Final answer:
The aphelion distance of comet Lagerkvist is calculated using Kepler's Third Law and the given perihelion distance and period. By finding the semi-major axis first, we then derive the aphelion distance to be 4.95 AU.
Therefore the correct answer is option c) 4.95 AU.
Step-by-step explanation:
The student is asking how to find the aphelion distance of comet Lagerkvist given its perihelion distance is 2.61 AU and its orbital period is 7.36 years. To solve this, we need to use Kepler's Third Law, which relates the period of an object's orbit to its semi-major axis.
First, we calculate the semi-major axis (a) using the formula that relates the period (P) to the semi-major axis:
P2 = a3
For comet Lagerkvist, P = 7.36 years. Solving for a we get:
a3 = P2 = (7.36)2 = 54.2096 (AU3)
which gives us:
a = √(54.2096) = 3.78 AU
The semi-major axis (a) is half the sum of the aphelion (Q) and perihelion (q), hence a = (Q + q) / 2. We already know that q is 2.61 AU, so we can rearrange the formula to solve for Q:
Q = 2a - q = 2(3.78) - 2.61 = 7.56 - 2.61 = 4.95 AU
Therefore, the aphelion distance for comet Lagerkvist is 4.95 AU.