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Gravity field surrounding Earth from a macroscopic perspective. Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
The gravitational constant is a physical constant that is difficult to measure with high accuracy. [7] This is because the gravitational force is an extremely weak force as compared to other fundamental forces at the laboratory scale. [d] In SI units, the CODATA-recommended value of the gravitational constant is: [1]
This is the International Gravity Formula 1967, the 1967 Geodetic Reference System Formula, Helmert's equation or Clairaut's formula. [ 18 ] An alternative formula for g as a function of latitude is the WGS ( World Geodetic System ) 84 Ellipsoidal Gravity Formula : [ 19 ]
Derivation of Newton's law of gravity Newtonian gravitation can be written as the theory of a scalar field, Φ , which is the gravitational potential in joules per kilogram of the gravitational field g = −∇Φ , see Gauss's law for gravity ∇ 2 Φ ( x → , t ) = 4 π G ρ ( x → , t ) {\displaystyle \nabla ^{2}\Phi \left({\vec {x}},t ...
Gauss's law for gravity is often more convenient to work from than Newton's law. [1] The form of Gauss's law for gravity is mathematically similar to Gauss's law for electrostatics, one of Maxwell's equations. Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electrostatics bears to Coulomb's law.
Diagram of an educational toy that balances on a point: the center of mass (C) settles below its support (P) A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. [13] Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be the same.