GRAVITATIONAL FIELDS

Calculation of gravitational field intensity of central body

F_G:  Magnitude of the force of gravity (N)
G:  universal gravitation constant (G = 6.67 x 10^-11 N.m²/kg²)
g:  gravitational field intensity of the body (N/kg)
m:  Mass of a body influenced by the gravitational field of the central body (kg)
M_:  Mass of the central body (kg)
r_:  Distance between the centres of the two bodies (m)
F_c:  Centripetal force between the two bodies (N)


Kepler’s Third Law of Planetary Motion:

The constant of proportionality of the central body	The constant of proportionality of the sun

C_S:  The constant of proportionality of the central body (m³/s²)
G:  universal gravitation constant (G = 6.67 x 10^-11 N.m²/kg²)
M_:  Mass of the central body (kg)
r_:  Distance between the centres of the two bodies (m)
T:  Period of the object undergoing uniform circular motion (s)

GRAVITATIONAL POTENTIAL ENERGY

E_G: Gravitational potential energy of the body with respect to central body (J)
G:  universal gravitation constant (G = 6.67 x 10^-11 N.m²/kg²)
m:  Mass of a body influenced by the gravitational field of the central body (kg)
M_:  Mass of the central body (kg)
r_:  Distance between the centres of the two bodies (m)
g:  gravitational field intensity of the body (N/kg)

Gravitational potential energy is always is negative.  As r approaches to infinity, E_G approaches to zero.

Approximate formula in case the difference between r1 and r2 is not much:

ESCAPE FROM A GRAVITATIONAL FIELD

v:  Escape speed is the minimum speed needed for an object to escape the gravitational pull of another object at a given distance.  To escape the object from the potential well of a central body, total mechanical energy must equal zero.  At the escape velocity, any object will escape from the central body and never come back again to the central body.

E_T = E_K + E_G = 0
E_K = - E_G

ORBITAL SPEED

v:  Orbital speed. Orbital speed is the speed is required for an object to stay in orbit above a central body.  Speed of the object undergoing uniform circular motion (m/s).  This is a constant speed (m/s) and perpendicular to the gravitational force.

F_G = F_C

ORBITAL KINETIC ENERGY:

ORBITAL GRAVITATIONAL POTENTIAL ENERGY:

ORBITAL TOTAL ENERGY:

Escape energy is the minimum kinetic energy needed to give an object its escape speed.