How a binary system affects gravity on members?

[proteus13]

Hi, I have a rather simple question, how does a binary system with a common center of gravity affect the gravity on both members of the system.

If we have a case of a single planet and ignore the star it orbits, the center of gravity should be in the dead middle of that planet.

If we consider Earth and its moon, the center of gravity of both falls still in the radius of the planet. Does this mean gravity pulls down towards the center of gravity of the binary system instead of the actual center of the planet?

If so, what would happen if the moon is much closer to Earth, like it used to be billions of years ago, making the center of gravity pop out of the surface of the planet? Would that affect gravity on Earth significantly? Following the same logic, as the moon distances itself further from Earth, will that increase the gravity of the planet?

Also a formula on how exactly a member of a binary system affects the gravitational pull on the surface of the other member would be nice, if not too much trouble.

Thanks

 

[zhermes]

These are all good questions, but some of your concepts are a little off.
Most importantly: keep in mind the principle of superposition. The gravitational potential (and therefore, force) from two bodies will simply be the addition of the two by themselves. There is no additional effect from a binary per se.

Hi, I have a rather simple question, how does a binary system with a common center of gravity affect the gravity on both members of the system.

If you consider the gravity of one object alone, you can just add that of the second object. I.e: The Earth pulls you down. If the moon were directly above you (relative to the Earth below), it would very slightely decrease the overall strength of gravity towards the earth.

If we consider Earth and its moon, the center of gravity of both falls still in the radius of the planet. Does this mean gravity pulls down towards the center of gravity of the binary system instead of the actual center of the planet?

Yes.

If so, what would happen if the moon is much closer to Earth, like it used to be billions of years ago, making the center of gravity pop out of the surface of the planet?

The center of gravity ("center of mass" [COM] is a more common term) would move CLOSER to the center of the earth.

 

[proteus13]

Yes.

Does this mean gravity on Pluto actually pulls up towards the barycenter instead of down towards the planet? That would be odd... See the animated gifs I posted below

The center of gravity ("center of mass" [COM] is a more common term) would move CLOSER to the center of the earth.

I think you are wrong, at least common logic suggests otherwise, if Earth had no moon, then the center of gravity would be in its dead middle, and the planet won't wobble as it orbits the sun, adding a moon pulls that center away from the core of Earth, making a barycenter which is located a few thousand kilometers under the surface of Earth, the further the moon moves away the less it pulls the barycenter away from Earths center, the closer it gets the more it pulls it, if the moon was closer, Earth would wobble much more, because the barycenter will fall outside the planet, and the Earth/moon system will behave much like Pluto and Charon

[PLAIN]http://img543.imageshack.us/img543/3694/bary.gif


[PLAIN]http://img153.imageshack.us/img153/5300/plutocharon.gif


Even if I am wrong on those, let's assume Earth is much more dense and has the same mass but a much smaller radius, resulting in the center of gravity or mass or whatever falling outside the volume of Earth - how would that affect gravity on the planet? I mean the actual gravity on the planet itself, excluding the direct pull from the satellite.


Also, shouldn't the presence of the moon reduce the overall gravity of Earth, not only pulling the side it is facing up, but lowering the overall strength of gravity? Again, this is common logic speaking, since the so called barycenter is only an imaginary point, in fact gravity pull is distributed evenly and decays slowly as you move away from Earth, it is not like gravity pulls down to the actual barycenter IMO

 

[Janus]

Does this mean gravity on Pluto actually pulls up towards the barycenter instead of down towards the planet? That would be odd... See the animated gifs

The point towards which gravity appears to act from depends on your position with respect to the two bodies. The only time that it would appear to be towards the barycenter is if you were much further away from either body than the distance between them is.
If you are standing on Pluto, gravity pulls you towards Pluto's center, if you were standing on Charon, gravity pulls you towards the center of Charon.
Also, you must remember that both bodies are in orbit around the barycenter and thus are in free fall and thus at their centers, feel no gravity from the other. Any decrease in gravitational pull you would feel would due to tidal forces, which are the result of the differential gravity of one body across the diameter of the other.

I posted below




I think you are wrong, at least common logic suggests otherwise, if Earth had no moon, then the center of gravity would be in its dead middle, and the planet won't wobble as it orbits the sun, adding a moon pulls that center away from the core of Earth, making a barycenter which is located a few thousand kilometers under the surface of Earth, the further the moon moves away the less it pulls the barycenter away from Earths center, the closer it gets the more it pulls it, if the moon was closer, Earth would wobble much more, because the barycenter will fall outside the planet, and the Earth/moon system will behave much like Pluto and Charon.

No. The relative position of the barycenter is proportional to the masses of the bodies. Thus the Earth-Moon barycenter is located 1/82 of the distance from the Earth's center to the Moon's center. That relation remains constant no matter what the distance between the two bodies is. If you decreased the distance between the Earth and Moon by half, you would decrease the distance of the barycenter from the center of the Earth by half.

Even if I am wrong on those, let's assume Earth is much more dense and has the same mass but a much smaller radius, resulting in the center of gravity or mass or whatever falling outside the volume of Earth - how would that affect gravity on the planet? I mean the actual gravity on the planet itself, excluding the direct pull from the satellite.

It would become greater; a denser Earth would have a greater surface gravity. Tidal forces would also be smaller, since they would have a smaller diameter to work across.

Also, shouldn't the presence of the moon reduce the overall gravity of Earth, not only pulling the side it is facing up, but lowering the overall strength of gravity? Again, this is common logic speaking, since the so called barycenter is only an imaginary point, in fact gravity pull is distributed evenly and decays slowly as you move away from Earth, it is not like gravity pulls down to the actual barycenter IMO

Again, any influence the Moon has over the net gravitational pull felt on the surface of the Earth would be due to tidal forces. You would slightly lighter if the Moon were directly overhead or on the exact opposite side of the Earth, than you would if the Moon was on the horizon.

 

[proteus13]

Thanks a lot about this throughout explanation. However there is still something bothering me...


Based on what you said, Earth should wobble less if the moon is closer, and vice versa - wobble more as the moon goes further away. And that seems to escape reasonable logic - the wobble of the planet is due to the presence of the moon and its gravitational influence. Following the logic - if the moon is closer to Earth then it should influence its motion more, and as the moon goes further away, it s gravitational influence on Earth should decrease. After all if the moon is further away enough, it won't affect Earth's movement along its orbit at all.

There is geological evidence which suggests in the distant past tides were much higher than they are today... well not that distant exactly, about 250 million years ago. Since the moon itself didn't move that much in that time, I was wondering of mechanics which can result in lower overall gravity, since many of the dinosaurs shouldn't even be possible in the present day gravitational pull of the planet. My field is not astrophysics so I came here to investigate potential scenarios, which could result in lower gravity compared to present day, which would account for both the large specimen and the huge tides.

 

[Janus]

Thanks a lot about this throughout explanation. However there is still something bothering me...Based on what you said, Earth should wobble less if the moon is closer, and vice versa - wobble more as the moon goes further away. And that seems to escape reasonable logic - the wobble of the planet is due to the presence of the moon and its gravitational influence. Following the logic - if the moon is closer to Earth then it should influence its motion more, and as the moon goes further away, it s gravitational influence on Earth should decrease. After all if the moon is further away enough, it won't affect Earth's movement along its orbit at all.

There is geological evidence which suggests in the distant past tides were much higher than they are today... well not that distant exactly, about 250 million years ago. Since the moon itself didn't move that much in that time, I was wondering of mechanics which can result in lower overall gravity, since many of the dinosaurs shouldn't even be possible in the present day gravitational pull of the planet. My field is not astrophysics so I came here to investigate potential scenarios, which could result in lower gravity compared to present day, which would account for both the large specimen and the huge tides.

You're thinking about it from the wrong direction. Tidal forces will increase as the bodies near each other, but tidal forces, or even gravitational forces do not determine where the barycenter is. (if you were to suddenly decrease the mass of both the Earth and the Moon by the same ratio, thereby decreasing the gravitational pull between them, the barycenter would not move).

A better way to think about it is two people holding hands a swinging a circle with one being much lighter than the other. The lighter one will travel in a bigger circle than the heavier one. If they draw closer together, the lighter one travels in a smaller circle, so the heavier one also has to travel in a even smaller circle in response.

 

[proteus13]

So what you are saying is the ONLY possible way for Earth to have an overall lower gravity would be if it has lower mass and there is no other mechanic that could result in lower gravity?

 

[Janus]

So what you are saying is the ONLY possible way for Earth to have an overall lower gravity would be if it has lower mass and there is no other mechanic that could result in lower gravity?

Not overall. Tidal forces can reduce effective gravity at points of the surface and the rotation of the Earth reduces how much you weigh at the equator slightly.

 

[proteus13]

Such subtle and localized changes would hardly make a 100 tonn animal possible across the globe

 

[PangeaGravity]

I posted a reply to proteus13's last comment, yesterday. My response has disappeared. Can anyone explain why?

 

[Janus]

I posted a reply to proteus13's last comment, yesterday. My response has disappeared. Can anyone explain why?

Check your notifications.

 

[proteus13]

Seems like you didn't read the user agreement and rules upon registering, this forum is not a place for discussion on subjects outside the approved mainstream. A private message would be the appropriate way to express such opinions.

I guess according to the mainstream dinosaurs should not have existed, at least the biggest of them, they are simply not physically possible.Janus - I have another question, If gravity pushes down towards the planet, then somewhere within its volume there should be an area of zero gravity, the point where vectors of gravity meet and pretty much should cancel each other out, right?

If so, is that location influenced by the distance and gravitational pull of the moon?

 

[Janus]

Janus - I have another question, If gravity pushes down towards the planet, then somewhere within its volume there should be an area of zero gravity, the point where vectors of gravity meet and pretty much should cancel each other out, right?

If so, is that location influenced by the distance and gravitational pull of the moon?

No. That point is the CoG of the Earth and is what orbits the barycenter. The barycenter may shift with respect to it, but it does not shift with respect to the mass of the Earth.