$(a)$ Write the formula to find the magnitude of the gravitational force between the Earth and an object on the surface of the Earth.
$(b)$ What is the direction of acceleration due to gravity?

Find the weight of an object at a height $6400 \, km$ above the earth's surface. The weight of the object at the surface of the earth is $20 \, N$ and the radius of the earth is $6400 \, km$. (in $, N$)

$(i)$ How is the force of attraction dependent on the masses of objects and the distance between them?
$(ii)$ The mass of the Earth is $6 \times 10^{24} \, kg$ and that of a natural satellite is $6.5 \times 10^{20} \, kg$. If the distance between them is $3.35 \times 10^{6} \, km$, calculate the force exerted by the Earth on it. $(G = 6.7 \times 10^{-11} \, Nm^{2} kg^{-2})$

State whether the following statement is true or false:
The force of attraction between two bodies is called gravity.

$A$ person can jump higher on the surface of the Moon than on the Earth. Why?

$A$ man at the top of a tower throws an object horizontally,whereas he simply drops another. Will these two objects reach the earth at the same time?