The Earth's orbital period change is A: It would increase by 0.15 years
Using Kepler's third law which states that the square of the orbital period of the planet is directly proportional to the cube of its distance from the sun.
So, T² ∝ R³
T'²/T² = R'³/R³ where
- T = orbital period at R = 1 year
- R = initial axis length = 1 AU
- T' = orbital period at R'
- R' = final axis length = 1.1 AU.
So, making T' subject of the formula, we have
T' = [√(R'/R)³]T
T' = [√(1.1 AU/1 AU)³] × 1 year
T' = [√(1.1)³] × 1 year
T' = √1.331 × 1 year
T' = 1.15 × 1 year
T' = 1.15 years.
So, the change in the Earth's orbital period ΔT = T' - T
= 1.15 years - 1 year
= 0.15 years
Since this is positive, the orbital period increases by 0.15 years.
So, the Earth's orbital period change is A: It would increase by 0.15 years
Learn more about Kepler's third law here:
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