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Question
Assume that you are in another solar system and provided with the set of data given below consisting of the planets’ semi-major axes and time periods. Can you infer the relation connecting semi-major axis and time period?
| Planet (imaginary) | Time period (T) (in year) | Semi-major axis (a) (in AU) |
| Kurinji | 2 | 8 |
| Mullai | 3 | 18 |
| Marutham | 4 | 32 |
| Neithal | 5 | 50 |
| Paalai | 6 | 72 |
Solution
Time period `"T"^2 ∝ "a"^3`
T1 = 2; a1 = 8
a1 = 22 × 2 = 2T1 (T1 = 2)
a2 = 32 × 2 = `2"T"_2^2` (T2 = 3)
a3 = 42 × 2 = `2"T"_3^2` (T3 = 4)
a4 = 52 × 2 = `2"T"_4^2` (T4 = 5)
a5 = 62 × 2 = `2"T"_5^2` (T5 = 6)
∴ `"a" ∝ 2"T"^2`
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