0 Members and 1 Guest are viewing this topic.

The barycenter (or barycentre; from the Greek βαρύκεντρον) is the point between two objects where they balance each other. In other words, the center of gravity where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that lies outside the center of the greater body. For example, the moon does not orbit the exact center of the earth, instead orbiting a point outside the earth's center (but well below the surface of the Earth) where their respective masses balance each other.

If you tunnelled down to the barycenter, vertical gravitational forces would cancel out when the moon was aligned...

The force of gravity inside a perfect sphere (near enough) would be that due to the mass in the sphere below you. So if you say the earth's radius is 6000km and you tunnelled down 1000km the volume of earth beneath you would be (5/6)^3 of the whole earth.

The force of gravity inside a perfect sphere (near enough) would be that due to the mass in the sphere below you. So if you say the earth's radius is 6000km and you tunnelled down 1000km the volume of earth beneath you would be (5/6)^3 of the whole earth. Assuming that the earth had constant density (which it does not) then gravity would be reduced by this factor (x0.58). The fact that the core of the earth is more dense means that this would not be true but this is the principle. Of course if you tunneled down to the centre there would be no gravity.

I am puzzled as to the reference to the barycenter for answering this question.

Quote from: graham.d on 03/07/2008 15:39:02The force of gravity inside a perfect sphere (near enough) would be that due to the mass in the sphere below you. So if you say the earth's radius is 6000km and you tunnelled down 1000km the volume of earth beneath you would be (5/6)^3 of the whole earth. Assuming that the earth had constant density (which it does not) then gravity would be reduced by this factor (x0.58). The fact that the core of the earth is more dense means that this would not be true but this is the principle. Of course if you tunneled down to the centre there would be no gravity. You have forgotten that in this fictional tunnel the gravity from the portion of the Earth above the tunneler would exert an upward force on the tunneler.

Inside a solid sphere of constant density the gravitational force varies linearly with distance from the center,becoming zero at the center of mass.

So gravity at the bottom of a 1000km vertical tunnel would be 0.83x surface gravity,(assuming Earth's radius is 6000Km and Earth's density is uniform, which it isn't)

Alan, your answer seems somewhat bizarre given the original question. If you compressed the earth to half its radius then the gravity at the surface would be higher by a factor of 4 because the mass is the same but you are half the distance to the centre. If (and this was stated) the earth was constant density and you tunnel down to half the radius, the mass beneath you is 1/8th but you are half the distance to the centre. This gives half the gravity. I can do the maths (though rather boring to most

The gravitational force anywhere inside a uniform thick spherical shell, or a spherical cavity inside a volume of indefinite size is zero. This is one of the most counterintuitive facts about gravity.The reason is that the gravitational forces from all the other elements of the structure balance out and sum to zero.This means that for a uniform universe of indefinite extent the net gravitational force everywhere is zero but the moment any sort of irregularity appers these irregularities tend to grow whether they are areas of higher or lower density. A gravitating universe is always unstable and dynamic.Also the only universe in which there can be orbits with a long term metastability is one with an inverse square law of gravity

I also do not get your point balancing out as zero, this would only happen at the middle of the earths core.

No calculus needed, really.The force is proportional to the mass of the sphere beneath your feet (which is 4πρr3/3)ρ is density - we can assume it's fairly uniform.It's also proportional to 1/r2 because of the inverse square law.Between the two that makes it proportional to r. QED

Sophie, the reason for the calculus is only that it is not obvious that the field is zero everywhere inside a spherical shell. Knowing this means you don't need the calculus, but if you need to prove this, then I think you do need calculus.