gravitation
Basic Concepts and Formulae
F = -Gm1m2/r2 (gravitational force) (1)
The negative sign shows that the force is attractive.
When SI units are used the gravitational constant
G = 6.67 × 10-11 kg-1 m3 s-2
The intensity or field strength g of a gravitational field is equal to the force exerted on a unit
mass placed at that point.
g = -Gm/r2 (2)
The (negative) gravitational potential at a given point, due to any system of masses, is the
work done in bringing a unit mass from infinity up to that point.
The zero potential is chosen conventionally at infinity. Symbolically
(3)
(4)
(5)
Spherical Shell
The gravitational intensity due to a spherical shell of radius a.
g(r) = 0 (r < a) = -G M/r 2 (r > a) (6)
where r is measured from the centre of the shell. The potential
(7)
Uniform Solid Sphere
(8.a)
(8.b)
Potential energy of a uniform sphere
U = -3G M2/5a (9)
Basic Concepts and Formulae
F = -Gm1m2/r2 (gravitational force) (1)
The negative sign shows that the force is attractive.
When SI units are used the gravitational constant
G = 6.67 × 10-11 kg-1 m3 s-2
The intensity or field strength g of a gravitational field is equal to the force exerted on a unit
mass placed at that point.
g = -Gm/r2 (2)
The (negative) gravitational potential at a given point, due to any system of masses, is the
work done in bringing a unit mass from infinity up to that point.
The zero potential is chosen conventionally at infinity. Symbolically
(3)
(4)
(5)
Spherical Shell
The gravitational intensity due to a spherical shell of radius a.
g(r) = 0 (r < a) = -G M/r 2 (r > a) (6)
where r is measured from the centre of the shell. The potential
(7)
Uniform Solid Sphere
(8.a)
(8.b)
Potential energy of a uniform sphere
U = -3G M2/5a (9)
