Sun Earth Distance Calculation

The problem asks us to find the distance between the Sun and the Earth using a new unit system where the speed of light is considered unity (1). We are given the time it takes for light to travel this distance.

Key Information Provided

• Speed of light ($c$) = 1 (in the new unit system).
• Time taken ($t$) = 6 minutes 40 seconds.

Step 1: Convert Time to Seconds

First, we need to express the total time in a single unit, preferably seconds, to be consistent with standard calculations.

$t = (6 \text{ minutes} \times 60 \frac{\text{seconds}}{\text{minute}}) + 40 \text{ seconds}$

$t = 360 \text{ seconds} + 40 \text{ seconds}$

$t = 400 \text{ seconds}$

Step 2: Calculate Distance

We use the fundamental relationship between distance, speed, and time: Distance = Speed × Time.

In this specific problem:

• Speed ($c$) = 1 (unitless, as speed of light is taken as unity).
• Time ($t$) = 400 seconds.

Therefore, the distance ($d$) is:

$d = c \times t$

$d = 1 \times 400 \text{ seconds}$

$d = 400$

Since the speed of light is taken as 1 unit of distance per unit of time (here, seconds), the distance calculated is in these new units. The unit would effectively be 'light-seconds'.

Conclusion

The distance between the Sun and the Earth, in the new unit system where the speed of light is unity, is 400 units (or 400 light-seconds).