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The gravitational phenomenon is described with the help of gravitational fields. A Gravitational field is a region where two bodies experience a force due to gravitation attraction. The strength of the gravitational field is determined in terms of N/Kg. The value of the gravitational field is 9.8N/kg on earth’s surface. There is variation in the magnitude of the gravitational field from place to place. Interaction between the satellite and Earth is an example of the gravitational field.
The concept based on the gravitational field tells about two things: everybody modifies its own surrounding space, known as the gravitational field. And the second one is if any other body of mass m is placed in this field, it feels a force of attraction called gravitational force. It is because of the interaction with the gravitational field. Earth has its gravitational field; when any other body is brought into these fields, they experience the forces towards Earth’s centre.
Gravitational Field Intensity Due to a uniform spherical shell.
Let us take a thin uniform spherical shell of radius R mass M. We have three regions:
Inside the spherical shell.
On the surface of the spherical shell.
Outside the spherical shell.
Derive an expression for the gravitational Field intensity outside the spherical shell.
The gravitational field intensity at a point varies as per the mass of the source and the distance of the point.
Within the imaginary sphere, the source mass is M, and the distance of separation is r.
Assume that vector F is the gravitational force experienced by the test mass, then the gravitational field intensity at point A will be;
Vector E = Vector F divided by the mass m.
The direction of Vector E and Vector F is the same, then
E = F/m…….eq (1).
According to newton’s law of gravitation;
F = GMm/r2; from this, E=F/m is
E = GM/r2……. eq (2)
At r = ∞ , E = 0 then gravitational field intensity decreases as distance r decreases and becomes 0 at infinity.
Let us take the test mass at a point ‘A’. The distance between the test pass and the centre of the spherical shell is ‘r’.
Draw an imaginary spherical shell such that point ‘A’ lies on the surface.
From above equation E= -GM/r2 where G is constant then intensity of gravitational field outside the spherical shell is given by ;
⇒ E ∝ -1/r2
Example 1. If the gravitational force and mass of a substance are 48N and 6kg. Determine the gravitational field.
Solution: The given parameters are, F = 48 N and m = 6 kg
The formula for gravitational field intensity is given by,
g = F/m = 48/6 = 8 N/kg
Example 2: If r is the radius of earth. Determine gravitational field intensity at the surface of the earth?
Assume the particle be of mass m then, force to gravity FG
FG=GMm/r2
Gravitational Field Intensity =FG/m
= GMm/r2*m
=GM/r2 = g
So the field intensity on the surface of the earth is g
Example 3. The gravitational field intensity at 5,000 km from the earth’s centre is 4.8Nkg-1. The gravitational potential at the point is Gravitational field intensity, E +GM/R2
Gravitational Potential, V= GM/R.
Hence V/E =-R
On given Parameters;
Centre of earth E is 4.8N/kg
-E=-4.8 N kg-1
Gravitational Field Intensity R = 5000km
0r V =-ER=-4.8*5000 *103.
= 24*106JKg-1
Conclusion
This article explains gravitational field intensity outside the spherical shell. Gravitational field intensity is defined as the intensity of this field when it is applied to the point mass. A gravitational force’s intensity depends upon the source mass and the distance of the unit test mass from the source mass. The intensity of the gravitational field outside the spherical shell is given by E = -GM/r2.
