Study Notes on Earth Satellites for Class 11 Physics – Introduction, Mechanics, Applications

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Introduction:

Satellites are celestial bodies that orbit a planet due to gravitational attraction. Earth satellites are either natural, like the Moon, or artificial, like those launched for communication, weather monitoring, and scientific research. Understanding Earth satellites is a critical aspect of physics as it involves concepts of circular motion, gravitation, and orbital mechanics.

1. What are Earth Satellites?

Earth satellites are objects that orbit Earth due to its gravitational pull. They can be categorized into:

• Natural Satellites: Bodies like the Moon.

• Artificial Satellites: Man-made objects such as GPS satellites, communication satellites, and weather satellites.

2. Classification of Artificial Satellites

• Geostationary Satellites:

- Orbit at an altitude of about 35,786 km.

- Period of revolution equals the Earth's rotation period (24 hours).

- Remain stationary relative to a point on Earth.

- Used for telecommunications and weather forecasting.

• Polar Satellites:

- Orbit at lower altitudes (700-800 km).

- Travel over the poles in a nearly north-south direction.

- Provide high-resolution images of Earth's surface.

• Low Earth Orbit (LEO) Satellites:

- Altitude ranges between 180 km and 2,000 km.

- Used for surveillance, scientific observation, and the International Space Station (ISS).

3. Orbital Mechanics

3.1. Centripetal Force and Gravity

Satellites remain in orbit due to the centripetal force provided by Earth's gravitational pull.

• The gravitational force provides the necessary acceleration for circular motion.

• Force F = G M m / r², where M and m are the masses of Earth and the satellite, respectively, r is the distance from the Earth's center, and G is the gravitational constant.

3.2. Orbital Velocity

The velocity required to keep a satellite in orbit is called orbital velocity:

vₒ = √(GM / r)

- For Earth, G and M are constants.

3.3. Time Period of a Satellite

The time period of revolution, T, is given by:

T = 2π √(r³ / GM)

This relation is derived using Kepler's Third Law.

4. Energy of a Satellite in Orbit

4.1. Kinetic Energy (KE)

The kinetic energy of the satellite is:

KE = 1/2 m vₒ² = GMm / 2r

4.2. Potential Energy (PE)

The potential energy is:

PE = -GMm / r

4.3. Total Energy (TE)

The total energy of the satellite is:

TE = KE + PE = -GMm / 2r

The negative sign indicates that the satellite is bound to Earth.

5. Launching of Satellites

Satellites are launched using rockets at a specific angle and velocity to achieve orbit.

• Escape Velocity: The minimum velocity needed to escape Earth's gravitational pull is given by:

vₑₛₛ = √(2GM / R)

Where R is Earth's radius.

6. Applications of Satellites

• Communication: TV broadcasting, internet services.

• Navigation: GPS technology.

• Weather Forecasting: Monitoring climatic conditions.

• Space Exploration: Research on other planets and celestial phenomena.

• Military and Surveillance: Strategic reconnaissance.

Conclusion:

Earth satellites, both natural and artificial, play a vital role in scientific exploration, communication, and understanding Earth’s environment. The study of their motion and mechanics is foundational in physics, merging concepts of gravitation and circular motion. With advancements in technology, satellites continue to be an integral part of modern life and scientific discovery.