According to Newton’s law of gravitation, the gravitational force by particle m 1 m 1 on particle m 2 m 2 is attractive and directed along a line between the masses with a magnitude

F g r a v=G m 1 m 2 r 2.(2)(2)F g r a v=G m 1 m 2 r 2.

In the first activity, you will determine the time that the relative position of Earth with respect to Mars repeats. This is called the synodic period of Earth and Mars. You will write a simulation of Earth and Mars and will find the time between Earth-Mars-Sun alignment (also called a Mars opposition.)

In the second activity, you will launch a rocket to Mars and measure the time required for the trip.

For a rocket launched to Mars, there are three gravitational forces on the rocket:

1. F⃗ by Sun F→by Sun
2. F⃗ by Earth F→by Earth
3. F⃗ by Mars F→by Mars

During the launch when the rocket is very close to Earth, the dominant forces on the rocket are thrust and the gravitational force by Earth. However we only want to study the gravitational forces on the rocket after it runs out of fuel and is orbiting the Sun. Therefore, we should start our simulation of the rocket when there is no thrust and the rocket is sufficiently far from Earth.