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

Answer 1

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`