The gravitational and astronomical laws were originally formulated to explain

the motion of planets in the solar system and their orbits around the sun.

..............................were originally formulated to explain

the motion of planets in the solar system and their orbits around the sun.

The gravitational and astronomical laws

These laws (Newtonian and Keplerian) are equally applicable to

the orbits of artificial satellites placed around the earth.

.........................the orbits of artificial satellites placed around the earth.

These laws (Newtonian and Keplerian) are equally applicable to

Newton’s Law of Universal Gravitation

The force of attraction between two point masses m1 and m2 separated by a distance r is

where G is

is theUniversal gravitation constant(6.67259x10‐11 N m2 kg‐2).

the following is

Newton’s Law of Universal Gravitation

The force of attraction between two point masses m1 and m2 separated by a distanceris:

Consider the simple circular orbit shown in Figure. Assuming that the Earth is a ........................, we can treat it as ......................

sphere, we can treat it as a point mass

The centripetal force is required to

keep the satellite in a circular orbit is rnv^2/r, here v is the orbital velocity of the satellite.

......................................... that balances this centripital force is ..........................

The force of gravity (F)

Gm_{e}m/r^{2}

Theforce of gravity (F) that balances thiscentripetal forceis Gm_{e}m/r^{2}

,where m_{e} is

and m is

the mass of the Earth (5.97370x10^{24}kg)

the mass of the satellite

Theforce of gravity (F) that balances thiscentripetal forceis Gmem/r2

,whereme is the mass of the Earth (5.97370x10^{24}kg) and mis the mass of the

satellite. Equating the two forces gives:

Division bym eliminates the mass of the satellite from the equation, which

means that

the orbit of a satellite is independent of its mass

Orbital Period (T):

The time taken by a satellite to travel around its orbit once is known as the

period.

The period of an orbit simply depends on

its altitude

The period of the satellite is

the orbit circumference divided by the velocity:

T=2πr/v

orbital period =

For any given height above the Earth's surface, a satellite will

take a fixed time

to complete an orbit, regardless of the mass of the satellite.

for ................................................... a satellite will take a fixed time to complete an orbit, regardless of the mass of the satellite.

For any given height above the Earth's surface

Kepler’s laws of motion:

###
- law of orbits
- law of areas
- law of periods

Kepler’s laws of motion state that:

1.

Law of orbits: All planets travel in elliptical paths with the sun at one focus.

Kepler’s laws of motion state that:

2.

Law of areas: The radius vector from the sun to a planet sweeps out equal areas in equal times

- This empirical law discovered by Kepler arises from conservation of angular momentum.
- When the planet is closer to the sun,it moves faster, sweeping through a longer path in a given time.

Kepler’s laws of motion state that:

3.

Law of Periods: The ratio of the square of the period of revolution of a planet to the cube of its semimajor axis (radius of orbit) is the same for all planets revolving around the sun.

Kepler’s laws of motion

These laws are also applicable to

the artificial satellites placed in elliptical orbits (also called Keplerian orbits) around the earth at one focus.

define perigee

The point where the satellite most closely approaches the Earth

perigee more generally the

perifocus

apogee is also known as

apofocus

apogee or apofocus:

The point where the satellite is furthest from the Earth

semimajor axis is denoted by the symbol

a

semimajor axis:

The distance from the center of the ellipse to the perigee (or apogee)