Relativity has profound implications for the relative time experienced by objects orbiting an observer at speeds close to the speed of light. These effects are described by both special relativity (SR) and general relativity (GR).
In special relativity, time dilation occurs when objects move relative to each other at high speeds. According to the theory, as an object approaches the speed of light, time appears to pass more slowly for that object relative to a stationary observer. This effect is known as "velocity time dilation."
Let's consider an example where an observer is stationary while two objects are orbiting around them, each at a speed close to the speed of light. Relative to the stationary observer, both objects will experience time dilation. However, each object will observe the other object's clock as running slower than its own clock. This phenomenon is known as "time dilation symmetry."
In other words, from the perspective of one object, the other object's clock appears to be running slower due to its high speed. Simultaneously, from the viewpoint of the second object, the first object's clock also appears to be running slower due to its high speed. This symmetry arises from the principles of special relativity.
The combined effect of time dilation and the relative motion of the objects can result in interesting consequences. For instance, if one of the objects were to return to the stationary observer after completing an orbit, it would have experienced less time compared to the observer. This phenomenon is known as "time dilation in circular motion."
However, it's important to note that at speeds close to the speed of light, the laws of physics become increasingly complex, and our classical intuition may not hold true. Special relativity provides a framework to calculate these effects, incorporating the Lorentz transformation equations to describe the relationship between space and time coordinates for objects moving at high speeds.
General relativity also plays a role when considering objects orbiting in gravitational fields, such as around a massive body like a planet or a star. In this case, the curvature of spacetime caused by the gravitational field can further affect the flow of time, resulting in "gravitational time dilation." The combination of velocity time dilation and gravitational time dilation must be taken into account for accurate predictions.
To summarize, objects orbiting an observer at speeds close to the speed of light will experience time dilation due to their relative motion. This time dilation can be described by special relativity, incorporating the effects of velocity time dilation. When the objects are within a gravitational field, the additional effects of gravitational time dilation, as described by general relativity, must also be considered.