The electron revolves around the nucleus of an atom with an electrostatic force of attraction and the earth revolves around the sun with a gravitational force of attraction between the two. can the earth and the sun be simulated?? and how?
any advise please?
James,
Electrons cannot orbit the nucleus of their atoms. This is an old and incorrect model and has been known to be wrong for almost a century.
(simply because an accelerating charge radiates EM radiation - thus any orbiting electron will loose energy and spiral in to the nucleus).
By contrast, planets do indeed orbit their stars in computationally simple ways.
What type of modelling do you wish to do?
A hundred lines (or so) of FORTRAN is enough to build a Runge-Kutta integrator and thus perform dynamics modelling.
You could use a numerical approximation, such as a Runge Kutta method, to solve the equations of motion for the two-body system (sun and earth). But you don't really need to since Isaac Newton solved them analytically. See https://en.wikipedia.org/wiki/Gravitational_two-body_problem, for example.
If you want to include other planets in your simulation, things get much more interesting. I recently came upon this old paper on the n-body problem which gives a great summary: http://www.math.uvic.ca/faculty/diacu/diacuNbody.pdf.
In addition to responses already added, I would like to add a comment about the choice of integrator.
In the case of planetary motion, it would be wise to use leapfrog integration (https://en.wikipedia.org/wiki/Leapfrog_integration) instead of Runge-Kutta integration. Or some other higher order symplectic method. The reason is that a quantity very close to kinetic energy is conserved. Hence, using Leapfrog method your planet would continue orbiting around the sun, whereas using RK method it would (slowly) spiral outwards on inwards (depending of choice between explicit or implicit integration).
You can analyze the yearly motion of the Earth around the Sun by accurately measuring everyday the apparent angular diameter of the Sun using direct images of the disk or making the so- called timing of a transit through a meridian. Be careful to properly attenuate the irradiance and have good resolution images which means pay attention to refraction effect in the Earth atmosphere. You can use images from Space made available from MDI of SoHO mission and/or from HMI and AIA of SDO mission. Plotting the values obtained for 1 full Year you can deduce the ellipticity of the so- called Kepler orbital motion of the Earth and assuming the physical size of the Sun you can deduce the orbital parameters, including the distance to the Sun, etc.