Hello,
I would like to start by saying that I am new to the forum and not at all educated in physics. Keeping that in mind I ask that you forgive my ignorance.
A friend and I were discussing gravity and came to a disagreement that I was hoping someone here could help me understand. We imagined a bowling ball and a marble both placed in space 10 feet apart from each other. My friend says that the marble’s gravitational effect on the bowling ball will actually move the bowling ball toward the marble. He says that most of the movement will be on the part of the marble moving toward the bowling ball but that the bowling ball will be drawn to the marble some small distance.
Is this correct? It seems to me that the object with more mass would cancel out the smaller objects gravitational pull, so as to not move the bowling ball at all. I can understand that if both objects were orbiting the sun that the marble would have some effect on the bowling ball’s orbit around the sun, but it just doesn’t “seem” right that the bowling ball would move toward the marble.
Any help with this would be greatly appreciated.
Thanks.
Newton's 3rd law is usually restated today as the principle that momentum is conserved.
So for two objects of masses m and M, the sum of their momentums mv + MV will always be the same. If the two masses start "at rest" then we start off with v = V = 0, and so mv + MV = 0 + 0 = 0. If Newton's third law is to believed, if at some later time v, the velocity of the smaller mass, is not zero then V must also change so that mv + MV = 0. But this means MV = -mv or V = -(m/M)v. If M is much bigger than m, then V will be much smaller than (and opposite to) v.
Indeed, this math is built into Newton's law of Universal Gravitation, where F = G Mm/r^2 in the direction of the other mass. This is a force, which acts over time, t, to change momentum. But the change in velocity is inversely proportional to the mass. So we have mv = Ft and MV = -Ft. So v = Ft/m and V = Ft/M. And so we have mv + MV = m(Ft/m) + M(-Ft/M) = Ft - Ft = 0.
Newton's 3rd law survives today in even the most cutting edge physics, even when we learned that Newton's guess about the definition of momentum was a little wrong. So with just that little bit, just as the whole earth pulls a golf ball down, so a golf ball pulls the whole earth a tiny bit up.
m (golf ball) = 0.0459 kg
M (Earth) = 5.9736×10^24 kg
m/M = 7.68 × 10^-27 = 0.00000000000000000000000000768 which is a tiny, tiny number.
So for two objects of masses m and M, the sum of their momentums mv + MV will always be the same. If the two masses start "at rest" then we start off with v = V = 0, and so mv + MV = 0 + 0 = 0. If Newton's third law is to believed, if at some later time v, the velocity of the smaller mass, is not zero then V must also change so that mv + MV = 0. But this means MV = -mv or V = -(m/M)v. If M is much bigger than m, then V will be much smaller than (and opposite to) v.
Indeed, this math is built into Newton's law of Universal Gravitation, where F = G Mm/r^2 in the direction of the other mass. This is a force, which acts over time, t, to change momentum. But the change in velocity is inversely proportional to the mass. So we have mv = Ft and MV = -Ft. So v = Ft/m and V = Ft/M. And so we have mv + MV = m(Ft/m) + M(-Ft/M) = Ft - Ft = 0.
Newton's 3rd law survives today in even the most cutting edge physics, even when we learned that Newton's guess about the definition of momentum was a little wrong. So with just that little bit, just as the whole earth pulls a golf ball down, so a golf ball pulls the whole earth a tiny bit up.
m (golf ball) = 0.0459 kg
M (Earth) = 5.9736×10^24 kg
m/M = 7.68 × 10^-27 = 0.00000000000000000000000000768 which is a tiny, tiny number.
Actually, one of the ways of detecting small planets near stars is by measuring the small planets gravitational affect on the star. This is a bit more than a marble compared to a bowling ball, since about a million earth's could fit inside our sun.
We are learning about this kind of stuff in physics right now.
I think the formula for what you are talking about can be described as:
Fg = G(m1)(m2) / r^2
or
Force of Gravity = (6.67x10^-11) x (0.00356kg) x (7.39kg) / ((3m)^2)
Force of Gravity between both the marble and bowling ball is 0.000000000000195 N
In space, if there is no affecting gravitational field (ie: earth, nearby star, etc) then the two masses should move together at such speed that i cannot see them moving together very quickly at all
.
re edit: I must be messing up different laws, i keep trying to imagine it in my head, and it just seems logical that bowling ball would move slower than the marble in their attraction. I think i am forgetting about momentum?
edit: Didn't see Rpenner's calculations, he also mentions Gmm/r^2. His calculations seem more realistic. Mine are based on absolutely no outside interference, just the bowling ball and the marble in a controlled environment.
I think the formula for what you are talking about can be described as:
Fg = G(m1)(m2) / r^2
or
Force of Gravity = (6.67x10^-11) x (0.00356kg) x (7.39kg) / ((3m)^2)
Force of Gravity between both the marble and bowling ball is 0.000000000000195 N
In space, if there is no affecting gravitational field (ie: earth, nearby star, etc) then the two masses should move together at such speed that i cannot see them moving together very quickly at all
.re edit: I must be messing up different laws, i keep trying to imagine it in my head, and it just seems logical that bowling ball would move slower than the marble in their attraction. I think i am forgetting about momentum?
edit: Didn't see Rpenner's calculations, he also mentions Gmm/r^2. His calculations seem more realistic. Mine are based on absolutely no outside interference, just the bowling ball and the marble in a controlled environment.
Thank you everyone for your replies.
It makes sense to me that a planet can have an effect on a star if the planet is orbiting the star, but it very counterintuitive to my own logic that the object with less mass could actually move the larger object if there was no orbit taking place.
I am not in any way doubting the mathematics that were posted, and I realize that making at argument from my personal incredulity isn’t really an argument, but this just doesn't "feel" right. It seems that the gravitational force from the more massive object would cancel out the force from the less massive object, therefore the closer in mass the two objects were to one another, the longer it would take for them to come together.
Again, I am sure that I am wrong about this, but does anyone else understand what I'm saying, and is there a simple way to better understand this, or do I just need to sign up for a physics class?
It makes sense to me that a planet can have an effect on a star if the planet is orbiting the star, but it very counterintuitive to my own logic that the object with less mass could actually move the larger object if there was no orbit taking place.
I am not in any way doubting the mathematics that were posted, and I realize that making at argument from my personal incredulity isn’t really an argument, but this just doesn't "feel" right. It seems that the gravitational force from the more massive object would cancel out the force from the less massive object, therefore the closer in mass the two objects were to one another, the longer it would take for them to come together.
Again, I am sure that I am wrong about this, but does anyone else understand what I'm saying, and is there a simple way to better understand this, or do I just need to sign up for a physics class?
QUOTE
or do I just need to sign up for a physics class?
Excellent idea.
QUOTE (strowner+Apr 22 2009, 06:44 PM)
"...the closer in mass the two objects were to one another, the longer it would take for them to come together."
This is simply not true. A famous experiment, that Galileo reportedly carried out, was dropping to different weights from the Leaning Tower of Pisa and seeing which one hit the ground first - they both hit the ground at the same time. The more massive an object the more gravitational pull it has, but, it also takes a larger force to change it's state of motion.
This is simply not true. A famous experiment, that Galileo reportedly carried out, was dropping to different weights from the Leaning Tower of Pisa and seeing which one hit the ground first - they both hit the ground at the same time. The more massive an object the more gravitational pull it has, but, it also takes a larger force to change it's state of motion.
Strowner, i think something that will hep you in this case, is that the two masses share an equal bond per say, that is dependent on distance. The gravitational force felt by the marble is the same force felt by the bowling ball. There is no "cancel", you might be confusing yourself with the apparent "weight" (ie: no gravity is false, weightlessness is actually due to the absence of normal force).
Please correct me if i'm wrong, because i have my "equilibrium, centripetal force, gravity, etc" test tomorrow in physics class, which deals in eactly what we are discussing!
In the canadian curriculum, you can learn this stuff in the course called "Physics 12", it is the last highschool-physics course you can take, if that helps. You could take this course online probably, as it is not university-level physics. This is only Newtonian physics though, and unlike general relativity, not 100% accurate. That however is university-level physics, and you will need to go to post-secondary to learn that.
Please correct me if i'm wrong, because i have my "equilibrium, centripetal force, gravity, etc" test tomorrow in physics class, which deals in eactly what we are discussing!
In the canadian curriculum, you can learn this stuff in the course called "Physics 12", it is the last highschool-physics course you can take, if that helps. You could take this course online probably, as it is not university-level physics. This is only Newtonian physics though, and unlike general relativity, not 100% accurate. That however is university-level physics, and you will need to go to post-secondary to learn that.
Sort of offtopic, but related. I read this in my hawkings book "brief history of time", just wondering if i am understanding this right...
Orbit is the geodesic path things travel, the closest thing to a straight line in the 4rth dimension, but an apparent curve in the 3rd dimension? Is gravity in general also this geodesic path in the 4rth dimension? I don't want to hihjack this thread, if its much more complicated to explain than that, i can do pm's also.
Orbit is the geodesic path things travel, the closest thing to a straight line in the 4rth dimension, but an apparent curve in the 3rd dimension? Is gravity in general also this geodesic path in the 4rth dimension? I don't want to hihjack this thread, if its much more complicated to explain than that, i can do pm's also.
You want simple,
...think of a rubber band between two objects,under tension.
The initial force between the two objects is the total as seen
by both objects(if you disregard actual gravity for this point).
There is no "cancel" as in the example, only force between them
and any force applied to a mass will alter its momentum.
...think of a rubber band between two objects,under tension.
The initial force between the two objects is the total as seen
by both objects(if you disregard actual gravity for this point).
There is no "cancel" as in the example, only force between them
and any force applied to a mass will alter its momentum.
QUOTE (noksutau+Nov 10 2009, 12:55 AM)
You want simple,
...think of a rubber band between two objects,under tension.
The initial force between the two objects is the total as seen
by both objects(if you disregard actual gravity for this point).
There is no "cancel" as in the example, only force between them
and any force applied to a mass will alter its momentum.
This was the same analogy I was going to propose. Except I was going to say that if something heavy is pulling on one side of a rope with something light on the other, it's easy to think that the only force getting exerted is the force on the lighter object as it gets pulled. But I think that there necessarily has to be an "equal and opposite" amount of force that pulls on the heavy object. The amount that this force affects either object would be related to its inertia, meaning that the inertia of the heavier object causes it to require more energy for acceleration than the lighter one. So the same force on two differently weighted objects would result in different speeds in each other's direction proportional to the difference in inertia. Is this the same thing Rpenner said in maths? If not, I'm probably wrong.
Somehow F=MA seems to apply since gravity is the force of attraction between the two objects and it would be the same for each, i.e. the tension on either side of the "rope" connecting them. Then, to figure out the speed that each travels toward the other, you would just plug its mass into the equation to find the acceleration rate of either. Is it more complicated because of the inverse square relationship between distance between the objects and their mass in determining the gravitational force?
No matter, I think it's still as simple as recognizing that the same amount of force is present for both objects, as if they were being pulled by two ends of the same rope. So the bowling ball would get pulled with the same amount of force as the marble, but the same amount of force would have a much less significant effect on the bowling ball relative to the marble.
I hope I didn't completely pervert the truth of physics with this. Beware, I participate in this forum as a hobby and for interactive learning. DO NOT take anything I post as reliable science. I just share my hunches to see if it moves others along in their understanding and maybe adds fuel to the explanations from people who really know their stuff.
...think of a rubber band between two objects,under tension.
The initial force between the two objects is the total as seen
by both objects(if you disregard actual gravity for this point).
There is no "cancel" as in the example, only force between them
and any force applied to a mass will alter its momentum.
This was the same analogy I was going to propose. Except I was going to say that if something heavy is pulling on one side of a rope with something light on the other, it's easy to think that the only force getting exerted is the force on the lighter object as it gets pulled. But I think that there necessarily has to be an "equal and opposite" amount of force that pulls on the heavy object. The amount that this force affects either object would be related to its inertia, meaning that the inertia of the heavier object causes it to require more energy for acceleration than the lighter one. So the same force on two differently weighted objects would result in different speeds in each other's direction proportional to the difference in inertia. Is this the same thing Rpenner said in maths? If not, I'm probably wrong.
Somehow F=MA seems to apply since gravity is the force of attraction between the two objects and it would be the same for each, i.e. the tension on either side of the "rope" connecting them. Then, to figure out the speed that each travels toward the other, you would just plug its mass into the equation to find the acceleration rate of either. Is it more complicated because of the inverse square relationship between distance between the objects and their mass in determining the gravitational force?
No matter, I think it's still as simple as recognizing that the same amount of force is present for both objects, as if they were being pulled by two ends of the same rope. So the bowling ball would get pulled with the same amount of force as the marble, but the same amount of force would have a much less significant effect on the bowling ball relative to the marble.
I hope I didn't completely pervert the truth of physics with this. Beware, I participate in this forum as a hobby and for interactive learning. DO NOT take anything I post as reliable science. I just share my hunches to see if it moves others along in their understanding and maybe adds fuel to the explanations from people who really know their stuff.
OK Off topic a little, but to clarify that I wasn't wrong :
http://imagine.gsfc.nasa.gov/docs/ask_astr...rs/970518a.html
If we can't see them, how can we find out if there are planets around other stars?
The star moving in a straight line has no planets; the one which "wobbles" around a straight path is being influenced by an unseen planet's orbital motion. (Diagram courtesy David C. Black, NASA Ames Research Center)
Although we cannot see the planet itself, we can see the effect of the gravitational tug the planet exerts on its parent star. As the planet revolves around the star, it pulls the star first one way, then the other. The more massive the planet, the more noticeable its effect on the star will be. As the star moves through space, the planet's tugs show up as tiny deviations from a straight-line path. That's because the star and the planet actually move around the center of mass of the star-planet system, the point where one would balance a seesaw holding the star on one end and the planet on the other. For example, the Sun is a thousand times more massive than Jupiter, so the center of mass of the Sun-Jupiter system lies very close to the Sun. Nevertheless, an extraterrestrial observer measuring the Sun's motion through space would detect a slight wobble in the Sun's path, a wobble with a period of twelve years, the same time it takes Jupiter to orbit once around the center of mass. Smaller planets like the Earth also cause perturbations on the Sun's orbit, but they are so tiny they couldn't be detected across interstellar distances. Analysis of the wobbles can give information about the planet's mass, orbit, period and distance from the star.
http://astrosociety.net/education/publicat....html#detection
http://imagine.gsfc.nasa.gov/docs/ask_astr...rs/970518a.html
If we can't see them, how can we find out if there are planets around other stars?
The star moving in a straight line has no planets; the one which "wobbles" around a straight path is being influenced by an unseen planet's orbital motion. (Diagram courtesy David C. Black, NASA Ames Research Center)
Although we cannot see the planet itself, we can see the effect of the gravitational tug the planet exerts on its parent star. As the planet revolves around the star, it pulls the star first one way, then the other. The more massive the planet, the more noticeable its effect on the star will be. As the star moves through space, the planet's tugs show up as tiny deviations from a straight-line path. That's because the star and the planet actually move around the center of mass of the star-planet system, the point where one would balance a seesaw holding the star on one end and the planet on the other. For example, the Sun is a thousand times more massive than Jupiter, so the center of mass of the Sun-Jupiter system lies very close to the Sun. Nevertheless, an extraterrestrial observer measuring the Sun's motion through space would detect a slight wobble in the Sun's path, a wobble with a period of twelve years, the same time it takes Jupiter to orbit once around the center of mass. Smaller planets like the Earth also cause perturbations on the Sun's orbit, but they are so tiny they couldn't be detected across interstellar distances. Analysis of the wobbles can give information about the planet's mass, orbit, period and distance from the star.
http://astrosociety.net/education/publicat....html#detection
It's a more general idea, quite useful and worth investing time at it, that there is no asymmetric action from one body on another, but only interactions.
That is, gravitation puts forces on both objects, of identical intensity but opposed directions. Electrostatic forces as well act on both particles, for example. And other forces, too.
When objects are composed of several particles, this symmetric interaction of their particles means that the interaction between the bodies are symmetric as well.
This is consistent with the conservation of momentum, which needs both objects to change their speed in opposite directions so the sum of both momentums keeps the same.
So if one object is twice as heavy as the other, it will get the same force but only half the acceleration, and half the speed after a period of time, and half the speed combines with twice the mass to give the same momentum (but opposed, as are the forces). This is also consistent with the momentum gained by an object equalling the product of force and time.
That is, gravitation puts forces on both objects, of identical intensity but opposed directions. Electrostatic forces as well act on both particles, for example. And other forces, too.
When objects are composed of several particles, this symmetric interaction of their particles means that the interaction between the bodies are symmetric as well.
This is consistent with the conservation of momentum, which needs both objects to change their speed in opposite directions so the sum of both momentums keeps the same.
So if one object is twice as heavy as the other, it will get the same force but only half the acceleration, and half the speed after a period of time, and half the speed combines with twice the mass to give the same momentum (but opposed, as are the forces). This is also consistent with the momentum gained by an object equalling the product of force and time.
I think everyone who has posted something here has answered your question, just different parts of it, I'm just going to try and put it all together so as to make sense and answer your question in one post:
First of all we need to look at the definition of gravity which is: the force produced between two objects that cause them to attract to each other. It is NOT the force that, in your example, the marble exercises over the bowling ball and that the bowling ball exercises over the marble. It is not two different forces pulling in different directions, but ONE force that is pulling them together.
Then as "light in the tunnel" said, it seems like the bowling ball wouldn't move because the force (F) necessary to accelerate (a) it must be bigger because of it's mass (m), which is Newton's Second Law (F=m.a). The force that is necessary to accelerate (i.e. move) the bowling ball is much bigger than the force necessary to accelerate the marble, that doesn't means however that the bowling ball is not being slowly accelerated by the gravity between itself and the marble.
A practical example is the Earth and the Moon, as much as the Earth is ~ 4 times bigger than the Moon, the Moon's gravity is exercised upon the Earth (which we experience specially through tides) and the Earth's gravity is exercised on the Moon (which we experience specially through the Moon's orbit around the Earth).
Does that makes more sense?
EDIT:
Also, just going back to Newton's Second Law (F=m.a). Let's say that the F (gravity) between the marble and the bowling ball is 2J (for example's sake), that means that the gravity exercised in the bowling ball is 2J and in the marble is also 2J, the force is the same, but, because of their different masses, the acceleration (a) of both are going to be different. Let's say that the bowling ball weights 0.5kg (m1) and the marble 0.1kg (m2), then:
F=2J
m1=0.5kg
m2=0.1kg
We then need to figure out what the bowling ball's acceleration is (a1) and the marble's acceleration is (a2), we then end up with this equation:
First of all we need to look at the definition of gravity which is: the force produced between two objects that cause them to attract to each other. It is NOT the force that, in your example, the marble exercises over the bowling ball and that the bowling ball exercises over the marble. It is not two different forces pulling in different directions, but ONE force that is pulling them together.
Then as "light in the tunnel" said, it seems like the bowling ball wouldn't move because the force (F) necessary to accelerate (a) it must be bigger because of it's mass (m), which is Newton's Second Law (F=m.a). The force that is necessary to accelerate (i.e. move) the bowling ball is much bigger than the force necessary to accelerate the marble, that doesn't means however that the bowling ball is not being slowly accelerated by the gravity between itself and the marble.
A practical example is the Earth and the Moon, as much as the Earth is ~ 4 times bigger than the Moon, the Moon's gravity is exercised upon the Earth (which we experience specially through tides) and the Earth's gravity is exercised on the Moon (which we experience specially through the Moon's orbit around the Earth).
Does that makes more sense?
EDIT:
Also, just going back to Newton's Second Law (F=m.a). Let's say that the F (gravity) between the marble and the bowling ball is 2J (for example's sake), that means that the gravity exercised in the bowling ball is 2J and in the marble is also 2J, the force is the same, but, because of their different masses, the acceleration (a) of both are going to be different. Let's say that the bowling ball weights 0.5kg (m1) and the marble 0.1kg (m2), then:
F=2J
m1=0.5kg
m2=0.1kg
We then need to figure out what the bowling ball's acceleration is (a1) and the marble's acceleration is (a2), we then end up with this equation:
CODE
a1.m1=F
a1=F/m1
a1=2/0.5
a1=4m/s
a1=F/m1
a1=2/0.5
a1=4m/s
CODE
a2.m2=F
a2=F/m2
a2=2/0.1
a2=20m/s
a2=F/m2
a2=2/0.1
a2=20m/s
Now, those accelerations are obviously exaggerated, but for example's sake, that's how it works... Does it makes sense?
It would make even more sense if multiplying by G:
http://en.wikipedia.org/wiki/Gravitational_constant
And then expressing forces in Newton, and you'd get accelerations in m/s^2
With these accelerations, multiply by a time and you get speeds.
http://en.wikipedia.org/wiki/Gravitational_constant
And then expressing forces in Newton, and you'd get accelerations in m/s^2
With these accelerations, multiply by a time and you get speeds.
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