What does it mean to say that the gravity of the Earth is 9.8 m/s2?

Question

servidopolisxv · Accepted Answer

As per Law of Universal Gravitation the force of attraction between two bodies is directly proportional to the product of masses of the two bodies. it is also inversely proportional to the square of the distance between the two. That is the force of gravity follows inverse square law.
Mathematically

F_{G} \propto M_{1} \cdot M_{2}

Also

F_{G} \propto \frac{1}{r^{2}}

Combining the two we obtain the proportionality expression

F_{G} \propto \frac{M_{1} \cdot M_{2}}{r^{2}}

Follows that

F_{G} = G \frac{M_{1} \cdot M_{2}}{r^{2}}

Where G is the proportionality constant.
It has the value

6.67408 \times 10^{- 11} m^{3} k g^{- 1} s^{- 2}

r is the mean radius of earth and taken as

6.371 \times 10^{6} m

Mass of earth is

5.972 \times 10^{24} k g

If one of the body is earth the equation becomes

F_{G} = (G \frac{M_{e}}{r^{2}}) \cdot m

See this has reduced to

F = m g

Were

g = G \frac{M_{e}}{r^{2}}

Inserting the values

g = 6.67408 \times 10^{- 11} \frac{5.972 \times 10^{24}}{{(6.371 \times 10^{6})}^{2}}

Simplifying we obtain

g \approx 9.8 \frac{m}{s^{2}}

In other words if an object is dropped from a height h above the earth's surface, the object will fall towards earth with constant acceleration of

g = 9.8 \frac{m}{s^{2}}

RizerMix · Accepted Answer

Gravity is a force, and according to Newtons

alenahelenash · Accepted Answer

Quite detailed, interesting

What does it mean to say that the gravity of

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