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).
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