v: Orbital speed (m/s)
Mass of sun: mE = 1.98
x 1030 kg
Mass of the Earth: mE =
5.98 x 1024 kg
Mass of the moon: mE =
7.34 x 1022 kg
CALCULATION OF GRAVITATIONAL FIELD INTENSITY ON THE SURFACE OF THE EARTH:
g: gravitational field intensity
on the surface of the Earth
GRAVITATIONAL POTENTIAL ENERGY
Gravitational potential energy is always negative. As r approaches to infinity, EG approaches to zero.
ESCAPE FROM A GRAVITATIONAL FIELD
To escape an object from the orbit of the central body, the objects' total energy must be greater than zero. Since the gravitational potential energy of the object is always negative, and depends on the position of the object, the kinetic energy must be increased to make total energy greater than zero. This additional kinetic energy is called the binding energy. when the object escape from the central body, it will no longer to be bound to the central body.
In general, binding energy is the energy required to disassemble a whole into separate parts. Gravitational binding energy is the amount of additional kinetic energy needed by an orbiting object to escape from the orbit of the central body. To escape the orbiting object from the potential well of a central body, total mechanical energy must be greater than zero (positive value). Therefore, the formula for binding energy:
Binding Energy = 0 - total mechanical energy = - total mechanical energy
Example 1: Finding binding energy of an object currently orbiting around a central bodyTotal energy of object of orbiting around the central body:
Since the orbital gravitational potential energy does not change at the given location, kinetic energy must be increased to make the orbital total energy greater than zero.
Binding Energy = G M m / 2r
Example 2: Finding the binding energy of an object at rest on the surface of the Earth
Since the object at rest, kinetic energy of the object equals to zero and total energy of the object equals to gravitational potential energy of the object.
ET = - G ME m / rE
Binding Energy = 0 - total mechanical energy = - total mechanical energy = Binding Energy = G ME m / rE
Escape velocity is the minimum velocity needed for an object to escape the gravitational pull of another object at a given distance. To escape an object from the potential well of a central body, total mechanical energy must be greater than zero (positive value). At the escape velocity, any object will escape from the central body and never come back again to the central body.
The escape speed does not depend on the
direction in which a projectile is fired from a planet. Direction of the
escape speed is not important. Unless the object hits the central
body, the object will escape if its speed is greater than escape speed. Escape speed from the earth surface is 11.2 km/s.
KEPLERíS LAWS OF PLANETARY MOTION:
1. The planets move around the
sun in elliptical orbits, with the sun at one focus of the ellipses.
3. The square of the period of revolution of a planet about the sun is proportional to the cube of its mean distance from the sun.
C: The constant of proportionality of the central body (m3/s2)
The constant of proportionality of the central body
The constant of proportionality of the sun: Cs = 3.355 x 1018 m3/s2