Answer:
The nearest star would be approximately 4064km away from the sun.
Explanation:
The distance between the sun and the earth (in real life) is 147.36 × 10^6 km i.e. 1.4736 × 10^11m. In the analogy, we're told the distance from the earth to the grapefruit sized sun is only 15m. Hence, if we're to find a ratio of the real distance to the analogical distance, it would be given as
Real distance : Analogical distance
= 1.4736×10^11 : 15
= 9.824×10^9 : 1
This means that 1m in the analogical scale is equivalent to 9.824×10^9m in reality.
The nearest stars to the sun are about 4.22 light-years from the earth. In meters, that is
4.22 light-years × 9.461 × 10^15
= 3.9924 × 10^16m
Note: 1 light-year = 9.461 × 10^15m
Using the analogical scale, the nearest star would then be
(3.9924 × 10^16)/(9.824 × 10^9) = 4063925.08m = 4063.925km
Therefore, if the sun was the size of a grapefruit, the nearest star would be approximately 4064km away from the sun.
