# How do astronomers explain trajectories of planets?

I'm wondering how astronomers can explain the trajectories of planets because:

• planets spin, so have angular kinetic energy. Thanks to the mass-energy relationship this means space-time curvature.
• but due to this spinning, depending how their core is build up, they also create a magnetic field (coriolis effect). These can acts as external force on neighboring planets, which influences space-time again.

So it appears a lot of parameters influence space-time and therefore the trajectory of planets, but also our ways of observing the motion of planets. Are some parameters neglectable or how is one sure that what is observed is unaffected by the way we measure? (it almost looks like the Heisenberg uncertainty principle)

• The influence of the magnetic fields of all the other planets on Earth is totally insignificant. – Jon Custer Oct 5 '18 at 21:56
• Sometimes an effect is so small that they are not observable. Sometimes you might not know that people actually are taking small effects into consideration. – Bill N Oct 5 '18 at 22:15

$$F \propto \frac{1}{r^2},$$
where $$r$$ is the radial distance. With three additional assumptions, viz., (i) the Sun is substantially more massive than any particular planet, (ii) the radii of the Sun and planets are small enough compared to the distances between them to be negligible, and (iii) the planet-planet gravitational forces are small enough to be negligible, we can show that stable, closed orbits will be ellipses with the Sun at one focus. The particular attributes of an ellipse, e.g., its semimajor axis and eccentricity, will be determined by the initial conditions of the system. We can also show that each planet's orbital angular momentum will be conserved, and that the ratios of the orbital period and semimajor axis of the planets will obey a simple power law. These are Kepler's laws, which were emperically established before Newton was born. (Of course, it wouldn't make any difference if the model came before the empirical data.)