Scooby Don't - Enigmatic Puzzle

Question

Clues:

r(t)=e^(𝝅t/4)

• t₁ = 0
• t₂ = 8 ln(3)/𝝅
• t₃ = 2.0492
• t₄ = II . IV VII VII VI I

[contextual diagram]

Instructions: Name That Astronaut

_ _ _ _ A

Answer 1

Taking out my calculator, I find that all of the $r(t_i)$ numbers are close to integers, all within the 1-11 range that appears in the diagram.

• $r(t_1) = 1$
• $r(t_2) \approx 9$
• $r(t_3) \approx 5$
• $r(t_4) \approx 7$

So I think that the “astronaut” (or “cosmonaut”) you're looking for is:

LAIKA the dog, who was launched into space by the Soviets in 1957. Her name satisfies the letter pattern [AL][AI][IK][AK]A from the boxes connected to the numbers 1, 9, 5, 7 in the diagram.

The question title is:

a reference to Scooby-Doo, thus hinting at a dog. “Don't” may be a reference to the fact that Laika never returned from space, dying of overheating while in orbit.

OP Edit:

r(t4) is the number 2.47761 in roman numerals