If we deny the laws of physics, everything is possible. The heliocentric model and the geocentric model are kinematically equivalent [1]. They can describe the same apparent motion of celestial bodies using different underlying assumptions.

Mathematically it can be proven that any arbitrary motion can be described using nested epicycles [2], as demonstrated in the Fig 1. An infinite number of possible models are kinematically equivalent. You can convert between any 2 models by applying a coordinate system transformation. But the models are not dynamically equivalent, only one model obeys the laws of physics.

So how can we figure out, which motion is the real one? Wheter the sun orbits the earth (geocentrism) or the earth orbits the sun (heliocentrism)?

Physics only works in the Heliocentric Model

Physics is part of reality. We can not find any location where the laws of physics are violated, so we can assume that the laws of physics are valid everywhere. Newtons laws of motion and gravitation are universal. So lets investigate the physics of two proposed models:

• Geocentric Model, where the sun orbits the earth once per day (T_s = 24 h)
• Heliocentric Model, where the earth orbits the sun once per year (T_e = 365.256 d)

We can measure the distance to the sun (d = 149.6 × 10⁹ m) in many different ways which all get the same result. Examples are Stellar Aberration and Radar Ranging [3].

Using Newton's laws of motion and Newton's law of universal gravitation and knowing the orbital periods of the 2 models and the distance between earth and sun we can calculate the mass of the earth or sun respectively, required to physically hold the other object in orbit.

Let's see whether both models are physically possible:

Newtons Law of Motion and Gravitation

For circular orbits the centripetal acceleration acting on the orbiting body is the gravitational acceleration.

Simplifying assumptions: The orbiting body has much less mass than the central body and the orbits are perfect circles.

We can solve for the central mass M:

Knowing the size of the central body and its mass we can calculate the density of the central body:

The radius of the sun can be calculated from its apparent angular size:

The mass and density of the earth can be measured e.g. with Cavendish like experiements from the known radius of the earth R_e = 6371 km, which can be measured using many different methods, e.g. GPS or older methods like Measuring Earths Radius like Al-Biruni taking Refraction into account or using the orbital period and laser measured distance to the moon using equation (2).

Now lets calculate the mass of the sun and earth and their densities for the heliocentric and the geocentric model:

Heliocentric Model

A density of 1410 kg/m³ is reasonable and within the density of all known elemets of the periodic table. To compare, the density of water is 1000 kg/m³.

Geocentric Model

In the geocentric model the required mass of the earth to hold the sun in a 1 day period orbit is 11 orders of magnitudes more than the accepted measured mass of the earth.

Lets calculate the mean density of such an earth:

We know that the earth has not a density of 2.449 × 10¹⁴ kg/m³. So the assumption of a geocentric model is falsified by the laws of physics.

Such a high density would create a gravitational acceleration on the surface of the earth of 4.36 × 10¹¹ m/s², which is ridiculous.

Summary

The known laws of physics falsify the geocentric model. The heliocentric model on the other hand can be derived from the laws of physics.

Methods to Measure the distance to the Sun

There are several methods to measure the distance to the Sun, known as the astronomical unit (AU). Here are a few:

Radar Ranging: By bouncing radar signals off planets like Venus and measuring the time it takes for the signals to return, scientists can calculate the distance to the planet and then use Kepler's laws to determine the distance to the Sun. The distance to the sun was also measured by directly bouncing radar signals off the sun [4].

Transit of Venus: By observing the transit of Venus across the Sun from different locations on Earth, astronomers can measure the parallax shift and calculate the distance to the Sun.

Stellar Aberration: This method involves measuring the apparent shift in the position of stars due to Earth's motion around the Sun. The angle of this shift can be used to calculate the distance to the Sun.

Kepler's Laws: By observing the orbital periods and distances of planets, astronomers can use Kepler's laws of planetary motion to calculate the distance to the Sun.

Each of these methods has contributed to our understanding of the astronomical unit and the scale of our solar system. [5] [6] [7]

Stellar Abberation

In astronomy, stellar aberration is a phenomenon where celestial objects exhibit an apparent motion about their true positions based on the velocity of the observer: It causes objects to appear to be displaced towards the observer's direction of motion. We can measure stellar aberration of each star consistent with an earth orbiting the sun. We can even calculate the distance between earth and sun from the aberration angle. [8]

The aberration angle depends on the relative velocity between star and observer and the speed of light. The measured annular aberration angle is ϕ = 20.49552" = 9.936508 × 10⁻⁵ rad [9]

As we know the orbital period of the earth T = 365.256 days, we can calculate how far the earth travels in that period at the speed v, which we get from equation (10). This distance U is the circumference of a circle (orbit of earth) with a radius of d (distance between earth and sun).

We can solve for d and insert v from (10):

This is exactly the accepted mean distance between earth and sun, confirmed by many other methods.

References