One can easily find "Weight of the earth" by calculating the...

One can easily find "Weight of the earth" by calculating the mass of earth using the formula (in usual notation) (A) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}$ (B) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}^{2}$ (C) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{2}$ (D) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{3}$

One can easily find "Weight of the earth" by calculating the mass of earth using the formula (in usual notation)
(A) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}$
(B) $(\mathrm{g} / \mathrm{G}) \mathrm{Re}^{2}$
(C) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{2}$
(D) $(\mathrm{G} / \mathrm{g}) \mathrm{Re}^{3}$

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Key Concepts

Newton’s Law of Universal Gravitation

This principle states that any two masses in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It is the foundational law from which many other gravitational formulas, including those used to calculate planetary masses, are derived.

Gravitational Acceleration

Gravitational acceleration (commonly represented by g) is the acceleration experienced by any object due to the gravitational pull of a massive body like the Earth. It is directly related to the mass and the radius of the body and provides a practical means to measure or infer these quantities through experiments or observations at the surface.

Mass Determination from Surface Gravity

By equating gravitational acceleration with its theoretical expression g = GM/Re², where G is the gravitational constant and Re is the radius of the Earth, one can solve for the Earth's mass. This key concept shows how experimental measurements of surface gravity can be combined with universal laws to determine the mass or 'weight' of large celestial bodies.

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