Gravitation is one of the fundamental forces of nature that governs the motion of celestial bodies and objects on Earth. It is the attractive force that exists between any two masses, regardless of their size or distance. This universal phenomenon was first mathematically explained by Sir Isaac Newton in his Law of Universal Gravitation.
Newton’s Law of Gravitation
Newton stated that:
Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1m2
Where:
- F = Gravitational force between the bodies
- G = Gravitational constant (6.67×10−11 Nm2/kg26.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^26.67×10−11Nm2/kg2)
- m₁, m₂ = Masses of the two bodies
- r = Distance between their centers
Gravitational Constant (G)
- Discovered by Henry Cavendish in 1798 using the torsion balance experiment.
- It is a universal constant and remains the same everywhere in the universe.
Acceleration Due to Gravity (g)
On Earth, the gravitational pull produces an acceleration g, given by: g=GMR2g = \frac{GM}{R^2}g=R2GM
Where:
- M = Mass of Earth
- R = Radius of Earth
Value of g on Earth’s surface ≈ 9.8 m/s².
Factors Affecting g
- Altitude – g decreases with height above the Earth’s surface.
- Depth – g decreases as we move inside the Earth.
- Latitude – Due to Earth’s rotation, g is maximum at poles and minimum at the equator.
Kepler’s Laws of Planetary Motion
Johannes Kepler, based on Tycho Brahe’s observations, formulated three laws:
- Law of Orbits – Planets move in elliptical orbits with the Sun at one focus.
- Law of Areas – A line joining a planet to the Sun sweeps equal areas in equal time intervals.
- Law of Periods – The square of the orbital period is proportional to the cube of the semi-major axis of its orbit.
Applications of Gravitation
- Explains motion of planets, satellites, and space objects.
- Basis for launching artificial satellites.
- Helps predict tides due to the Moon and Sun.
- Determines escape velocity and orbital speed.
Escape Velocity
The minimum velocity required for an object to escape Earth’s gravitational pull without further propulsion: ve=2GMR(For Earth, ve≈11.2 km/s)v_e = \sqrt{\frac{2GM}{R}} \quad \text{(For Earth, } v_e \approx 11.2 \, \text{km/s)}ve=R2GM(For Earth, ve≈11.2km/s)
Conclusion:
Gravitation is a universal force that not only keeps planets in orbit but also governs everyday phenomena like falling objects. From Newton’s law to modern space exploration, understanding gravitation has been essential in expanding our knowledge of the universe.
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