Grav. field of spherical objects

In summary, the gravitational field created by a point of mass m is the same as that of a spherical object of the same mass outside the volume of the object. This is known as the shell theorem or Gauss' theorem. This is because the net gravity from a spherical shell is zero on the inside of the shell and the same as from a point mass at the center of the shell on the outside. This balancing effect is due to the varying distances of the mass from the object. To prove this, vector calculus is required.
  • #1
alexbib
62
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will the gravitational field created by a point of mass m be the same than that of a spherical object of same mass (outside the volume of the object)? If so, why is this? How does the sum of the grav forces created by all the points in the sphere add up to the same as a point-mass?
Thanks,

Alex
 
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  • #2
With Newtonian gravity the net gravity from a spherical shell is zero on the inside of the shell, and the same as from a point mass at the center of the shell from the outside. (I'm not sure about the shell itself.)

Proving this wihout calculus (or developing calculus as part of the proof) is pretty daunting.
 
  • #3
I think it's called the shell theorem, maybe you can find that on google?
 
  • #4
Yes, it's the same. In other words, if the mass of the Earth were compressed into a single point (ie a black hole) at the same distance from you (about 4000 miles) as the center of the Earth is now, you would feel the same amount of gravity.

The reason is that some of the mass of the Earth is further from you than the center and some of it is closer, and the net effect balances out that way. To prove it requires vector calculus.
 
  • #5


It is called the Gauss' theorem
 

1. What is the gravitational field of a spherical object?

The gravitational field of a spherical object is the force per unit mass experienced by another object placed at a certain distance from the center of the sphere. It is a vector quantity, meaning it has both magnitude and direction.

2. How is the gravitational field of a spherical object calculated?

The gravitational field of a spherical object is calculated using the formula g = GM/r^2, where g is the gravitational field, G is the universal gravitational constant, M is the mass of the spherical object, and r is the distance from the center of the sphere to the object experiencing the gravitational force.

3. Does the mass of a spherical object affect its gravitational field?

Yes, the mass of a spherical object has a direct impact on its gravitational field. The larger the mass, the stronger the gravitational field will be. This is because more massive objects have a greater gravitational pull.

4. How does the distance from a spherical object affect its gravitational field?

The distance from a spherical object has an inverse relationship with its gravitational field. As the distance increases, the gravitational field decreases. This means that the closer an object is to the sphere, the stronger the gravitational field will be.

5. Can the gravitational field of a spherical object be negative?

No, the gravitational field of a spherical object cannot be negative. It is always a positive value, as it represents the force of attraction between two objects. However, the direction of the field can be negative if it is pointing in the opposite direction of the force of gravity.

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