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Gravitation & Kepler Laws GK Questions & Answers
Sir Isaac Newton formulated the Universal Law of Gravitation in 1687, stating that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of their separation distance: F = G(m1·m2)/r^2. Henry Cavendish experimentally measured the universal gravitational constant G in 1798 using a torsion balance, determining its value as 6.674 × 10^-11 N·m^2/kg^2. At Earth’s surface, acceleration due to gravity averages g = GM/R^2 ≈ 9.8 m/s^2, varying from 9.83 m/s^2 at the poles to 9.78 m/s^2 at the equator due to equatorial centrifugal force and planetary oblateness. Planetary dynamics follow Johannes Kepler’s three laws: the Law of Ellipses (orbits are ellipses with the Sun at one focus), the Law of Equal Areas (areolar velocity dA/dt is constant, reflecting conservation of angular momentum), and the Harmonic Law (T^2 ∝ a^3). Orbital mechanics shows that circular orbital speed near Earth equals vo = √(GM/R) ≈ 7.92 km/s, while escape velocity is ve = √(2GM/R) ≈ 11.2 km/s. Geostationary satellites orbit at an altitude of approximately 35,786 km with a 24-hour period matching Earth's rotation.
High-yield conceptual summaries for competitive exams and rapid revision.
Newton's universal law of gravitation states that gravitational attraction between two point masses is directly proportional to their product and inversely proportional to distance squared.
The universal gravitational constant G equals 6.67430 × 10^-11 N·m^2/kg^2 and represents a universal physical constant independent of intervening medium.
Henry Cavendish measured the numerical value of G in 1798 using a sensitive torsion balance apparatus, which also enabled calculating Earth's mean density.
Acceleration due to gravity at Earth's surface follows g = GM/R^2, possessing a standard reference value of 9.80665 meters per second squared.
The value of g is maximum at the poles (approx 9.83 m/s^2) and minimum at the equator (approx 9.78 m/s^2) due to equatorial bulge and diurnal rotation.
Acceleration due to gravity decreases with increasing altitude above the surface according to g_h = g(1 - 2h/R) for altitudes much smaller than Earth's radius.
Below Earth's surface, gravitational acceleration decreases linearly with depth according to g_d = g(1 - d/R), becoming zero at Earth's geometric center.
Kepler's First Law (Law of Ellipses) states that all planets move in elliptical orbits with the Sun situated at one of the two foci.
Kepler's Second Law (Law of Equal Areas) establishes that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
Kepler's Second Law represents a direct physical consequence of the conservation of angular momentum under a central gravitational force.
Kepler's Third Law (Harmonic Law) states that the square of the orbital period T is directly proportional to the cube of the semi-major axis a (T^2 ∝ a^3).
Orbital velocity for a satellite in low Earth circular orbit equals approximately 7.92 km/s, governed by equating gravitational force to centripetal force.
Escape velocity from a celestial body is calculated via ve = √(2GM/R) = √(2) * vo, equaling approximately 11.2 km/s for Earth and 2.38 km/s for the Moon.
Geostationary satellites orbit at an altitude of 35,786 kilometers directly above the equator, completing one revolution in 23 hours, 56 minutes, and 4 seconds.
Polar satellites operate in Sun-synchronous low Earth orbits at altitudes of 600 to 800 kilometers, completing north-south passes useful for remote sensing.
Who formulated the Law of Universal Gravitation and the three fundamental Laws of Motion in his 1687 treatise 'Philosophiae Naturalis Principia Mathematica'?
Verified Explanation
Sir Isaac Newton published the 'Principia' in 1687, laying the foundations of classical mechanics with the three laws of motion and the inverse-square law of universal gravitation.
2ID: GK-GSCI-00925
hardSI Units & Fundamental Physical Constants
In celestial mechanics and gravitation, what is the CODATA internationally recommended value and SI unit dimension for Newton's universal gravitational constant (G)?
Verified Explanation
First measured experimentally in the laboratory by Henry Cavendish in 1798 using a torsion balance, Newton's constant of gravitation G governs the gravitational attractive force between two point masses: F = G m1 m2 / r^2. Its current CODATA recommended value is G = 6.67430(15) × 10^-11 m^3·kg^-1·s^-2.
3ID: GK-PERS-00157
easyLegendary Scientists
Which English polymath formulated the laws of classical mechanics and the law of universal gravitation in his monumental 1687 treatise 'Philosophiae Naturalis Principia Mathematica'?
Verified Explanation
Sir Isaac Newton laid the foundations of classical physics in the Principia, formulated the laws of motion and gravitation, and co-invented infinitesimal calculus.
4ID: GK-PERS-00537
easyLegendary Scientists
Which 17th-century English polymath published the 'Philosophiae Naturalis Principia Mathematica' in 1687, laying down the three universal laws of motion and the law of universal gravitation?
Verified Explanation
Sir Isaac Newton's 1687 'Principia' formulated the laws of motion and universal gravitation, forming the foundation of classical mechanics and modern physics.
5ID: GK-INVN-00007
easyPhysics & Engineering Inventions
Who discovered the universal law of gravitation and formulated the three laws of motion in 'Principia Mathematica' (1687)?
Verified Explanation
Newton formulated classical mechanics, calculus, optics, and gravitation.
6ID: GK-INVN-00151
easyPhysics & Engineering Inventions
Who formulated the Law of Universal Gravitation and the three fundamental Laws of Motion in his masterwork 'Philosophiae Naturalis Principia Mathematica' (1687)?
Verified Explanation
Sir Isaac Newton laid the classical foundations of mechanics and gravitational physics, describing universal gravitation and how forces govern motion.
7ID: GK-INVN-00591
easyPhysics & Engineering Inventions
Who formulated the Three Laws of Motion and the Universal Law of Gravitation, published in the groundbreaking 'Philosophiae Naturalis Principia Mathematica' in 1687?
Verified Explanation
Sir Isaac Newton formulated the three fundamental laws of classical mechanics and the law of universal gravitation in his masterwork 'Principia Mathematica', transforming physics and astronomy.
8ID: GK-PERS-00059
easyLegendary Scientists
Which English polymath formulated the Three Laws of Motion and the Universal Law of Gravitation in his 1687 masterpiece "Philosophiae Naturalis Principia Mathematica"?
Verified Explanation
Newton co-invented calculus, constructed the first reflecting telescope, and established classical mechanics as the foundation of physics.
9ID: GK-PERS-00513
hardLegendary Scientists
In which landmark 1687 scientific work did Sir Isaac Newton formulate the three laws of motion and the law of universal gravitation, establishing classical mechanics?
Verified Explanation
Newton's "Principia Mathematica", published under the encouragement and funding of Edmond Halley, is universally regarded as the foundational treatise of physics.
10ID: GK-PERS-00592
easyLegendary Scientists
Which English mathematician and physicist formulated the three fundamental laws of motion and the law of universal gravitation in his 1687 masterwork 'Philosophiae Naturalis Principia Mathematica'
Verified Explanation
Sir Isaac Newton laid the foundations of classical mechanics and optics, demonstrating that the motions of objects on Earth and celestial bodies are governed by the same natural laws.
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