viii.2. Unlocking the Mysteries of Gravitation: The Universal Law Revealed
|
Understanding Concept |
|
|
Mathematical Representation |
F∝ M × m F∝ 1 / d2 Combining both we get: F ∝ M × m / d2 or F = G (M × m / d2 ), where G is the Universal Gravitational Constant. |
|
Value of G |
The constant G, called the universal gravitational constant, has an accepted value of: F × d2 = G M × m or, G= F × d2 / M × m
|
|
Perceptibility |
|
|
Universality |
|
|
Example: The mass of the earth is 6 × 1024 kg and that of the moon is 7.4 × 1022 kg. If the distance between the earth and the moon is 3.84 × 105 km, calculate the force exerted by the earth on the moon. (Take G = 6.7 × 10–11 N m2 kg-2) Solution: The mass of the earth, M=6 × 1024 kg The mass of the moon, m=7.4×1022 kg d = 3.84×105km = 3.84×105×1000m = 3.84 × 108 m G= 6.7×10–11 N m2 kg–2 The force exerted by the earth on the moon is F = G (M × m / d2) = 6.7×10−11 N m2 kg-2 × 6 × 1024 kg × 7.4 × 1022 kg / (3.84 × 108 m)2 = 2.02 × 1020 N. |