Let's denote the new unit of length as "u" (for unity) and the distance between the Sun and the Earth as "d" in this new unit. We are given that the speed of light in a vacuum is unity, which means the speed of light is equal to 1 unit per unit of time (u/t).

We know that the speed of light in a vacuum is approximately 299,792,458 meters per second in the International System of Units (SI).

Now, we are given that light takes 8 minutes and 20 seconds to cover the distance between the Sun and the Earth. We need to convert this time into the new unit "u."

First, let's convert the time to seconds:

8 minutes = 8 minutes * 60 seconds/minute = 480 seconds 20 seconds = 20 seconds

Total time taken by light = 480 seconds + 20 seconds = 500 seconds

Since we are considering the speed of light to be unity in the new unit, the distance "d" in the new unit can be calculated as follows:

Distance (d) = Speed * Time = 1 u/t * 500 seconds = 500 u

Therefore, the distance between the Sun and the Earth in terms of the new unit "u" is 500 units.