Gravity does have an effect on electromagnetic radiation, including radio waves and visible light, as it interacts with space-time curvature. This effect is described by the theory of general relativity proposed by Albert Einstein. According to general relativity, massive objects like stars and planets can curve the fabric of space-time, influencing the path of light and other forms of electromagnetic radiation that pass through their vicinity.
When electromagnetic waves travel near massive objects, such as stars, their path is indeed curved due to the gravitational field of the object. This effect is known as gravitational lensing. Gravitational lensing can cause the apparent position or direction of the light to be deflected as it passes near a massive object. However, this deflection is generally small unless the radiation passes extremely close to a very massive object, such as a black hole.
For electromagnetic radiation originating from stars moving through space at near-light speeds, the situation is slightly different. When an object is in motion relative to an observer, there is a phenomenon called the Doppler effect that affects the perceived wavelength of the radiation. The Doppler effect causes the wavelength of the light to be shifted towards shorter wavelengths (blue shift) if the object is moving toward the observer or towards longer wavelengths (red shift) if the object is moving away.
In the case of stars moving at near-light speeds, the light they emit experiences both the gravitational lensing effect from other massive objects and the Doppler effect due to their own motion. These effects can combine in complex ways, and the resulting observed direction of the light can be influenced. However, the overall deflection or change in direction is typically small and generally not noticeable for stars moving at typical speeds in space.
It's worth noting that astronomers and physicists take these effects into account when studying the light emitted by stars and other astronomical objects. The field of gravitational lensing, in particular, has provided valuable insights into our understanding of the distribution of matter in the universe and has been used to detect and study distant objects that would otherwise be difficult to observe directly.