If you were able to travel at the speed of light on Earth and stay over one place without moving, you would not be able to complete any orbits around the Earth. This is because according to the theory of special relativity, as an object with mass approaches the speed of light, its relativistic mass increases, and the energy required to accelerate it further also increases. As a result, an object with mass cannot reach or exceed the speed of light.
Furthermore, even if you could travel at nearly the speed of light, you would still experience time dilation. Time dilation means that time passes more slowly for a moving object relative to a stationary observer. From your perspective, time would pass more slowly compared to someone on the surface of the Earth. This effect becomes more pronounced as you approach the speed of light, but you would still perceive time as passing.
So, if you were somehow able to travel at an extremely high speed approaching the speed of light, you would experience time dilation and would not be able to complete any orbits around the Earth.