Gravitation energy of a spherical shell

In summary, the formula for calculating the gravitation energy of a spherical shell is E = -3/5 * (G * M^2 / R). The negative sign in the formula indicates that the energy is always lost or released when the shell is formed. The mass and radius of the shell directly affect its energy, with an increase in mass resulting in an increase in energy and an increase in radius resulting in a decrease in energy. The gravitation energy of a spherical shell is not constant and can change over time. It is also a type of gravitational potential energy and can be converted into other forms, such as kinetic energy, through interactions with other objects.
  • #1
I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##.

Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give ##U = \iiint \frac{GM^2}{8 \pi r^4} dv = \frac{-GM^2}{2R}##.

Is my solution correct?
 
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  • #2
Yes, that looks correct.
 

1. What is the formula for calculating the gravitation energy of a spherical shell?

The formula for calculating the gravitation energy of a spherical shell is E = -3/5 * (G * M^2 / R), where E is the energy, G is the gravitational constant, M is the mass of the shell, and R is the radius of the shell.

2. What is the significance of the negative sign in the formula for gravitation energy of a spherical shell?

The negative sign in the formula represents the fact that the energy of a spherical shell is always negative. This means that the energy is always released or lost when the shell is formed, as it takes energy to pull the particles of the shell together.

3. How does the mass and radius of a spherical shell affect its gravitation energy?

The gravitation energy of a spherical shell is directly proportional to the mass of the shell and inversely proportional to the radius of the shell. This means that as the mass of the shell increases, its energy also increases, while as the radius of the shell increases, its energy decreases.

4. Is the gravitation energy of a spherical shell constant?

No, the gravitation energy of a spherical shell is not constant. It depends on the mass and radius of the shell, which can change over time. As the shell attracts more matter or expands, its energy will change accordingly.

5. How is the gravitation energy of a spherical shell related to its gravitational potential energy?

The gravitation energy of a spherical shell is a type of gravitational potential energy. It represents the energy that is stored in the gravitational field of the shell and is released when the shell is formed. This energy can also be converted into other forms, such as kinetic energy, when the shell interacts with other objects through gravity.

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