Many good experiments have been done over the past 2 centuries to detect the Earth's motion. They used well understood properties of light. I will highlight 3 scientists: Arago, Airy, and Michelson. Reference frames are non-relativistic or Euclidean in these calculations. Light is assumed to need the aether to propagate, and the concept of absolute motion is considered feasible (a common sense extrapolation)
First Arago early in the 19th century attempted to use focus of a telescope to detect the Earth's motion. Reasoning that if he would observe a star for an entire year, it would come to a point where the telescope would have to be refocused as the Earth went from the closest point of approach to the farthest distance from the star in its orbit. But he found he never had to refocus his telescope.
Airy's experiment, 1871, took advantage of light moving slower thru glass and water than air. He set up 2 telescopes side by side. If the Earth was moving, the telescope with water would have to be tilted more as light moving slower in the water would take longer to traverse the telescope length. Tilting it accordingly would prevent the light from striking the side of the telescope. Here is an illustration of this point with a person who is moving in the rain, who must tilt the umbrella to keep the rain from getting him wet.
Similarly with a telescope,
However no tilt was needed. His experiment, since it could not detect the obvious smaller object motion around the larger of the Earth orbit of the Copernican principle, was called Airy's Failure.
In a book about Relativity by Arthur Miller in the next century, he quotes a comment by Lorentz about Airy's Experiment:
The underline in the picture of the publication itself states: "Briefly, everything occurs as if the Earth were at rest, and the relative rays were the absolute rays."
However, both experiments could be said to have successfully detected no motion in the Earth. But if it actually detected the true motionlessness of the Earth, it is no failure at all. The naming of Airys experiment, "Airy's Failure" exhibits the bias in the scientific community coming out of the Rennaissance period It is related to Galileo's findings, and willingness to overthrow scientific method based on an philosophical bias, using the struggles between Galileo and the Catholic Church to pillory a an experimnental finding which could even be potentially construed to support the Bible's creation story. Galileo before his death came to recognize the wisdom in the religion and recanted the philosophical implications of his early deductions. That reconciliation looks very wise.
* Pictures from the Journey Movie