Obtain the relation between the universal gravitational constant and the gravitational acceleration on the surface of the earth.
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There are two constants generally associated with gravity. The first, usually denoted with a capital G, is the universal constant. It’s value is 6.67408e-11 m^3 kg*-1 s^-2 (or (m^3)/(kg s^2)). It is used in Newton’s Law of Universal Gravity:
F = (G · M1 · M2) / r^2
If you consider a small mass on the surface of a given planet, then the G, M1 and r values are fixed and combined, and the equation simplifies to
W = M2 · g
where W is the weight, or force of gravity; the small g is a constant for the given planet’s mass and radius. On Earth’s surface, g is about 9.8 m/s^2, or 32 ft/sec*2. A similar constant can be computed for different planets and/or different elevations above the surface of the planet. Elevations *below* the surface, as in a deep (really deep) well are complicated by other factors, but can be computed.
F = (G · M1 · M2) / r^2
If you consider a small mass on the surface of a given planet, then the G, M1 and r values are fixed and combined, and the equation simplifies to
W = M2 · g
where W is the weight, or force of gravity; the small g is a constant for the given planet’s mass and radius. On Earth’s surface, g is about 9.8 m/s^2, or 32 ft/sec*2. A similar constant can be computed for different planets and/or different elevations above the surface of the planet. Elevations *below* the surface, as in a deep (really deep) well are complicated by other factors, but can be computed.
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