On the Surface of a Spherical Shell

All entities with mass or energy, including stars, galaxies, planets and even light, are attracted to (or gravitate toward) one another due to gravitation, a natural phenomenon.

The gravitational field is the field of force surrounding a body of finite mass in which another body would experience an attractive force proportional to the product of their masses and inversely proportional to the square of their distance. The strength of the gravitational field is measured by its intensity. It is the gravitational force acting on a one-unit mass. N/kg is the unit of measurement for gravitational field intensity.

Gravitational field

A gravitational field is the force field that occurs in space around any mass or group of masses. The gravitational field extends in all directions, but as the distance from the item grows, the amount of the gravitational force diminishes. It is measured in newtons per kilogramme (N/kg), a unit of force per mass. A gravitational field is similar to electric and magnetic fields for electrically charged particles and magnets.

The gravitational force F between two point masses M and m separated by a distance r acts along the line connecting their centres and is proportional to the masses and inversely proportional to the square of their separations, according to Newton’s Law of Gravitation.

F∝ Mm/r²

The proportionality constant in the SI unit system is G, the gravitational constant, which has a value of 6.67 x 10-11 Nm² kg ². Newton’s Law of Gravitation is re-written as follows:

F = GMm/r²

The gravitational field is defined as the gravitational force per unit mass that a tiny mass would experience at that location. It is a vector field that is in the direction of the force experienced by the mass. The magnitude of the resultant gravitational field strength g, at a distance r from M, for a point particle of mass M is

g=GM/r²

The gravitational force exerted on a mass m, usually known as its weight, is as follows:

F = mg

Gravitational field intensity

The force on a unit mass put at any location in the gravitational field defines an object’s gravitational field intensity or strength. So, if we transfer a unit test mass from infinity to a gravitational field, then the gravitational force acting on that unit test mass owing to a comparable larger mass for which the gravitational field is produced is known as gravitational field intensity.

A gravitational field interacts between the source mass and the test mass in a non-contact force. If the force acting on a body of mass m at a point in the gravitational field is F, then the intensity of the gravitational field at that point is –

g or E = F/m

Where g = gravitational field strength

F = gravitational force

M = mass of an object

Principle of superposition

The Principle of Superposition states that the total gravitational field can be calculated by putting the two vectors together. This may seem self-evident, but it is not valid for all forces in physics: strong forces between elemental particles and strong gravitational fields near black holes do not follow this rule. However, outside of black holes, simply adding the forces as vectors works great for gravity as well as for electric and magnetic fields. Finally, superposition works for any number of masses, not just two: the total gravitational field is the vector sum of all the individual masses’ gravitational fields.

Gravitational field intensity on the surface of a spherical shell

Consider a thin uniform spherical shell in space with radius ‘R’ and mass ‘M.’ A three-dimensional object divides space into three pieces.

– Inside the spherical shell.

– On the surface of the spherical shell.

– Outside the spherical shell.

On the Surface of Spherical Shell –

Consider a unit test mass at a point ‘P’ on the spherical shell’s surface at a distance ‘r’ from the centre, then r = R.

E = -GM/R²

⇒ E = Constant

Conclusion

A spherical shell divides space into three pieces – Inside the spherical shell, On the surface of the spherical shell, Outside the spherical shell. Gravitational field intensity on the surface of the spherical shell: r = R, E = -GM/R² ⇒ E = Constant. The force on a unit mass put at any location in the gravitational field defines an object’s gravitational field intensity or strength. The gravitational force applied on the unit test mass due to a comparable larger mass for which the gravitational field  produced is known as gravitational field intensity. The Principle of Superposition states that the total gravitational field can be calculated by putting the two vectors together.