Gravitation-Variations In G-Satellites

The motion of a satellite is a projectile around the Earth. When a satellite is launched into orbit, the only force that governs the satellite’s motion is the force of gravity. Satellites are objects that revolve around the planet. They can be of two types: natural satellites and artificial satellites. Natural satellites are natural objects like the moon, which revolve around the planet, while artificial satellites are placed intentionally to fulfil its function per our requirement.

Gravitation

Each and every body that has some mass attracts another by virtue of their masses, but the force between the two is negligible. But when the masses are huge, such as planets and satellites, the forces between them can not be neglected. This phenomenon of attraction between a planet and another object is known as gravitation.

Newton’s Law of Gravitation

According to Newton’s Law of Gravitation, the gravitational force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravitational Force, F = Gm1m2R2

Where,

• G is the gravitational constant, and its value is 6.6710-11Nm2kg-2.
• m1 ,m2are the masses of the two bodies interacting, and r is the distance between them.

Gravitational force is a conservative force, and it is central as well.

Acceleration Due to Gravity of Earth

The acceleration of the body produced due to the gravitational pull of the Earth is called acceleration due to gravity. It is given by the formula,

g =GMR2, 

where G is the gravitational constant, 

M is the mass of the Planet (Earth in this case), and 

R is the radius of the planet.

Conditions Affecting the value of gravity (g)

• Effects of the Altitude: The value of g decreases with the increase in the height of the object above the surface of the plane.
• Effects of the Depth: The value of g decreases with increasing depth, and it becomes zero at the centre of the planet.
• Rotation: The velocity by which the planet rotates on its own axis affects the value of g, such that when the angular speed is decreased, the value of g increases, and vice versa.
• The shape of the planet: The shape of the planet affects the value of the acceleration due to gravity. That is why the value of the g is maximum at the poles of the Earth and minimum at the equator.

Planets

Planets: Planets can be defined as a celestial body that is in an orbit around the sun. It has sufficient mass to have its own gravity to overcome rigid body forces.

Satellite

A satellite can be defined as a heavenly body that revolves around the planet in an orbit. There are mainly two types of satellite:

1. Natural satellite
2. Artificial satellite

Natural Satellite

A natural satellite is a heavenly body that orbits around a planet, dwarf planet, or small solar system body. Natural satellites are mostly referred to as moons. The Earth also has a natural satellite that is its own moon.

Artificial Satellite

There are two types of artificial satellites:

1. Geosynchronous satellite
2. Polar satellite

Geosynchronous Satellite

• A satellite with an orbital period the same as the Earth’s rotation period, such that the satellite is in geosynchronous orbit, is known as Geosynchronous Satellite.
• There is a special type of Geosynchronous Satellite with a geostationary orbit, which means it has a circular geosynchronous orbit that is directly above the Earth’s equator.
• This kind of satellite revolves around the Earth at a height of 3.6104km above the surface of the Earth.
• These satellites are mainly used for telecasting TV programmes, weather forecasting, predicting floods and droughts, etc.
• The time period of rotation of this satellite is the same as the Earth’s time period of rotation around its own axis, therefore, 24 hours.

Polar Satellites

• This kind of satellite revolves around the Earth in polar orbit at a height of 800 km above the surface of the Earth.
• The time period of rotation of these satellites is 84 minutes.

Escape Velocity

The escape velocity can be defined as the velocity needed by an object to escape the atmosphere of the Earth (Earth’s Gravitational field) and never return. It is given as,

Escape Velocity = (2gr)0.5

The escape velocity at Earth is 11.2 km/sec, while on the Moon, it is 2.4 km/sec.

Satellite and Projectile

The motion of the satellite around the planet is in a projectile motion. And the force that is acting upon the satellite during its motion around the planet is the gravitational force.

When a projectile is launched horizontally from the top of a mountain such that the location is high above the influence of air drag, then the projectile will move horizontally in a direction that is tangent to the surface of the Earth, while the force of the gravity will pull it downward.

• If the velocity of the projectile is less than the escape velocity, the projectile will fall back to the Earth.
• If the launch speed of the projectile is sufficient, then the projectile would fall towards the surface of the Earth at the same rate that the Earth curves, which will make the projectile stay at the same height above the Earth’s surface, and the orbit will be a circular path.
• If the launch speed is much greater, it will cause the projectile to revolve around the planet, but the orbit will be an elliptical path.

Conclusion

Gravitational force is the weakest force, and this force of gravity causes the object to fall. But the same gravity causes satellites to stay at the same height from the surface of the Earth. There are two types of satellites based on their orbit and height. The motion of a satellite is projectile.