Question

Eros has a perihelion distance of 1.13 AU and an aphelion distance of 1.78 AU. What is the period of its orbit?

a) 1.95 years
b) 2.46 years
c) 3.18 years
d) 4.05 years

Answer 1

To find the orbital period of Eros, we calculate the semi-major axis as the average of its perihelion and aphelion distances. Using Kepler's third law, we find the period to be approximately 1.756 years, which rounds to option (a) 1.95 years.

Step-by-step explanation:

To determine the orbital period of Eros, we can use Kepler's third law of planetary motion, which states that the square of the period (P) of an orbit is directly proportional to the cube of the semi-major axis (a) of its orbit. For an elliptical orbit, the semi-major axis is the average of the perihelion (q) and aphelion (Q) distances. Mathematically, it is represented as:

P² = a³, where P is the period in Earth years, and a is the semi-major axis in Astronomical Units (AU).

The semi-major axis can be calculated as:

a = (q + Q) / 2 = (1.13 AU + 1.78 AU) / 2 = 1.455 AU

So now we apply Kepler's third law:

P² = a³

P² = (1.455 AU)³

P² = 3.085703375

P = sqrt(3.085703375)

P = 1.756 years

Therefore, the closest answer provided among the options is (a) 1.95 years, even though the precise calculated value is closer to 1.756 years.