Chapter 5
Gravitation
Abstract Chapter 5 involves problems on gravitational field and potential for
various situations variation of g, rocket motion, orbital motion of planets, satellites
and meteorites, circular and elliptic motion, bound and unbound orbits, Kepler’s
laws, equation of motion under various types of forces.
5.1 Basic Concepts and Formulae
F = −Gm 1 m 2 /r
2 (gravitational force)
(5.1)
The negative sign shows that the force is attractive.
When SI units are used the gravitational constant
G = 6.67 × 10
−11 kg
−1 m
3 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/r
2
(5.2)
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
g = −
∂ V
∂r
(5.3)
V = −Gm/r
(5.4)
The potential energy
U = −G Mm/r
(5.5)
189
Gravitation
Abstract Chapter 5 involves problems on gravitational field and potential for
various situations variation of g, rocket motion, orbital motion of planets, satellites
and meteorites, circular and elliptic motion, bound and unbound orbits, Kepler’s
laws, equation of motion under various types of forces.
5.1 Basic Concepts and Formulae
F = −Gm 1 m 2 /r
2 (gravitational force)
(5.1)
The negative sign shows that the force is attractive.
When SI units are used the gravitational constant
G = 6.67 × 10
−11 kg
−1 m
3 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/r
2
(5.2)
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
g = −
∂ V
∂r
(5.3)
V = −Gm/r
(5.4)
The potential energy
U = −G Mm/r
(5.5)
189