ("Big G"). No mention of shape or size at all.

 

Where it can get confusing is when you start talking about gravity between two objects when one was is "standing" upon the other and the larger mass is rotating. Two entirely different things.

 

Shape and size determine surface gravity and tidal forces.

 

Actually, this is also incorrect. Again, you are confusing gravity with other forces. Shape and size effect rotational motion and centripetal force. Spin a basket ball and it spins nice and easy. Spin an oblong hunk of rock and it doesn't spin so nice and easy.

 

Tidal forces are generated by a large mass object (the moon) exerting an attractive force (gravity) on a large fluid body (the oceans). The moon pulls the water molecules towards it in a periodic fasion. Since the oceans are so large and this force has been acting for SUCH a long time, a nice wave dynamic is formed that we call tides.

 

To answer Steve's question, every single object of mass effects every other object of mass in the universe. The problem is that the effect is SO small that it usually cannot be measured. To get a gravitic effect noticeable in anything other than a high energy particle lab would take one serious hunk of mass. One so large that its presence would have to be solely a plot device.

[ajackson]

Re: Determining Gravitic Pull

 

The above explanation of tides is incorrect. Tidal effect is caused by differential gravitational effects -- as the near side of the earth is only 378,000 km from the moon, and the far side is 391,000 km, while the average distance is 384,400 km, the force of lunar gravity on the near side is about 7% stronger than on the far side, which has the net effect of stretching the earth slightly. As the oceans are somewhat more fluid than the body of the earth, they move more.

[keithcurtis]

Re: Determining Gravitic Pull

 

Thanks, ajackson, you saved me from a lot of typing.

 

As for other people's comments, the use of the word "shape" was unfortunate; I was merely trying to tie my intro to the quote. I meant the radius of the object ('shape' in very poor parlance) in relation to the mass could make decided differences in the the interaction of two bodies at near distances.

Hence my comment about tidal forces. On the surface of a earth-massed Neutron star (I know, I know, bear with me for the purposes of the analogy), surface gravity would act very differently than on the surface of the earth. It would have very little difference when describing the broad motions of the earth-luna system if the earth were replaced by a hunk of neutronium. I would guess (without doing a lick of math) that the moon would still be outside it's Roche limit.

 

Keith "But this is digression, unless Steve is positing a Neutron Star character" Curtis

[Hawksmoor]

Re: Determining Gravitic Pull

 

Boring...

 

This is the part that is less fun, when all the math geeks come out and take over the game.

 

Gravity = Stuff Falling.

 

All stuff falls at the same rate.

 

Big Stuff Small Stuff

 

Really Really Really Really Big Stuff like Kronos the Titanian Eternal goes Desolid at 1 AU.

 

Really Really Big Stuff like Ego the Living Planet is just an SFX.

 

Hawksmoor

[ajackson]

Re: Determining Gravitic Pull

 

The roche limit is determined by the density of the moon, not the density of the planet, so yes, it would be unaffected

 

Incidentally, the densities I gave for white dwarfs and neutron stars are upper limits; density can vary significantly. Typical white dwarf density is more on the order of 1 ton/cc (20 levels DI). Neutronium density ranges from 10^14 to 10^15 (46-50 levels).

[ajackson]

Re: Determining Gravitic Pull

 

Oops. I made one mistake on the schwarzchild radius comment: I forgot that shrinking reduces mass. Change it to (DI + 2/3 Growth - 2 * Shrinking) >= 90.

 

Not that any of this stuff is likely to come up in a typical game. A character with 33 levels of increased mass, and a Str of 175, is outside the power level of most games, and characters in games at that power level are unlikely to be concerned about a measly 1g gravity field.

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Hmmm...looks like I came a little late to this party. Most of the math has already been presented, and pretty well. A number of years ago, just for fun, I calculated how much DI someone would need to be able to curl up inside their own Schwarzchild radius if they tucked their arms & legs close in to their bodies. I'll see if I can dig that up, because it's also possible (IIRC) that I did a sort of sliding scale of gravitic potential to go with it, between 0 DI and whatever the max was.

 

By the way, shape does have an effect on how one object's gravity affects another. For example, if the mass of the Earth were reorganized so that, keeping its current average density, it formed a cylinder that was 1 million miles long, then at any given point along the length of that cylinder you'd feel a lot less than 1g because you'd be much further away from most of its mass than you are now. Likewise, if the Earth were in fact hollow (leaving aside the structural problems with that) if you were inside the hollow space at the center of the Earth, you'd be in free-fall, and that's at any point inside the hollow sphere, not just at the exact center. That's because if you draw two conic sections whos points touch at your location, and then calculate the mass in each conic section as well as the gavitic pull those masses exert on the point, you'll find they balance out. The cone that takes in mass from the side of the sphere closer to you has less mass in it, but the mass is closer to you; the cone that takes in the area further away from you has more mass in it, but the mass is further away. They balance out.

 

Now, I'm perfectly aware that in the "cylinder" case above, what's really been done is to change the average spacial density of the matter distribution by deforming it into a radically non-spherical form, but you get the idea. Topology does play a role in the gravitational pull you feel from an object, assuming the object is non-spherical (and the more radical the deformation, the more it will vary from the equations being used for an idealized sphere).

 

I'll see if I can dig up the calcs I mentioned.

[ghost-angel]

Re: Determining Gravitic Pull

 

All stuff falls at the same rate.

Until you take into account Air Resistance in which case all objects obtain a Terminal Velocity based in part on Mass and part on Surface Area.

[Steve Long]

Re: Determining Gravitic Pull

 

This is the part that is less fun, when all the math geeks come out and take over the game.

 

That's the whole point of my asking. I want some reasonably "accurate" basis for making a decision, then I'm going to get this math 'n' science crap outta the way and boil it down for you, the faithful reader, into something with sufficient dramatic realism that you can easily and enjoyably use it in your game... without having to worry about the math.

[keithcurtis]

Re: Determining Gravitic Pull

 

...And bless you sir, for doing it!

 

Keith "putting stuff behind the curtain" Curtis