Question

What is a gravitational field and how its strength be measured

Answer 1

A gravitational field is the field generated by a massive body, that extends into the entire space. Every object with mass m experiences a force F when immersed in a gravitational field. The intensity of the force is equal to
$F= \frac{GM}{r^2} m$
where $G=6.67 \cdot 10^{-11} m^3 Kg^{-1} s^{-2}$ is the gravitational  constant, M is the mass of the source of the field (e.g. the mass of a planet), and r is the distance between the object and the source of the field. The force is always attractive. 

A possible way to measure the intensity of a gravitational field is by measuring the acceleration a of the object immersed in this field. In fact, for Newton's second law we have:
$F=ma$
but since 
$F= \frac{GM}{r^2} m$
we can write
$a = \frac{GM}{r^2}$
Therefore, by measuring the acceleration of the object, we also measure the intensity of the field.