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Chapter 4: Problem 18

The orbit of a spacecraft about the Sun has a perihelion distance of \(0.1 \mathrm{AU}\) and an aphelion distance of \(0.4 \mathrm{AU}\). What is the semimajor axis of the spacecraft's orbit? What is its orbital period?

Short Answer

Expert verified
The semimajor axis of the spacecraft's orbit is 0.25 AU and its orbital period is approximately 0.158 years.

Step by step solution

01

Calculate the Semimajor Axis

To calculate the semimajor axis 'a', average the perihelion and aphelion distances. Hence, \(a = \frac{(D_{perihelion} + D_{aphelion})}{2} = \frac{(0.1AU + 0.4AU)}{2} = 0.25AU\).
02

Calculate the Orbital Period

To calculate the orbital period 'P', use Kepler's third law: \(P^{2} = a^{3}\). Solving for P, we get \(P = \sqrt{a^{3}} = \sqrt{(0.25)^{3}} = 0.158 years\).

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