how to calculate gravity

Newton’s Law of Universal Gravitation states that the gravitational force ((F)) between two objects is:
[ F = G \frac{m_1 m_2}{r^2} ]
where:

(G) is the gravitational constant ((6.674 \times 10^{-11} , \text{Nm}^2/\text{kg}^2)),

(m_1) and (m_2) are the masses of the objects (e.g., Earth and an apple),

(r) is the distance between their centers.

For Earth’s surface gravity ((g)), simplify by considering Earth’s mass ((M)) and radius ((R)):
[ g = \frac{F}{m} = G \frac{M}{R^2} \approx 9.8 , \text{m/s}^2 ]
Steps to calculate (g):

Mass of Earth ((M)): (5.972 \times 10^{24} , \text{kg}).

Earth’s radius ((R)): (6.371 \times 10^6 , \text{m}).

Plug into the formula:
[ g = \frac{(6.674 \times 10^{-11})(5.972 \times 10^{24})}{(6.371 \times 10^6)^2} \approx 9.8 , \text{m/s}^2 ]

Practical use:

Predict object motion (e.g., falling apples).

Space missions (e.g., calculating lunar gravity).

Variations:

(g) decreases with altitude (larger (r)).

Other planets: Substitute their (M) and (R).

This foundational law bridges celestial mechanics and everyday physics.