Intuitive

Newton's law of Gravity tells us that the $\color{blue}{\text{gravitational force}}$ between $\color{red}{\text{two}}$ $\color{orange}{\text{masses}}$ gets smaller as the masses are removed $\color{magenta}{\text{further away from each other}}$.

In addition, it tells us that the exact strength of the $\color{blue}{\text{gravitational force}}$ is determined by the $\color{olive}{\text{gravitational constant}},$ the $\color{red}{\text{two}}$ $\color{orange}{\text{masses}}$ of the objects in the system and the $\color{magenta}{\text{distance between them}}$.

So given an object with some known $\color{red}{\text{mass}}$, we can immediately calculate the $\color{blue}{\text{force}}$ it exerts onto another $\color{orange}{\text{mass}}$.

Concrete

Abstract

Newton's law is the static limit of the Einstein equation.

Why is it interesting?

Newton's law of gravity is a universal law allows us to understand how two planets attract each other, but also why an apple falls onto the earth. It tells us that any two massive objects attract each other.

In addition, it allows us to accurately predict the movements of planets in the solar system. For example, we can use Newton's law to predict the motion of the moon.

It is still used nowadays, for example, by NASA and ESA to design orbits or to work out spacecraft trajectories for space missions.

Famous examples are the Apollo missions in the 60s and 70s. Their routes were calculated using Newton's law to take the attraction of the earth and moon into account. Another example, are the many satellites that orbit the earth nowadays. Thus, in some sense, Newton's law makes satellite television, GPS systems and also the Mars rover possible.

Definitions

• $\color{blue}{\vec F}$ is the force between the two masses.
• $\color{olive}{ G}$ is the gravitational constant.
• $\color{red}{m_1}$ and $\color{orange}{m_2}$ are the masses of the two objects in questions.
• $\color{magenta}{r}$ is the distance between the two objects.