Running FORTRAN programs using modules in Ubuntu:

gfortran -o file.exe usedmodule1.o usedmodule2.o program.f90 ./file.exe

## Earth’s orbit around the Sun

To do a simulation of the Earth revolving around the sun, we will be using Newton’s Law of Gravitation, which says

**F = GMm/r ^{2}**

where, **G = 6.67384e^{-11} m^{3} kg^{-1} s**

^{-2 }(gravitational constant ) and

**M = 1.989e**(mass of sun).

**kg**^{30}We also know the speed of the Earth and its distance from the Sun at the perihelion (closest point to the Sun).

**Distance = 147.098 e^{9} m **and

**Speed = 30287.0 m/s**

Hence, we have the equation of motion and the required initial conditions. With every graph we will plot a point at (0,0) which will represent the Sun.

The acceleration depends on r, so for every x and y we need to calculate r = √(x^{2} + y^{2}). Also we need to calculate the Θ to resolve the velocity components.

Θ = tan^{-1}(y/x). Remember that tan^{-1 }always gives values between -π/2 and π/2. Just add π to Θ when x is negative to get rid of this inconvenience.

To make the animation look cooler, we can add labels to display additional information. The module plotting.f90 needs to be tweaked a bit (a subroutine needs to be added to write the necessary labels). You can find the modified modules and the program below. Comment in case of any problems.

**Download links:** writing.f90 plotting_v2.f90 earth.f90

## Respond to Part 4: Animation of the Earth revolving around the Sun