Determining Gravitic Pull

[Cancer]

Re: Determining Gravitic Pull

 

As someone who wears the "math geek" badge with a sense of bitter pride ...

 

Simple gravity is pretty straightforward. Tides could be important but are hugely difficult in the general case.

 

I can imagine a metamorph that would boost himself into C-shaped dumbbell, put all the mass at the ends of the C, arrange the poles (ends of the C) on either side of the target, then rack the density up to get induced local gravity, and let the tidal shear rip the target apart. One can almost do the math for that on the back of an envelope.

 

But that's simplest of many tidal-shear style attacks I can imagine, and the others get really icky fast.

 

And just think, we haven't even mentioned the really fascinating effects of General Relativity! Put someone under and intense enough gravity field ... and we're talking circum-black-hole here ... and their clocks slow down, and the energy level in their emitted light (laser guns) drops, too. It's one hell of a set of sfx for a SPD and EB Drain, though....

[prestidigitator]

Re: Determining Gravitic Pull

 

Thinking from the perspective of translating the simple attractive force into the baseline game terms, I approached the problem by wondering what it would take to affect someone ("target") with average mass (100kg) as if with a game Str of 5 (pushing at full force, which comes to the force it takes to lift 50kg in the Earth's average surface field; this also comes to a damage/Grab effect of 1d6, which is nice) at a distance ("radius") of 4 hexes (the maximum distance for a Range Modifier of zero).

 

It turns out that an object ("source") would have to be approximately 4.7x10^12 kg to have this effect, which is about 35 mass doublings due to Growth/Density Increase. Every doubling of the source's mass should double this force (+5 Str). [EDIT: Every halving of the source's mass should halve the force (-5 STR).] Every doubling of the target's mass should double the force (+5 Str). Every halving of the target's mass should halve the force (-5 Str). Every doubling of radius (next range increment) should divide the force by four (-10 Str). That makes it pretty simple.

 

EDIT: BTW, assuming we can approximate each character as a point mass, the, "distance," should be that between the centers of the two characters, which may well be constrianed by the size of both characters. So Density Increase could be the more effective route if an attacker simply wants to walk up to people and have them stick to him.

[garou]

Re: Determining Gravitic Pull

 

All stuff falls at the same rate.

And technically speaking, that's not even true - g should increase as the distance r decreases, and a very heavy object should fall towards the earth faster than a very light object.

 

Of course, it's still going to be 9.8 m/s^2, because you're never going to actually be able to measure the difference with most instruments.

[ajackson]

Re: Determining Gravitic Pull

 

But that's simplest of many tidal-shear style attacks I can imagine, and the others get really icky fast.

 

Not to mention that any of the tidal-shear attacks require masses close to a billion tons, and if you can throw around that level you might as well just generate a point singularity and wobble it around inside of them. Sure, the rate at which a billion ton black hole actually absorbs matter is negligible, but you still don't want it moving through you (we won't mention hawking radiation, though generating a small black hole and then letting it evaporate a second later will give you explosions that will crack continents).

 

And just think, we haven't even mentioned the really fascinating effects of General Relativity! Put someone under and intense enough gravity field ... and we're talking circum-black-hole here ... and their clocks slow down, and the energy level in their emitted light (laser guns) drops, too. It's one hell of a set of sfx for a SPD and EB Drain, though....

 

Well, unless you're very close to black hole status, it really doesn't matter.

 

Hm..ponder statting up a villian who is a human-sized black hole. Hm. Mass would be about half that of Jupiter, so he'd disintegrate planets. I think that might be a Plot Device character.

 

A character who controlled a primordial micro black hole (say, 1.5e11 kg, for 1g at 1 meter; lifetime of such a black hole is about 10 GYr) is possibly viable as a character. The black hole produces 1g at 1 meter, or Str 0 at 1 hex on a character with no increased mass, which is fairly negligible. It also produces approximately 16 gigawatts of hawking radiation (4 tons/second) with an effective temperature of 800 billion kelvin.

 

If he can also construct quantum black holes, a black hole that will evaporate in one second has a mass of 228 tons and explodes with a force of 5 million megatons, producing a crater somewhere around 15 kilometers deep. This is not quite an extinction-level event, but will produce major global effects.

[prestidigitator]

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.

To be entirely accurate, you actually need to consider a point mass for the F=Gm1m2/r^2 relationship to hold. That means that to calculate the entire force exerted upon an object by another you must perform a double integral: consider an infinitesimal volume of the source and how it affects an infinitesimal volume of the affected mass, then add up all the effects over the volumes of both objects. In reality shape can have a very dramatic effect.

 

To help illustrate this, consider the following thought experiment:

Take two planets of equal size and mass which are a small distance apart and connected by an infintesimally small thread (of zero, or very, very near zero mass), thus making them, "one object," with an absurdly exagerated dumbell shape. The center of mass of this object is going to be midway between the planets (the centerpoint of the thread). All objects in this problem are at rest.

 

Now stand a man on one of the planets, in a location that is closest to the other planet (just next to the connecting thread). Will he start to fall toward the center of mass (i.e. upward toward the center of mass)? Hmm. Maybe it isn't so farfected in our minds, but NOW move the planets twice as far apart (leave everything else the same, so the gravitational fields produced by each planet are the same). Will the man still fall upward? Now move the planets a billion times farther apart. Will the man still fall upward? Now extend the distance between the planets toward infinity. The force of gravity is indeed very dependent upon shape.

[Mister E]

Re: Determining Gravitic Pull

 

As kind of a joke, and to make a point nobody ever got, I started this thread a little while ago:

 

http://www.herogames.com/forums/showthread.php?t=34588&highlight=Planetary+Size+Template

 

It didn't get much response, but it was fun to fool around with. Check it out. The Earth is really big, it turns out.

 

 

Doctor Anomaly: That business about freefalling inside a hollow Earth is fascinating... but I think they should also mention the alternative Pellucidarian Theory in Physics classes.

 

An Edgar Rice Burroughs, (creator of Tarzan), joke.

 

 

~ Mister E

[prestidigitator]

Re: Determining Gravitic Pull

 

And technically speaking' date=' that's not even true - g should increase as the distance r decreases, and a very heavy object should fall towards the earth faster than a very light object.[/quote']

Yes, the force of attraction decreases with radius. Two objects of equal mass falling from the same height should experience exactly the same acceleration, however. The attractive force is proportional to the affected mass, and the acceleration due to a give force is inversely proportional to the affected mass. In a Newtonian sense:

F = m g® = ma

a = g®

Showing that, if the acceleration of gravity is a function of radius alone, acceleration is also a function of only radius (not the mass of the falling object).

 

Now if air resistance is considered, objects might fall at different rates due to their differences in shape, size, and mass. Two objects of identical shape and size will generally fall at different rates in the atmosphere: the heavier one will in fact fall faster. Two objects of identical mass and shape but different size will generally fall at different rates as well: the smaller one will fall faster.

[Drachasor]

Re: Determining Gravitic Pull

 

It's easiest to base calculations of this off of F=mg, where g=9.8m/s/s

We need only concern ourselves with the acceleration towards the mass, which is g=9.8m/s2

 

You have to take into account the difference in distances from and masses between the Earth and the character.

 

Now, the mass of the earth is

Me= 5.9742 x 1024 kg

 

The radius of the Earth is:

 

Re= 6.378 x 106m

 

So the ratio (Q):

Q = Me/Re2 = 1.468 x 1011

 

So let "m" be the mass of the character, "d" be the distance from him, and "f" be the fraction of gravity you want. Then:

 

(g / Q x m / r2) = fg

 

So the mass of the character is m = f x Q x r2

 

If you are interested in 1/10 gravity at 2m, then

 

.1 x 1.468 x 1011x 4 = 5.872 x 1010

 

This jives with the work previous people have done. Anyhow, I think the equation is fairly simple, and you only need to have one hard number: Q.

 

Q = Me/Re2 = 1.468 x 1011

m = f x Q x r2

 

Again, where m is the mass of the character,

r is the distance (in meters, and there are 2 meters per hex) and

f is the fraction of earth gravity you want at that distance.

 

-Drachasor

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Edit: thanks to ajackson point out a couple of very idiotic errors on my part (using an inverse factor at one point, for example) the table has been corrected to what it should have been.

 

Okay, I found the calcs I'd mentioned earlier. When I did these originally, I didn't factor in Shrinking as a possibility, and I assumed that only one character would have active levels of DI going at a time. With that in mind, the basic formula I used was (Levels of DI + Range Mod - 33) x 5 and, like ajackson, I used a +2 as the range mod for "adjacent" (with -0 for a range of 2-4 hexes, -2 for 5-8 hexes, and so on -- the usual).

 

Here's the basic assumptions I used in my calculations:

 

Initial character height: 2m

 

Initial character mass: 100 kg

 

Assuming that if someone "curls up" they'll be about half their usual height, I used a Newtonian radius of ½m which yields an event horizon circumference of Pi, rounded to 3.1416m (the Schwarzchild radius is not needed for this).

 

I initially calculated the gravitational pull at a distance of 1 hex (center-of-mass to center-of-mass, assuming the character using DI is standing in the center of his hex and the character being affected by any gravitational pull is standing at the center of an adjacent hex).

 

Further, I assumed a static Schwarzchild hole and not a Kerr-Newman hole for the type of singularity that would form when the character using DI managed to curl up inside his own Schwarzchild radius. (This seemed a more-or-less safe assumption as it's unlikely he'd have an significant rotational velocity. Besides, and idealized or 'static' Schwarzchild hole is much simpler to model.)

 

As for constants, I used

 

G = 1.327 x 10^11 km^3/sec^2/solar mass (1.98892 x 10^30 kg)

c = 2.998 x 10^5 km/sec

 

With a desired circumference of 3.1416m, crunching the numbers yields a mass of 3.36782609565 x 10^26 kg

 

(For reference, the Earth's mass is approx. 10^25 kg, and if the Earth were crushed into a singularity, it would have an event horizon with a circumference of 1.855 cm)

 

81 levels of DI (405 points) gives a mass of 2.00 x 10^26 kg, and 82 levels of DI (410 points) gives a mass of 4.00 x 10^26. Since our calculated mass is between those, 82 levels of DI is necessary for the character to be able to curl up inside his own Schwarzchild radius.

 

At that density, another character in a hex adjacent to the character using 82 levels of DI would feel a gravitational pull of 2,251,799,813,685,240g.

 

At that same distance (adjacent hex) the character feeling the pull would feel 1g at 31, 2g at 32, 4g at 33, and so on. In other words, for every level of DI past 31, x2 g. Thus 82 levels, being 51 levels past 31, gives a gravitational pull of 2,251,799,813,685,240g.

 

For reference, I've reproduced my original table below, showing the mass of the character using DI as related to the levels of DI in use, and the gravitational attraction he causes at a variety of distances (corresponding to the standard HERO range chart).

 

Or, in a shorter form, with DI = Levels of DI in use, Range = HERO range modifier (using +2 for adjacent) the gravitational attraction is:

 

g = 2^(DI -33 + Range)

 

					Range In Hexes

Mass in kg	Levels	Adjacent		2-4			5-8			9-16			17-32			33-64			65-128			129-256			257-512			513-1024

2.50 x 10^10	28	.125 			
5.00 x 10^10	29	.25 			
1.00 x 10^11	30	.5 			.125 			
2.00 x 10^11	31	1			.25 			
4.00 x 10^11	32	2			.5 			.125 			  	 	 	  	 	 	
8.00 x 10^11	33	4			1			.25 			  	 	 	  	 	 	
1.60 x 10^12	34	8			2			.5 			.125 	 	 	  	 	 	 
3.20 x 10^12	35	16			4			1			.25 	 	 	  	 	 	 
6.40 x 10^12	36	32			8			2			.5 	 	 	.125 	 	 	 			 
1.25 x 10^13	37	64			16			4			1	 	 	.25 	 	 	 			 	
2.50 x 10^13	38	128			32			8			2	 	 	.5 	 	 	.125			 			 
5.00 x 10^13	39	256			64			16			4			1			.25 			  			  		 		
1.00 x 10^14	40	512			128			32			8			2			.5 			.125 			 		 	 		
2.00 x 10^14	41	1,024			256			64			16			4			1			.25 			  		  		
4.00 x 10^14	42	2,048			512			128			32			8			2			.5 			.125		 		 
8.00 x 10^14	43	4,096			1,024			256			64			16			4			1			.25 		  		 
1.60 x 10^15	44	8,192			2,048			512			128			32			8			2			.5 			.125 		 
3.20 x 10^15	45	16,384			4,096			1,024			256			64			16			4			1			.25 		 
6.40 x 10^15	46	32,768			8,192			2,048			512			128			32			8			2			.5 			.125
1.25 x 10^16	47	65,536			16,384			4,096			1,024			256			64			16			4			1			.25
2.50 x 10^16	48	131,072			32,768			8,192			2,048			512			128			32			8			2			.5
5.00 x 10^16	49	262,144			65,536			16,384			4,096			1,024			256			64			16			4			1
1.00 x 10^17	50	524,288			131,072			32,768			8,192			2,048			512			128			32			8			2
2.00 x 10^17	51	1,048,576		262,144			65,536			16,384			4,096			1,024			256			64			16			4
4.00 x 10^17	52	2,097,152		524,288			131,072			32,768			8,192			2,048			512			128			32			8
8.00 x 10^17	53	4,194,304		1,048,576		262,144			65,536			16,384			4,096			1,024			256			64			16
1.60 x 10^18	54	8,388,608		2,097,152		524,288			131,072			32,768			8,192			2,048			512			128			32
3.20 x 10^18	55	16,777,216		4,194,304		1,048,576		262,144			65,536			16,384			4,096			1,024			256			64
6.40 x 10^18	56	33,554,432		8,388,608		2,097,152		524,288			131,072			32,768			8,192			2,048			512			128
1.25 x 10^19	57	67,108,864		16,777,216		4,194,304		1,048,576		262,144			65,536			16,384			4,096			1,024			256
2.50 x 10^19	58	134,217,728		33,554,432		8,388,608		2,097,152		524,288			131,072			32,768			8,192			2,048			512
5.00 x 10^19	59	268,435,456		67,108,864		16,777,216		4,194,304		1,048,576		262,144			65,536			16,384			4,096			1,024
1.00 x 10^20	60	536,870,912		134,217,728		33,554,432		8,388,608		2,097,152		524,288			131,072			32,768			8,192			2,048
2.00 x 10^20	61	1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304		1,048,576		262,144			65,536			16,384			4,096
4.00 x 10^20	62	2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608		2,097,152		524,288			131,072			32,768			8,192
8.00 x 10^20	63	4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304		1,048,576		262,144			65,536			16,384
1.60 x 10^21	64	8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608		2,097,152		524,288			131,072			32,768
3.20 x 10^21	65	17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304		1,048,576		262,144			65,536
6.40 x 10^21	66	34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608		2,097,152		524,288			131,072
1.25 x 10^22	67	68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304		1,048,576		262,144
2.50 x 10^22	68	137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608		2,097,152		524,288
5.00 x 10^22	69	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304		1,048,576
1.00 x 10^23	70	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608		2,097,152
2.00 x 10^23	71	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216		4,194,304
4.00 x 10^23	72	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432		8,388,608
8.00 x 10^23	73	4,398,046,511,104	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864		16,777,216
1.60 x 10^24	74	8,796,093,022,208	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728		33,554,432
3.20 x 10^24	75	17,592,186,044,416	4,398,046,511,104	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456		67,108,864
6.40 x 10^24	76	35,184,372,088,832	8,796,093,022,208	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912		134,217,728
1.25 x 10^25	77	70,368,744,177,664	17,592,186,044,416	4,398,046,511,104	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824		268,435,456
2.50 x 10^25	78	140,737,488,355,328	35,184,372,088,832	8,796,093,022,208	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648		536,870,912
5.00 x 10^25	79	281,474,976,710,656	70,368,744,177,664	17,592,186,044,416	4,398,046,511,104	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296		1,073,741,824
1.00 x 10^26	80	562,949,953,421,312	140,737,488,355,328	35,184,372,088,832	8,796,093,022,208	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592		2,147,483,648
2.00 x 10^26	81	1,125,899,906,842,620	281,474,976,710,656	70,368,744,177,664	17,592,186,044,416	4,398,046,511,104	1,099,511,627,776	274,877,906,944		68,719,476,736		17,179,869,184		4,294,967,296
4.00 x 10^26	82	2,251,799,813,685,240	562,949,953,421,312	140,737,488,355,328	35,184,372,088,832	8,796,093,022,208	2,199,023,255,552	549,755,813,888		137,438,953,472		34,359,738,368		8,589,934,592

Mass in kg	Levels	Adjacent		2-4			5-8			9-16			17-32			33-64			65-128			129-256			257-512			513-1024

[prestidigitator]

Re: Determining Gravitic Pull

 

Thinking from the perspective of translating the simple attractive force into the baseline game terms, I approached the problem by wondering what it would take to affect someone ("target") with average mass (100kg) as if with a game Str of 5 (pushing at full force, which comes to the force it takes to lift 50kg in the Earth's average surface field; this also comes to a damage/Grab effect of 1d6, which is nice) at a distance ("radius") of 4 hexes (the maximum distance for a Range Modifier of zero).

 

It turns out that an object ("source") would have to be approximately 4.7x10^12 kg to have this effect, which is about 35 mass doublings due to Growth/Density Increase. Every doubling of the source's mass should double this force (+5 Str). [EDIT: Every halving of the source's mass should halve the force (-5 STR).] Every doubling of the target's mass should double the force (+5 Str). Every halving of the target's mass should halve the force (-5 Str). Every doubling of radius (next range increment) should divide the force by four (-10 Str). That makes it pretty simple.

 

EDIT: BTW, assuming we can approximate each character as a point mass, the, "distance," should be that between the centers of the two characters, which may well be constrianed by the size of both characters. So Density Increase could be the more effective route if an attacker simply wants to walk up to people and have them stick to him.

I thought I would put this more succinctly:

Baseline is 5 Str (1d6) of effect for a source mass equal to 35 levels of Growth/Density Increase (about 5 trillion kilograms) acting on a normal sized (100kg) target at a 4-hex distance. Then:

• Each doubling of either source or target mass adds +5 Str
  
  
• Each halving of either source or target mass adds -5 Str
  
  
• Each doubling of range adds -10 Str
  
  
• Ranges under 4 hexes can probably be ignored (treated the same as 4 hexes) for simplicity

For simplicity it is probably easiest just to ignore anything that comes to less than 5 Str, and impose force on the character with less mass since the one with greater mass could be assumed to have enough Str to easily resist it (if both masses are roughly equal you could have them both affected, which could get fun).

[ajackson]

Re: Determining Gravitic Pull

 

(And I assume he meant to write ".5" and not "5." at the end of his equation. )

Nope, I meant 5 -- x2 mass = x2 gravity = +5 strength (if you want dice, multiply by 1).

 

Assuming that if someone "curls up" they'll be about half their usual height, I used a Newtonian radius of ½m which yields an event horizon circumference of Pi, rounded to 3.1416m (the Schwarzchild radius is not needed for this).

 

I used the range at which escape energy is equal to 9 x 10^16 J/kg. Since escape energy is equal to m*a*r, and r is 0.5, a would be 1.8x10^16 m/s^2.

 

Further, I assumed a static Schwarzchild hole.

As did I.

 

As for constants, I used

 

G = 1.327 x 10^11 km^3/sec^2

c = 2.998 x 10^5 km/sec

What odd units. Your value of G is very strange, as it's missing a mass unit (I used 6.67x10^-11 m^3 kg^-1 s^-2), and since you're using km rather than m, you'll need to do some unit conversion.

 

I was using a radius of 1 meter, incidentally, but that should only make a difference of one level of DI.

 

With a desired circumference of 3.1416m, crunching the numbers yields a mass of 1.69329389601 x 10^26 kg

I get about twice that

80 levels of DI (400 points) gives a mass of 1.00 x 10^26 kg

More or less. I get 0.6 to 1.2 x that. Looks like I miscomputed slightly, it should be 81-82 levels, not 90 levels.

 

At that density, another character in a hex adjacent to the character using 81 levels of DI would feel a gravitational pull of 25g.

Acceleration = GM/r^2. 6.67e-11 x 1.7e26 / 4 = 2.8x10^15 m/s^2 or 280 trillion Gs.

 

At that same distance (adjacent hex) the character feeling the pull would feel no appreciable pull when 31 levels of DI were in use, ½g at 32 levels, 1g at 33, and so on. In other words, for every level of DI past 31, add ½g.

 

No, for every level past 31, double gravity.

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Nope' date=' I meant 5 -- x2 mass = x2 gravity = +5 strength (if you want dice, multiply by 1).[/quote']

I'll have to go back and check my original procedures. Hmmm...

What odd units. Your value of G is very strange' date=' as it's missing a mass unit (I used 6.67x10^-11 m^3 kg^-1 s^-2), and since you're using km rather than m, you'll need to do some unit conversion.[/quote']

Per solar mass. Left that out.

I was using a radius of 1 meter' date=' incidentally, but that should only make a difference of one level of DI.[/quote']

I figured that half of 2m was 1m ( ) so for a sphere with a diameter of 1m, you'd need a radius of 1/2m. Newtonian, of course. A radius of 1/2m gives a circumference of Pi meters, natch.

Acceleration = GM/r^2. 6.67e-11 x 1.7e26 / 4 = 2.8x10^15 m/s^2 or 280 trillion Gs.

Dropped a couple of powers of 10. Gah.

No' date=' for every level past 31, double gravity.[/quote']

And that was just a silly mistake on my part. Looks like I inadvertantly used the inverse instead. Gonna have to refigure that lot...

 

Edit: I suppose I should also have said that using this:

 

C = (4*Pi*G*M)/c^2

 

For finding the mass to go with a circumference of 3.1416m (1m diameter Newtonian)

 

C = circumference of event horizon

G = gravitational constant

M = mass of singularity (in solar masses)

c = speed of light

 

When I cranked that through, I got 1.69329389601 x 10^-4 solar masses, and when you plug in a solar mass of 1.98892 x 10^30 kg, you get a result of 3.36782609565 x 10^26 kg for a singularity that has an event horizon with a circumference of 3.1416m

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Oh, and note: now that ajackson pointed out that stupid inversion error (.5 instead of 2) I've fixed the table so it's correct for the assumptions I made.

 

I'll rep you tomorrow afternoon sometime, ajackson.

[Super Squirrel]

Re: Determining Gravitic Pull

 

Oh' date=' and note: now that ajackson pointed out that stupid inversion error (.5 instead of 2) I've [i']fixed[/i] the table so it's correct for the assumptions I made.

 

I'll rep you tomorrow afternoon sometime, ajackson.

I repped him too. I only wish Steve Long had asked for help in a field I know like Serial Killers or Psychology in General.

[Blue Jogger]

Re: Determining Gravitic Pull

 

I thought I would put this more succinctly:

Baseline is 5 Str (1d6) of effect for a source mass equal to 35 levels of Growth/Density Increase (about 5 trillion kilograms) acting on a normal sized (100kg) target at a 4-hex distance. Then:

• Each doubling of either source or target mass adds +5 Str
  
  
• Each halving of either source or target mass adds -5 Str
  
  
• Each doubling of range adds -10 Str
  
  
• Ranges under 4 hexes can probably be ignored (treated the same as 4 hexes) for simplicity

For simplicity it is probably easiest just to ignore anything that comes to less than 5 Str, and impose force on the character with less mass since the one with greater mass could be assumed to have enough Str to easily resist it (if both masses are roughly equal you could have them both affected, which could get fun).

 

But ranges under 4 are the most interesting.

• You can put 25 kg objects into orbit around him at 2 hexes away. It's like having an annoying 0 STR TK for free.
  
• Realize at one hex away, 300 kg objects whirl around him. (+10 STR for half distance, +8 STR for circumference getting smaller) Basically, you have Casual STR TK.

[ajackson]

Re: Determining Gravitic Pull

 

When I cranked that through, I got 1.69329389601 x 10^-4 solar masses, and when you plug in a solar mass of 1 x 10^30 kg

 

Solar mass is, unfortunately, 2 x 10^30 kg (actually 1.989e+30)

[ajackson]

Re: Determining Gravitic Pull

 

But ranges under 4 are the most interesting.

• You can put 25 kg objects into orbit around him at 2 hexes away. It's like having an annoying 0 STR TK for free.
  
• Realize at one hex away, 300 kg objects whirl around him. (+10 STR for half distance, +8 STR for circumference getting smaller) Basically, you have Casual STR TK.

 

Um...no. Remember, this is gravity. The amount of force is proportional to the mass of the object, so it's 5 strength on a 100 kg object, but -5 strength on a 25 kg object.

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Solar mass is' date=' unfortunately, 2 x 10^30 kg (actually 1.989e+30)[/quote']

(sigh)

 

Someone just knock me over and fill in the grave. I can't seem to get anything right these days.

 

I'll refigure stuff. Tomorrow.

[ajackson]

Re: Determining Gravitic Pull

 

Ok, here's my table. Rather than listing Gs, I'm listing what Str of effect is applied to a normal mass (50-100 kg; 70 kg is used on the mass table) character, assuming that 1g = Str 10. S indicates that you are within the schwarzchild radius. For characters with non-standard mass, add 5x DI/growth or -15x shrinking to the effective strength.

 

DI Mass    0    1    2    4    8    16   32   64   128  256  512  1024 
25 2.3e+09 -20  -30  -40  -50  -60  -70  -80  -90  -100 -110 -120 -130 
26 4.7e+09 -15  -25  -35  -45  -55  -65  -75  -85  -95  -105 -115 -125 
27 9.4e+09 -10  -20  -30  -40  -50  -60  -70  -80  -90  -100 -110 -120 
28 1.9e+10 -5   -15  -25  -35  -45  -55  -65  -75  -85  -95  -105 -115 
29 3.8e+10 0    -10  -20  -30  -40  -50  -60  -70  -80  -90  -100 -110 
30 7.5e+10 5    -5   -15  -25  -35  -45  -55  -65  -75  -85  -95  -105 
31 1.5e+11 10   0    -10  -20  -30  -40  -50  -60  -70  -80  -90  -100 
32   3e+11 15   5    -5   -15  -25  -35  -45  -55  -65  -75  -85  -95  
33   6e+11 20   10   0    -10  -20  -30  -40  -50  -60  -70  -80  -90  
34 1.2e+12 25   15   5    -5   -15  -25  -35  -45  -55  -65  -75  -85  
35 2.4e+12 30   20   10   0    -10  -20  -30  -40  -50  -60  -70  -80  
36 4.8e+12 35   25   15   5    -5   -15  -25  -35  -45  -55  -65  -75  
37 9.6e+12 40   30   20   10   0    -10  -20  -30  -40  -50  -60  -70  
38 1.9e+13 45   35   25   15   5    -5   -15  -25  -35  -45  -55  -65  
39 3.8e+13 50   40   30   20   10   0    -10  -20  -30  -40  -50  -60  
40 7.7e+13 55   45   35   25   15   5    -5   -15  -25  -35  -45  -55  
41 1.5e+14 60   50   40   30   20   10   0    -10  -20  -30  -40  -50  
42 3.1e+14 65   55   45   35   25   15   5    -5   -15  -25  -35  -45  
43 6.2e+14 70   60   50   40   30   20   10   0    -10  -20  -30  -40  
44 1.2e+15 75   65   55   45   35   25   15   5    -5   -15  -25  -35  
45 2.5e+15 80   70   60   50   40   30   20   10   0    -10  -20  -30  
46 4.9e+15 85   75   65   55   45   35   25   15   5    -5   -15  -25  
47 9.9e+15 90   80   70   60   50   40   30   20   10   0    -10  -20  
48   2e+16 95   85   75   65   55   45   35   25   15   5    -5   -15  
49 3.9e+16 100  90   80   70   60   50   40   30   20   10   0    -10  
50 7.9e+16 105  95   85   75   65   55   45   35   25   15   5    -5   
51 1.6e+17 110  100  90   80   70   60   50   40   30   20   10   0    
52 3.2e+17 115  105  95   85   75   65   55   45   35   25   15   5    
53 6.3e+17 120  110  100  90   80   70   60   50   40   30   20   10   
54 1.3e+18 125  115  105  95   85   75   65   55   45   35   25   15   
55 2.5e+18 130  120  110  100  90   80   70   60   50   40   30   20   
56   5e+18 135  125  115  105  95   85   75   65   55   45   35   25   
57   1e+19 140  130  120  110  100  90   80   70   60   50   40   30   
58   2e+19 145  135  125  115  105  95   85   75   65   55   45   35   
59   4e+19 150  140  130  120  110  100  90   80   70   60   50   40   
60 8.1e+19 155  145  135  125  115  105  95   85   75   65   55   45   
61 1.6e+20 160  150  140  130  120  110  100  90   80   70   60   50   
62 3.2e+20 165  155  145  135  125  115  105  95   85   75   65   55   
63 6.5e+20 170  160  150  140  130  120  110  100  90   80   70   60   
64 1.3e+21 175  165  155  145  135  125  115  105  95   85   75   65   
65 2.6e+21 180  170  160  150  140  130  120  110  100  90   80   70   
66 5.2e+21 185  175  165  155  145  135  125  115  105  95   85   75   
67   1e+22 190  180  170  160  150  140  130  120  110  100  90   80   
68 2.1e+22 195  185  175  165  155  145  135  125  115  105  95   85   
69 4.1e+22 200  190  180  170  160  150  140  130  120  110  100  90   
70 8.3e+22 205  195  185  175  165  155  145  135  125  115  105  95   
71 1.7e+23 210  200  190  180  170  160  150  140  130  120  110  100  
72 3.3e+23 215  205  195  185  175  165  155  145  135  125  115  105  
73 6.6e+23 220  210  200  190  180  170  160  150  140  130  120  110  
74 1.3e+24 225  215  205  195  185  175  165  155  145  135  125  115  
75 2.6e+24 230  220  210  200  190  180  170  160  150  140  130  120  
76 5.3e+24 235  225  215  205  195  185  175  165  155  145  135  125  
77 1.1e+25 240  230  220  210  200  190  180  170  160  150  140  130  
78 2.1e+25 245  235  225  215  205  195  185  175  165  155  145  135  
79 4.2e+25 250  240  230  220  210  200  190  180  170  160  150  140  
80 8.5e+25 255  245  235  225  215  205  195  185  175  165  155  145  
81 1.7e+26 260  250  240  230  220  210  200  190  180  170  160  150  
82 3.4e+26 265  255  245  235  225  215  205  195  185  175  165  155  
83 6.8e+26 270  260  250  240  230  220  210  200  190  180  170  160  
84 1.4e+27 S    265  255  245  235  225  215  205  195  185  175  165  
85 2.7e+27 S    S    260  250  240  230  220  210  200  190  180  170  
86 5.4e+27 S    S    S    255  245  235  225  215  205  195  185  175  
87 1.1e+28 S    S    S    S    250  240  230  220  210  200  190  180  
88 2.2e+28 S    S    S    S    S    245  235  225  215  205  195  185  
89 4.3e+28 S    S    S    S    S    S    240  230  220  210  200  190  
90 8.7e+28 S    S    S    S    S    S    S    235  225  215  205  195  

[Dr. Anomaly]

Re: Determining Gravitic Pull

 

Ok' date=' here's my table. Rather than listing Gs, I'm listing what Str of effect is applied to a normal mass (50-100 kg; 70 kg is used on the mass table) character, assuming that 1g = Str 10. S indicates that you are within the schwarzchild radius. For characters with non-standard mass, add 5x DI/growth or -15x shrinking to the effective strength.[/quote']

That would give a pretty close approximation of the STR needed to resist being pulled towards the character using scads of DI...a potentially important point. Good thought!

[Mister E]

Re: Determining Gravitic Pull

 

Ok' date=' here's my table. Rather than listing Gs, I'm listing what Str of effect is applied to a normal mass (50-100 kg; 70 kg is used on the mass table) character, assuming that 1g = Str 10. S indicates that you are within the schwarzchild radius. For characters with non-standard mass, add 5x DI/growth or -15x shrinking to the effective strength.[/quote']This is amazing. So is your chart in meters or Hexes?

[ajackson]

Re: Determining Gravitic Pull

 

This is amazing. So is your chart in meters or Hexes?

 

Hexes.

[prestidigitator]

Re: Determining Gravitic Pull

 

But ranges under 4 are the most interesting.

• You can put 25 kg objects into orbit around him at 2 hexes away. It's like having an annoying 0 STR TK for free.
  
• Realize at one hex away, 300 kg objects whirl around him. (+10 STR for half distance, +8 STR for circumference getting smaller) Basically, you have Casual STR TK.

Eh. SFX. If you want to place little stuff in orbit it is probably easiest just to do things with Extra Limbs for a character who is really that heavy and still small (read: lots of DI, little Growth). Put IPE and some Limitations on it if you really want.

 

That way you can avoid the effects of air resistence on orbital paths anyway.

[prestidigitator]

Re: Determining Gravitic Pull

 

Ooh. Here's an interesting thought. There are already rules for using Movement as Str. Maybe anyone with an appropriate Skill (e.g. SS: Orbital Mechanics, PS: astronaut, or Navigation: Space) could also turn one or two appropriate Movement Skill Levels (or Overall Skill Levels) into +5 Str to resist the gravitational attraction while they are moving.

[ajackson]

Re: Determining Gravitic Pull

 

Ok, I statted up your basic primordial black hole. It's kind of a lot of points, but it has potential as a plot device.

 

Primordial Black Hole
       The Primordial Black Hole is a tiny black hole, forged at the start
of the universe, and which has been gradually decaying due to hawking
radiation ever since then. The primordial black hole given here will evaporate
in another twenty billion years or so, but in the interim it's an interesting
object for scientists to investigate.
       A basic PBH has the following package of powers:

Cost    Power
155     'Great Strength': +155 Str (should probably have zero end or similar
       on it). Max lift 200 million tons.
62      'Great Mass': +31 Body
62      'Heavy': +31" knockback resistance (200 million tons)
50+     'Hard to Hit': +10 (or more) DCV. Actual size corresponds to 51 levels
       of shrinking, for +102 DCV, but beyond a certain point any attack is
       an area effect. As it glows like a small star, it does not get the
       normal bonuses to concealment and stealth. Diameter is 3x10^-16 meters,
       or about 1/8 the size of a proton.
53      'Too Small to Touch': desolid, persistent, always on
400     'Hypergravity Field': 5d6 physical RKA, affects solid(+2), AVLD
       does body (+2.5), continuous(+1), damage shield (+0.5), persistent (+1),
       always on (-0.5). The defense is being internally tough; the gravity
       field will rip flesh at 10 cm but steel at only 1mm (no material
       can actually avoid some damage, but a small enough hole is ignorable)
541     'Hot': 8d6+1 energy RKA, affects solid(+2), AP (+0.5), continuous(+1),
       damage shield (+0.5), penetrating (+0.5), persistent (+1), always on
       (-0.5) persistent, armor piercing, always on (0.5). I computed this
       based on 1 kW = 2 DC, +1 DC per x2.
234     'Hot Aura': 15d6 EB, affects solid (+2), area effect megascale(+1.25),
       continuous (+1), persistent (+1), always on (-0.5), centered on self
       (-0.25), reduced by range (-2d6 at 1 hex, -4d6 at 2 hexes, and reduced
       by range from then out). Computed as above, but 1 MW = 2 DC.
495     'Radiation Source': 24d6 energy blast, NND does body vs
       LS: radiation(+2), affects solid (+2), megascale area (+1.25),
       continuous(+1), persistent (+1), always on (-0.5), centered on
       self (-0.25), reduced by range(-0.25) (-2d6 at 1 hex, -4d6 at 2 hexes,
       and reduced by range from then out, so at 250-500 hexes, where it ends,
       damage is reduced to zero at 2,000 hexes). This is assuming
       that 20 rads/sec is 1d, and each x2 is +1d.
151     'Gravity Well': 10" flight, affects substantial (+2), area effect
       megascale (+1.25), persistent (+1), usable vs others, increased
       mass 32 levels (+9), always on (-0.5), reduced by range (acts as 1g
       or +10 Str at 1 meter, 0.25g or +0 Str at 1 hex, -10 Str at 2 hex,
       and reduced by range from then out). This is a crappy way to do a
       gravity field, but I don't know of a better one.
450     'Invulnerable': armor, PD 100, DR 100, hardened x2
333     'Invulnerable': force field, PD 100, DR 100, hardened x2, persistent,
       always on. Feel free to adjust the defenses upwards; black holes are
       not really subject to physical forces.
45      Life Support: total
3031    Total
For a more massive black hole, adjust as following for each level of extra
mass:
5       +5 Str
2       +1 Body
2       +1 knockback resistance
27      +1 DC on hypergravity field
-43     -2 DC on 'hot' field 
-31     -2 DC on 'hot aura'
+75     +5 to effective Str of 'gravity well'
+37     Total