If you were able to travel at the speed of light, you would experience some fascinating phenomena due to the principles of special relativity. One of the key aspects of special relativity is time dilation, which means that time appears to pass more slowly for objects moving relative to an observer at rest.
If you were traveling at the speed of light, however, things become a bit more complicated. According to the theory of relativity, it is impossible for a massive object with rest mass to accelerate to the speed of light. So, assuming you are an object with rest mass, it is not physically possible for you to travel at the speed of light.
However, let's consider a scenario where you are traveling very close to the speed of light, such as 99.9% of the speed of light. In that case, time dilation effects would still be significant. From your perspective, time would appear to slow down relative to an observer at rest on Earth.
If you were to travel at such a high speed in a circular path around the Earth, you would observe some interesting effects. Since you are moving close to the speed of light, time dilation would cause time to pass more slowly for you compared to someone at rest on Earth. As a result, you would age more slowly than the people on Earth.
However, it's important to note that as you move close to the speed of light, the relativistic effects become increasingly significant. The length contraction effect would cause the distance around the Earth to appear shorter for you, and it would result in a compressed view of the Earth.
So, to answer your question, if you were able to travel at such high speeds near the speed of light, you would see yourself circling the Earth from a distorted and compressed perspective due to length contraction. However, it's important to remember that this scenario is purely hypothetical, as no massive object with rest mass can reach or exceed the speed of light according to our current understanding of physics.