According to Karl Popper, any scientific theory must be falsifiable. What does this entail?
A falsifiable theory leads to predictions which would be invalidated by some conceivable observation. For example, Newtonian dynamics predicts that in a uniform gravitational field, two objects with different masses will have the same acceleration due to gravity. It implies that if we drop a feather and a ball bearing inside a vacuum chamber, the ball bearing will not fall faster, as long as the theory is valid. This is in fact what happens.
Newton’s theory was very successful at describing the celestial motion of the known planets, but in the 19th century it did not correctly predict the orbit of Uranus. This fact would have falsified the theory, or greatly limited its precision. However, Urbain Le Verrier knew that the gravitational field of an unknown planet could be pulling Uranus into its observed orbit, and predicted where and how massive such a planet would be. Astronomers pointed their telescopes at the expected location and discovered Neptune. If no planet had existed at that location, this prediction would have been wrong, and the inconsistency with Newtonian dynamics would have remained valid.
A planet orbits in an ellipse, and the point where it moves closest to the sun is called the perihelion of its orbit. This point gradually precesses around the sun due to gravitational forces exerted by other planets. The same Le Verrier compared observations of Mercury to the perihelion precession rate derived from Newton’s theory, and found a discrepancy of nearly half an arcsecond per year. He predicted the existence of another planet closer to the sun to explain his result, but no planet was ever observed and this problem remained open.
To explain other puzzling observations, Albert Einstein abandoned the Galilean transformations of Newton’s theory for a framework which uses Lorentz transformations in four dimensions. General Relativity describes gravitation as an effect of spacetime curvature. It simplifies to Newtonian dynamics at lower energy levels. According to this theory, the perihelion of Mercury’s orbit should precess by an additional 0.43 arcseconds per year, matching the observed value.
Still, the intuitive simplicity of Einstein’s theory did not automatically mean that it was a valid replacement for Newtonian dynamics. During the total solar eclipse of 1919, measured deflection of starlight agreed with the value derived from General Relativity, a highly publicized result. Decades passed before additional predictions were conclusively validated.