Question

Using the same schematic above for the transiting exoplanet, if the period is 3.6201 days, what is the semi-major axis of the orbit? Answer in AU to two decimal places:

a) 0.83 AU
b) 1.25 AU
c) 2.17 AU
d) 4.06 AU

Answer 1

To find the semi-major axis of the exoplanet's orbit, we can use Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis. Given the period of 3.6201 days, the semi-major axis is approximately 2.17 AU.

Step-by-step explanation:

To find the semi-major axis of the exoplanet's orbit, we can use Kepler's third law, which states that the square of the orbital period (p) is proportional to the cube of the semi-major axis (a).

Given the period (p) of 3.6201 days, we can square it to get p² = 13.1209.

To find the semi-major axis (a), we can solve for it by taking the cube root of p². So, a = (p²)^(1/3) = (13.1209)^(1/3) = 2.117 AU.

Therefore, the semi-major axis of the orbit is approximately 2.17 AU, so the correct answer is c) 2.17 AU.