Question

Kepler’s third law can be used to derive the relation between the orbital period, P (measured in days), and the semimajor axis, A (measured in AU), of an orbiting body. The relation is given by the equation P2 = kA3, where k is a constant value for all bodies orbiting that star. The semimajor axis of Mars is 1.52 AU, and its orbital period is about 687 days. What is the value of the constant k?

A.
4.52 × 102
B.
7.44 × 10-6
C.
1.34 × 105
D.
2.21 × 10-3

Answer 1

C. 1.34×10
`{5}`

Explanation:

Given that the orbital period P=687 DAYS

and semimajor axis A=1.52 AU, then if P
`{2}`=kA³

then 687²=k×1.53³

k=687²÷3.5815

=1.34×10⁵