Y is everything attracted to a place with a gravitational force
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The centre of mass of an object is not in general the point from which its gravitational attraction may be assumed to act. Instead the centre of mass (for a rigid body) is the point at which its inertial mass may be assumed to be located when an external force acts on it (it tells us how the Earth responds to the gravity of the Sun for example). This doesn’t help us to understand why for spheres the centre of gravitational attraction is actually at the same place as the centre of mass.
From symmetry we can indeed safely say that the gravitational attraction due to a sphere like the (idealized) Earth acts along the line connecting the attracted body to the centre. That is because the sideways pull of one hemisphere will be cancelled by the opposite sideways pull of the other hemisphere, so the only surviving component of the force is parallel to the line. That gives us the direction of the force. But why should the distance to the centre of attraction be the same as the distance to the actual, geometric centre? It’s not guaranteed by symmetry.
The fact that these distances are indeed the same is actually a special feature of spheres which is a deep consequence of the fact that gravity follows an inverse square law. Any other force law (e.g. an inverse cube law) would not mean objects were attracted to the centre of the Earth but to some other nearer or further point lying on the same line. Likewise the centre of mass is not the centre of attraction for geometrical objects other than spheres. You have to learn some mathematics to see why this is true but it is something that Newton understood.
Finally your question asks, why downwards? It’s a fair question. Again, symmetry would not prevent it acting upwards, as long as it acted along the same line we have been talking about. The answer is because firstly for ordinary matter we only ever find positive amounts of mass and energy, and secondly for a force like gravity two positive quantities attract. It is the opposite of what happens for electromagnetism where two positive charges repel. I won’t go into the deep reasons for the difference - but we think we understand that as well (see this post: Why does gravity pull towards the center of the Earth and do not repulse instead?)…
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Pallaw Kumar
Pallaw Kumar
Updated Jan 19, 2014
Gravity or gravitational force is exerted by an object by the virtue of its mass. By nature, it is always attracting, i.e one object always tends to pull other objects toward itself.
Now Earth can be assumed as a solid sphere. So by symmetry we know that its centre of mass is at the centre. (centre of mass is a point at which all the matter of a body can be assumed to be concentrated) This means the whole Earth can be thought as a point mass situated at its centre with the same mass as that of Earth. So the resultant of the gravitational force exerted on us by each point of the earth, finally points towards this centre.
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Tushar Nair
Tushar Nair, Physics Maniac,Future Mechanical Engineer
Answered May 14, 2016
Actually its nature who has made this gravitational pull as attractive in nature. Hence gravitational force of earth always tends to attract other bodies towards earth. Now here comes a big question why towards its centre? If your are aware of rigid body dynamics, the centre of mass of a sphere is at its centre. And earth is a sphere( not accurately,but roughly speaking). Hence earth’s whole mass is supposed to be concentrated at its centre. Since gravitational forces acts along the line joining the centre hence earth attracts all bodies to a place where its effect becomes negligible ie. the body comes under equillibrium. Since the centre of mass is at centre hence the equillibrium posotion of zero force is at its centre. Therefore eearth pull every objects towards its centre.
From symmetry we can indeed safely say that the gravitational attraction due to a sphere like the (idealized) Earth acts along the line connecting the attracted body to the centre. That is because the sideways pull of one hemisphere will be cancelled by the opposite sideways pull of the other hemisphere, so the only surviving component of the force is parallel to the line. That gives us the direction of the force. But why should the distance to the centre of attraction be the same as the distance to the actual, geometric centre? It’s not guaranteed by symmetry.
The fact that these distances are indeed the same is actually a special feature of spheres which is a deep consequence of the fact that gravity follows an inverse square law. Any other force law (e.g. an inverse cube law) would not mean objects were attracted to the centre of the Earth but to some other nearer or further point lying on the same line. Likewise the centre of mass is not the centre of attraction for geometrical objects other than spheres. You have to learn some mathematics to see why this is true but it is something that Newton understood.
Finally your question asks, why downwards? It’s a fair question. Again, symmetry would not prevent it acting upwards, as long as it acted along the same line we have been talking about. The answer is because firstly for ordinary matter we only ever find positive amounts of mass and energy, and secondly for a force like gravity two positive quantities attract. It is the opposite of what happens for electromagnetism where two positive charges repel. I won’t go into the deep reasons for the difference - but we think we understand that as well (see this post: Why does gravity pull towards the center of the Earth and do not repulse instead?)…
1.4k Views · View Upvoters
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Shonya KhanComment...
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Pallaw Kumar
Pallaw Kumar
Updated Jan 19, 2014
Gravity or gravitational force is exerted by an object by the virtue of its mass. By nature, it is always attracting, i.e one object always tends to pull other objects toward itself.
Now Earth can be assumed as a solid sphere. So by symmetry we know that its centre of mass is at the centre. (centre of mass is a point at which all the matter of a body can be assumed to be concentrated) This means the whole Earth can be thought as a point mass situated at its centre with the same mass as that of Earth. So the resultant of the gravitational force exerted on us by each point of the earth, finally points towards this centre.
2.9k Views · View Upvoters
Upvote · 7
Shonya KhanComment...
Promoted by CareSpace
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Tushar Nair
Tushar Nair, Physics Maniac,Future Mechanical Engineer
Answered May 14, 2016
Actually its nature who has made this gravitational pull as attractive in nature. Hence gravitational force of earth always tends to attract other bodies towards earth. Now here comes a big question why towards its centre? If your are aware of rigid body dynamics, the centre of mass of a sphere is at its centre. And earth is a sphere( not accurately,but roughly speaking). Hence earth’s whole mass is supposed to be concentrated at its centre. Since gravitational forces acts along the line joining the centre hence earth attracts all bodies to a place where its effect becomes negligible ie. the body comes under equillibrium. Since the centre of mass is at centre hence the equillibrium posotion of zero force is at its centre. Therefore eearth pull every objects towards its centre.
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