The recently dwarf planet Eris has an orbital period about the Sun, P, of 557 years. According to Kepler's 3ʳᵈ Law, what is the semi-major axis, a, of its orbit?
A) 55.7 AU
B) 38.4 AU
C) 72.1 AU
D) 67.7 AU

Question

Quizplus · Accepted Answer

Kepler's 3rd Law states that the square of the orbital period (P^2) is directly proportional to the cube of the semi-major axis of its orbit (a^3). Given that Eris has an orbital period (P) of 557 years, we can use the relation P^2 = a^3, where P is in Earth years and a is in Astronomical Units (AU), to find the semi-major axis. For the Earth, P = 1 year and a = 1 AU, serving as our reference. Rearranging the formula to solve for a gives us a^3 = P^2. Substituting P = 557 years into the equation, we get a^3 = 557^2. Solving for a gives us a ≈ 67.7 AU, making option D the correct answer.

The Recently Dwarf Planet Eris Has an Orbital Period About