1. The binding energy of a satellite is the energy required for it to escape its orbit around the Earth and move to infinity. The total energy of a satellite in orbit is given by: E = - GMm/2r. where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is tRead more

    The binding energy of a satellite is the energy required for it to escape its orbit around the Earth and move to infinity.

    The total energy of a satellite in orbit is given by:
    E = – GMm/2r.
    where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the orbital radius.

    To escape to infinity, the satellite must be provided with additional energy equal to:
    + GMm/2r
    This additional energy ensures that the total energy E becomes zero, allowing the satellite to escape Earth’s gravitational pull.

    Thus, the binding energy of a satellite is:
    Binding energy = GMm/2r.

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  2. Uses of Geostationary Satellites Geostationary satellites play a vital role in global communication by relaying radio, television, and telephone signals. They are also instrumental in studying the upper layers of the atmosphere and contribute significantly to weather forecasting. These satellites heRead more

    Uses of Geostationary Satellites

    Geostationary satellites play a vital role in global communication by relaying radio, television, and telephone signals. They are also instrumental in studying the upper layers of the atmosphere and contribute significantly to weather forecasting.
    These satellites help determine the precise shape and dimensions of the Earth and assist in researching meteorites. Additionally, they are valuable for studying solar radiation and cosmic rays.

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  3. Geostationary satellites play a crucial role in global communication. A single satellite cannot provide coverage over the entire Earth due to the planet's curvature, which blocks a large portion of the surface from view. To overcome this, three satellites are placed in a geostationary orbit, spacedRead more

    Geostationary satellites play a crucial role in global communication. A single satellite cannot provide coverage over the entire Earth due to the planet’s curvature, which blocks a large portion of the surface from view. To overcome this, three satellites are placed in a geostationary orbit, spaced 120° apart. These satellites, equipped with radio transponders, enable line-of-sight communication between any two points on Earth.

    Such satellites are known as synchronous communication satellites (SYNCOMS). The geostationary orbit is also referred to as the Clarke geosynchronous orbit or Clarke arc, named after the renowned science writer Arthur C. Clarke, who first proposed the concept of communication satellites in 1945.

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  4. Different Theories About Planetary Motion. Since ancient times, scientists have studied the motion of celestial objects like the Sun, planets, and the Moon. Some significant theories about planetary motion are as follows: (i) Geocentric Model Around 100 A.D., the Greek astronomer Ptolemy introducedRead more

    Different Theories About Planetary Motion. Since ancient times, scientists have studied the motion of celestial objects like the Sun, planets, and the Moon. Some significant theories about planetary motion are as follows:

    (i) Geocentric Model
    Around 100 A.D., the Greek astronomer Ptolemy introduced the geocentric model in his book The Almagest. This model suggested that the Earth is stationary at the center of the universe, and all celestial objects, including the Sun, Moon, and planets, revolve around it. The planets were believed to move in small circular paths called epicycles, whose centers followed larger circular paths known as *deferents*.

    (ii) Aryabhata’s Contribution
    In 498 A.D., Indian mathematician and astronomer Aryabhata proposed that the Earth rotates on its axis and revolves around the Sun, along with other planets. He explained various phenomena like solar and lunar eclipses, as well as the formation of days and nights. However, his groundbreaking ideas were not communicated to the Western world during his time.

    (iii) Heliocentric Model
    In 1543, Polish astronomer Nicolaus Copernicus proposed the heliocentric theory, suggesting that the Sun is at the center of the solar system, while the Earth and other planets revolve around it.

    (iv) Contributions of Brahe and Kepler
    To validate Copernicus’s heliocentric model, Danish astronomer Tycho Brahe (1546–1601) conducted detailed observations of planetary motion without telescopes. His data were later analyzed by his assistant, Johannes Kepler (1571–1630). Using Brahe’s observations, Kepler formulated three fundamental laws of planetary motion. These laws significantly supported the Copernican model and laid the groundwork for Newton’s law of gravitation.

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  5. The escape velocity vₑ is the minimum velocity a body needs to escape the gravitational pull of a planet or celestial body without any additional propulsion. It depends on the gravitational acceleration g or, equivalently, the mass Mₑ and radius R of the celestial body. The formula for escape velociRead more

    The escape velocity vₑ is the minimum velocity a body needs to escape the gravitational pull of a planet or celestial body without any additional propulsion. It depends on the gravitational acceleration g or, equivalently, the mass Mₑ and radius R of the celestial body.

    The formula for escape velocity is:
    vₑ = √(2gR) or equivalently} \quad vₑ = √((2GMₑ)/R)

    This shows that escape velocity is determined by the gravitational characteristics of the celestial body and is independent of the mass of the escaping object m. Thus, objects of different masses have the same escape velocity from the same location.

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