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## Understanding the Laws of Planetary Orbits

In the realm of astronomy, the relationship between the Earth and the Sun has always been a fascinating subject. Professor Richard Muller, however, makes a daring claim rooted in Einstein’s general theory of relativity: “According to this theory, both the Sun orbits the Earth, and the Earth orbits the Sun.” Before delving into the intricacies of Professor Muller’s assertion, let’s revisit Kepler’s third law, which plays a crucial role in understanding the motion of planets. This law establishes a connection between the time it takes for a planet to complete an orbit around the Sun (T) and its distance from the Sun (R).

## The T|R Law and Celestial Bodies

Observing the celestial bodies in our solar system, we discover that not only do they adhere to Kepler’s third law but also have their own variation of the T|R law. For instance, the Moon and countless human-made satellites that orbit the Earth follow a similar pattern, albeit with a distinction. The Earth’s gravitational force, due to its smaller mass compared to the Sun, exerts weaker acceleration at the same distance. This realization prompts us to wonder if this pattern extends beyond our solar system.

## Universal Application of T|R Laws

As we explore the cosmos, we find that T|R laws are indeed present among objects orbiting a common planet. Jupiter’s moons and the rocks constituting its scant ring are prime examples. Moreover, an interesting observation emerges: when we examine the Sun and the Earth’s paths, we notice a striking disparity.

## The Dilemma: Earth or Sun?

Pre-Einstein, this discrepancy puzzled astronomers, inviting speculation about whether the Earth orbits the Sun or vice versa. Professor Muller enters the scene, drawing on Einstein’s theory of gravity to suggest that the Sun orbits the Earth to the same extent that the Earth orbits the Sun. At this juncture, a critical decision lies before us: should we believe him?

### Muller versus Kepler

To comprehend Muller’s viewpoint, we must examine Einstein’s approach to gravity and motion. According to Einstein, both Sun-centered (heliocentric) and Earth-centered (geocentric) coordinates are equally valid. In other words, depending on the coordinates we choose and how we perceive them, the motion can appear differently. However, Muller takes a step too far when he claims that both the Sun orbits the Earth and the Earth orbits the Sun. In my opinion, this is where he commits an error. He overlooks the fact that gravitational orbits possess unique properties, such as adhering to T|R laws.

## The Coordinate-Independence of T|R Laws

In evaluating Muller’s claim, we encounter a critical fact: T|R laws, including Kepler’s third law, are not influenced by the choice of coordinates. We can demonstrate this by carefully analyzing velocities and curvatures in the solar system. The quantities T (measured by a local clock on either the Sun or the Earth) and R (estimated by light-travel time) remain unambiguous, regardless of the coordinate system employed.

This realization is pivotal. The failure of the Sun’s path to satisfy the Earth’s T|R law persists across all coordinate systems. Consequently, we can confidently state that the Sun does not orbit the Earth.

## Gravitational Orbits and the T|R Law

Every T|R law, including Kepler’s third law for the Sun and its counterparts for other celestial bodies, serves as a litmus test for identifying gravitational orbits. This principle extends beyond the eight planets and encompasses all objects within the Sun’s gravitational influenceâ€”moons, asteroids, and satellites. Any trajectory that does not abide by these laws, even approximately, cannot be classified as a gravitational orbit.

## Debunking Muller’s Assertion

Hence, we can definitively conclude that the Earth does not orbit the Sun, nor does the Earth’s Moon or any human-made satellite. Additionally, Saturn does not orbit the rocks that compose its magnificent rings. To suggest otherwise is to misinterpret and misapply the teachings of Einstein’s theory.

In the following post, we will delve deeper into this argument, examining alternative methods proposed by readers and discussing their merits and drawbacks. But first, we will fortify the foundation of today’s argument.