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![**Asteroid Orbital Calculation**
An asteroid has a perihelion distance of 2.0 AU and an aphelion distance of 4.0 AU. Calculate its orbital semimajor axis.
*Explanation:*
The perihelion distance (the point in the orbit closest to the Sun) is 2.0 Astronomical Units (AU), and the aphelion distance (the point in the orbit farthest from the Sun) is 4.0 AU. The orbital semimajor axis, which is half the longest diameter of an elliptical orbit, can be calculated using the following formula:
\[
a = \frac{r_{perihelion} + r_{aphelion}}{2}
\]
Inserting the given values:
\[
a = \frac{2.0 \, \text{AU} + 4.0 \, \text{AU}}{2} = \frac{6.0 \, \text{AU}}{2} = 3.0 \, \text{AU}
\]
Therefore, the orbital semimajor axis of the asteroid is 3.0 AU.](https://content.bartleby.com/qna-images/question/3fe8677b-d2b4-4cf1-b1ed-08820154fcb5/8d47d7dd-9373-4d45-8587-d89a609b2402/f5bw76e_processed.png)
Transcribed Image Text:**Asteroid Orbital Calculation**
An asteroid has a perihelion distance of 2.0 AU and an aphelion distance of 4.0 AU. Calculate its orbital semimajor axis.
*Explanation:*
The perihelion distance (the point in the orbit closest to the Sun) is 2.0 Astronomical Units (AU), and the aphelion distance (the point in the orbit farthest from the Sun) is 4.0 AU. The orbital semimajor axis, which is half the longest diameter of an elliptical orbit, can be calculated using the following formula:
\[
a = \frac{r_{perihelion} + r_{aphelion}}{2}
\]
Inserting the given values:
\[
a = \frac{2.0 \, \text{AU} + 4.0 \, \text{AU}}{2} = \frac{6.0 \, \text{AU}}{2} = 3.0 \, \text{AU}
\]
Therefore, the orbital semimajor axis of the asteroid is 3.0 AU.
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