- In the previous projectile motion example, we used the gravitational force with the expression
and gravitational acceleration as being constant near the Earth's surface.
- However, the gravitational force between masses is most generally given by Newton's law of universal gravitation:
Here,
is called the universal gravitational constant. The force is attractive and along the direction connecting the two masses.
- This expression should be used when studying the motion of planets and moons.
- Let's study the motion of a planet (mass
)moving under the gravitational force of the Sun (mass
). If we take the sun at the origin, the vector expression of the force acting on the planet would be:
- Since the orbit of the planet will be at a plane (2D), the position vector
and accordingly the acceleration vector
would have two components as:
- Newton's 2
law as
and also velocity expressions for the x- and y-components:
- Now, we have a set of equations.