Light exerts a small pressure. Because it has a finite speed, light from the sun strikes the Earth at a small angle, but the effect is very small. If gravity acted at that same angle, the Earth’s orbit would gradually increase. I am told it would double in about two centuries.
But why do people think “nothing moves faster than the speed of light”? It’s because they think they know something and they don’t. Remember, light is electromagnetic, and gravity is not.
Two conductors separated by an insulator form a capacitor and will store an electric charge. The charge is stored in the insulator. The amount of charge depends on the material in the insulator and scientists call that (Greek letter) eta. If the insulator is a vacuum, the charge does not go to zero. A vacuum will store an electric charge. The measurement for a vacuum is called eta sub zero.
When a charge moves it generates a magnetic field in whatever material surrounds the path, called core. The amount of field depends on the material in the core and scientists call that (Greek letter) mu. If the core is a vacuum the field does not go to zero. A vacuum will store a magnetic field. The measurement for a vacuum is called mu sub zero.
Engineers use a simple formula to calculate the speed at which a signal moves through a transmission line based on the measured mu and eta. If you plug in mu sub zero and eta sub zero you get the speed of light in a vacuum, exactly.
MATTER is made of electrically charged particles. MATTER can’t move faster than the speed of light. Gravity does not involve charged particles, so its speed is not limited.