# 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

## 2 Answers

Like all things in physics, the trajectories are explained by comparing empirical data to values calculated from a physical model. In this case, the model is the inverse-square nature of the gravitational force between each planet and the Sun,

$$F \propto \frac{1}{r^2},$$

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.)

Deviations from Kepler's occur for primarily two reasons. The first is that the planet-planet interactions are large enough to produce small effects we can measure through detailed observations of the planetary orbits. The result of these interactions is that orbital parameters such as semimajor axis and eccentricity will slowly evolve. These deviations can be accounted for in the model by including the planet-planet interactions.

The second reason is due to relativistic effects, which you suggest in your question. Specifically, Mercury's perihelion position (its point of closest approach to the Sun) precesses, so that not only does Mercury move along its orbital path, but the path itself very slowly rotates around the Sun. The precession can be calculated by including planet-planet interactions (especially Venus), but the observed value exceeds the calculated value by an amount that is well larger than the uncertainties in either one. General Relativity predicts the difference in the perihelion shift with excellent agreement.

Astronomers use Newton gravity to explain the orbitals of planets. In addition to this they take into account effects due to general relativity. These effects are very small but measurable for the solar system. The leading one is the famous orbital precession effect. The effect of rotation that you suggests, also known as frame dragging, is much smaller than this and has not been demonstrated in the solar system. The effect of magnetic field should be extremely small compared to kinetic effects. Only very light objects solar radiation pressure also plays a role.