View Full Version : Momentum and Gravity

wannabe writing

11-17-2012, 04:17 PM

Hypothetical: If something's was thrown and while airborne then entered an area with stronger gravity what would happen to the object. What would happen to the momentum of the object. Would it just drop, alter it's trajectory or would all these factors be dependent on the magnitude of the increase in gravity?

GeekTells

11-17-2012, 04:35 PM

The very short answer is that the object would be affected by the new gravity.

OK, that's a tad lame. Lemme try again. :)

You throw an object that weighs one pound in normal Earth gravity. It crosses into a zone with 2X Earth gravity. It's mass remains the same, but it's now a 2 pound object. It's trajectory, speed, inertia, and momentum are all affected accordingly.

I am not a math guy, so you may not want to pay attention to anything I said.

King Neptune

11-17-2012, 06:46 PM

He's right. It would start acting as if it were twice as heavy. Therefore, you have to specify the initial weight, initial velocity (that includes direction), initial gravitational force , and the new gravitational force for it to be possible to determine exactly what would happen. The acceleration caused by the Earth's gravity is 32 feet per second .per second.

If I had all of the information, then I would be able to make a graph. If the difference in gravity is small, then there would be little noticeable change. And gravity is unfocussed, so the stronger gravity would not be like day and night; the difference would be averaged with the original over a long distance. SO it is likely that the stronger gravity was effecting the object when it was thrown, but the stronger gravity was a small proportion of the total gravity. If there were such a region on Earth, then people might say, "The gravity is stronger in the Sacramento area; someone who weighs 175 normally weighs 200 there, but he weighs 185 in San Francisco and 190 on the east side of the bay.

RichardGarfinkle

11-17-2012, 07:17 PM

This is a little more complicated than it sounds like.

Objects have an intrinsic characteristic called mass (yes, I'm being sloppy with the meaning of intrinsic, but that doesn't matter here). A kilogram is a measure of mass.

A pound is not a measure of mass. The unit of mass in imperial measure is called the slug (I'm not kidding about that). A slug is about 14.5 kilograms.

http://en.wikipedia.org/wiki/Slug_%28mass%29

A pound is a measure of weight. Weight is not an intrinsic characteristic. It's a measure of the force due to gravity. The force of gravity on an object of mass m1 exerted by another object of mass m2 is

Gm1m2/r2.

Where G is Newton's Constant of Universal Gravitation.

This force is not a number, it's a vector (a number with a direction). It points toward the center of the object with mass m2 (or downward as we usually call it). If you put a scale under the object the scale will measure the downward force.

But suppose your object has another force acting on it (say another gravitational source nearby). Then two force vectors will need to be added together to determine the total force on the object. If the second source is straight up from the first source, it's gravitational attraction will work directly against the initial object's gravitational attraction. If it's in another direction it's gravitational attraction will work partially against the original object's attraction (if it's directly downward, it will add to it).

In any case, the weight measured takes some work to calculate, but regardless the mass will not change (barring excessive speed or other relativistic affect).

ETA: The momentum of the object will be affected by the sum of all forces acting upon it. The actual calculations in a complicated system require some calculus. This is especially true if the two sources of gravity are moving relative to each other.

Bufty

11-17-2012, 07:45 PM

Jeepers - it sounds complicated enough to me-how can it get more complicated?

What exactly is being 'thrown' here, wannabe - a paper aeroplane? a marble? a dart? a dagger? a spear? a hot-cross bun? a sumo wrestler? a man out of a cannon?

And from what direction (in relation to the flight of the object) does the new pull of gravity come?

sprogspasser

11-17-2012, 08:00 PM

Then two force vectors will need to be added together to determine the total force on the object. If the second source is straight up from the first source, it's gravitational attraction will work directly against the initial object's gravitational attraction. If it's in another direction it's gravitational attraction will work partially against the original object's attraction (if it's directly downward, it will add to it).

This certainly. But in a story world:

If we assume that there is a magical barrier between two worlds that some objects can be thrown across but gravities of two worlds do not act on each other then an object thrown passing through the barrier will carry its original velocity and momentum. On the other side its velocity and momentum on crossing the barrier become its initial conditions. Object will then act same as a native object with those initial conditions on that world with its gravity.

RichardGarfinkle

11-17-2012, 08:03 PM

This certainly. But in a story world:

If we assume that there is a magical barrier between two worlds that some objects can be thrown across but gravities of two worlds do not act on each other then an object thrown passing through the barrier will carry its original velocity and momentum. On the other side its velocity and momentum on crossing the barrier become its initial conditions. Object will then act same as a native object with those initial conditions on that world with its gravity.

Oh sure. But if you're changing the rules that much, then things work as you choose them to. And that's not what the OP was asking.

RichardGarfinkle

11-17-2012, 08:08 PM

Jeepers - it sounds complicated enough to me-how can it get more complicated?

What exactly is being 'thrown' here, wannabe - a paper aeroplane? a marble? a dart? a dagger? a spear? a hot-cross bun? a sumo wrestler? a man out of a cannon?

And from what direction (in relation to the flight of the object) does the new pull of gravity come?

We can also make it more complicated by considering other forces like air resistance.

StormChord

11-18-2012, 08:36 PM

We can also make it more complicated by considering other forces like air resistance.

No, thank you. Air resistance is a pain in the derrière. We're already dealing with a boundary between two gravity fields, a concept that doesn't necessarily make sense with normal physics anyway. We don't need to bring in fluid dynamics to the mix.

Anyway, if it's a clear cutoff, then basically the object will begin moving as if its mass had increased by the factor of the gravitic increase. It will also fall faster, based on the new acceleration due to gravity. For example, if it was thrown up in an arc where the highest point was exactly on the boundary between the two gravities, it would fall faster on the second half of the arc, and the parabola would be lopsided. The total horizontal distance covered would also be less than if the gravity had remained constant.

blacbird

11-18-2012, 11:51 PM

Actually, it's not too hard to find a real-world situation which is at least partly analogous to this fantasy idea. We've sent objects, including humans, to the moon. That involves travel from one gravitational field (Earth) to another (Luna), the latter being about 1/6 as powerful as the former. The gravitational acceleration on the moon is proportionately less than that on earth, and objects would fall that much proportionately slower.

Now, in this instance, there's a steady transition of gravitational influence from one to the other, instead of some instantaneous "boundary", but the gravitational affects would be the same, assuming we're dealing with realism in the of mass of the moving object.

caw

wannabe writing

11-23-2012, 09:21 AM

Hi everyone thank you so much for your feedback. It's greatly appreciated and you've given me a lot to think about. My apologies for the delay work was crazy this week.

girlyswot

11-23-2012, 04:13 PM

Actually, it's not too hard to find a real-world situation which is at least partly analogous to this fantasy idea. We've sent objects, including humans, to the moon. That involves travel from one gravitational field (Earth) to another (Luna), the latter being about 1/6 as powerful as the former. The gravitational acceleration on the moon is proportionately less than that on earth, and objects would fall that much proportionately slower.

Now, in this instance, there's a steady transition of gravitational influence from one to the other, instead of some instantaneous "boundary", but the gravitational affects would be the same, assuming we're dealing with realism in the of mass of the moving object.

caw

It doesn't travel from one field to the other. Both fields coexist, but their relative effect changes according to the distance from each body.

A pound is not a measure of mass. The unit of mass in imperial measure is called the slug...A pound is a measure of weight.

Sorry to be a pedant, but this is not correct. A pound is the Imperial unit for mass. Pound-force is a unit of weight. A slug is thirty two and a bit pounds (all to do with the acceleration due to gravity) - it is a mass, but it is not an Imperial unit.

blacbird

11-23-2012, 11:29 PM

It doesn't travel from one field to the other. Both fields coexist, but their relative effect changes according to the distance from each body.

Well, yes, but in practical terms as an object nears either, the proximal one dominates. The moon has no feelable effect on a human being on the surface of the earth, or anywhere near it. In real physical terms, gravity is a field generated by (or related to, depending on your interpretation of physics) everything having mass in the universe. But in terms of the story idea, the earth-moon dichotomy illustrates pretty clearly how a transition of gravitational influence would work.

caw

Showpony

11-28-2012, 04:24 PM

I'll try to simplify it and keep the math out of it. When something is thrown, it travels in an arc. The shape of the arc is not round, like part of a circle. The shape of the arc is a segment of a parabola. If you don't know what that is, please look it up - if you're dealing with gravity, this shape is very important.

The force of gravity will dictate the shape of the parabola. Less force of gravity will yield a "gentler" parabola. A stronger force of gravity will make the parabola "steeper" or "tighter".

Something to keep in mind. The horizontal velocity of a projectile is not affected by the force of gravity. Gravity only affects the vertical velocity of the item. So a projectile that is covering 100 mph horizontally will continue to do so after it enters an area of stronger gravitaty. However, it will fall faster.

Hopefully that makes sense.

--- D

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