Reasoning: The critical tangential velocity required for a satellite to revolve in a stable circular orbit at height h above the Earth is given by the formula:

v_c = √(GM / (R + h))

Here, G is the gravitational constant, M is the Earth's mass, and R is the Earth's radius. As orbital height h increases, the denominator (R + h) increases, which reduces the required tangential velocity v_c.

Reasoning: Escape velocity is the minimum launch speed needed for a spacecraft to escape the Earth's gravitational pull and journey into interplanetary space without falling back. Since Mangalyaan was destined for Mars, its launch velocity had to be at least equal to or greater than the escape velocity of Earth.

Reason: Escape velocity is the absolute minimum velocity necessary for an object to overcome the gravitational pull of the Earth. If its velocity is less than the escape velocity, the spacecraft cannot leave Earth's gravitational field and will remain trapped in an orbit or fall back to Earth.

Reason: Escape velocity is expressed by vesc = √(2GM / R). Because the Moon has a much smaller mass (approx. 1/81 of Earth's mass) and smaller radius than the Earth, its surface gravity is weaker. Therefore, escape velocity on the Moon is only about 2.37 km/s, which is much less than on Earth (11.2 km/s).

Reason: For a satellite of mass m orbiting at height h, the required centripetal force is provided by the Earth's gravitational force:

mv_c² / (R + h) = GMm / (R + h)² ⇒ v_c = √(GM / (R + h))

Because G, M, and R are constants, for any predetermined orbital altitude h, there is only one exact tangential velocity v_c that maintains orbital equilibrium.

Reason: As shown by the critical velocity relation vc = √(GM / (R + h)), velocity is inversely proportional to the square root of the orbital radius √(R + h). Thus, as altitude h increases, orbital velocity decreases rather than increases.

A manmade mechanical instrument launched into space that revolves around the Earth or any other planetary body in a predetermined orbit is called an artificial satellite.

Classification based on operational functions:

1. Weather Satellites: Collect real-time atmospheric data (air pressure, cloud motion, moisture, wind velocity) to forecast weather conditions and issue cyclone alerts (e.g., INSAT, METSAT).
2. Communication Satellites: Transmit telecom signals, telephone calls, high-speed mobile data, and Internet traffic across global ground stations (e.g., GSAT series).
3. Broadcasting Satellites: Relay radio programs, television telecasts, and live educational broadcasts worldwide.
4. Navigational Satellites: Transmit precise timing signals to pinpoint exact latitude, longitude, and elevation of objects on land, sea, or air (e.g., IRNSS / NavIC, GPS).
5. Military / Reconnaissance Satellites: Monitor international borders, track defense movements, provide strategic intelligence, and guide military missiles.
6. Earth Observation Satellites: Map mineral deposits, forest cover, agricultural crops, ocean resources, and survey drought or disaster zones (e.g., IRS series, Cartosat).
7. Scientific / Space Research Satellites: Equipped with space telescopes to observe celestial bodies, black holes, and the cosmos without atmospheric distortion (e.g., Astrosat, Hubble Space Telescope).

The defined gravitational trajectory or path along which an artificial satellite revolves around the Earth is called its orbit.

Classification of orbits based on altitude above Earth's surface:

1. High Earth Orbit (HEO):
   • Height: Greater than or equal to 35,780 km.
   • Period of Revolution: Approx. 24 hours (matching Earth's rotation period).
   • Characteristics: When placed in the equatorial plane, the satellite appears stationary relative to a fixed observer on Earth; hence called a Geostationary satellite. Critical velocity is ~3.08 km/s. Used for telecommunications, weather monitoring, and broadcasting.
2. Medium Earth Orbit (MEO):
   • Height: Between 2,000 km and 35,780 km.
   • Period of Revolution: Takes about 2 to 24 hours (typically ~12 hours).
   • Characteristics: Often placed in inclined or polar elliptical orbits. Primarily used for satellite navigation systems (e.g., GPS, NavIC).
3. Low Earth Orbit (LEO):
   • Height: Between 180 km and 2,000 km.
   • Period of Revolution: Takes only about 90 minutes to complete one circle around Earth.
   • Characteristics: Used for Earth observation, scientific exploration, space laboratories (e.g., International Space Station, Hubble Space Telescope).

• A geostationary satellite is situated at an altitude of 35,780 km and orbits strictly in the equatorial plane of the Earth (orbital inclination = 0°).
• Because it revolves directly over the equator, the Earth's natural spherical curvature prevents the satellite from establishing a direct line-of-sight view to the North and South polar regions (high latitudes above 75°–80°).
• Therefore, signals cannot be sent easily to polar regions, so geostationary satellites cannot monitor the poles. Polar studies instead require polar-orbiting satellites with a 90° inclination.

A satellite launch vehicle (SLV) is a powerful multi-stage rocket system specifically designed to carry artificial satellites or space probes from the surface of the Earth, lift them to the desired orbital altitude, and impart the required tangential velocity to insert them into orbit.

ISRO's Polar Satellite Launch Vehicle (PSLV):

The PSLV is India's highly dependable four-stage launch vehicle employing alternating solid and liquid propulsion:

1. 1st Stage (Solid): Houses the primary core solid propellant motor (HTPB fuel) supported by attached solid booster motors to produce strong liftoff thrust.
2. 2nd Stage (Liquid): Powered by the high-thrust liquid-fueled Vikas engine utilizing unsymmetrical dimethylhydrazine (UDMH) fuel and nitrogen tetroxide (N₂O₄) oxidizer.
3. 3rd Stage (Solid): A high-performance solid rocket motor providing upper-altitude velocity increment.
4. 4th Stage (Liquid): Twin liquid propellant engines that perform precision thrust adjustments to accurately inject the payload satellite into its predetermined orbit.
5. Payload Fairing (Heat Shield): Located at the nose cone to shield the satellite payload from atmospheric friction and aerodynamic heat during ascent through Earth's dense atmosphere.

• In a single-stage rocket, the heavy weight of empty fuel tanks and engine parts must be carried all the way into space, which requires a huge amount of fuel.
• In a multi-stage rocket, once a stage uses up its fuel, its empty body is detached and dropped off safely.
• Dropping the empty stage greatly reduces the total weight of the rocket.
• With much less rocket weight, the next stage engine can easily speed up the rocket to orbit using far less fuel, making space missions practical and cost-effective.