According to the theory of relativity, as an object with mass approaches the speed of light, its relativistic mass increases, making it more and more difficult to accelerate further. As a result, it is not possible for an object with mass to travel at the speed of light. Thus, we cannot directly apply the concept of a spaceship traveling at the speed of light in this scenario.
However, let's assume a hypothetical situation where we have a massless object, such as a photon, traveling at the speed of light. In that case, the time it takes for the object to complete an orbit around the Sun would be determined by the circumference of the orbit divided by the speed of light.
The circumference of an orbit is given by 2π times the radius. In this case, if the spaceship is 108.01 million km away from the Sun, we can consider that as the radius of the orbit.
Using these values, the circumference of the orbit would be approximately 2π * 108.01 million km.
To calculate the time it takes for the object to complete the orbit, we divide the circumference by the speed of light, which is approximately 299,792 kilometers per second.
So, the time it takes for the spaceship (assuming it could travel at the speed of light) to complete an orbit around the Sun would be:
Time = (2π * 108.01 million km) / (299,792 km/s)
Calculating this, we find:
Time ≈ 2.285 years
Therefore, it would take approximately 2.285 years for a spaceship (hypothetically traveling at the speed of light) to complete an orbit around the Sun at a distance of 108.01 million km.