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[parent] example calculating orbital periods (Example)

Calculating Periods

Imagine an object is traveling around the Sun. What would be the orbital period of the object if its orbit has a semimajor axis of $50$ AU?

Solution

From Kepler's third law of planetary motion, we know that (when we use units of years and AU)

$\displaystyle P^2 = a^3 $

If the object's orbit has a semimajor axis of AU ($a = 50$), we can cube and then take the square root of the result to get $P$

$\displaystyle P = \sqrt{a^3} $

$\displaystyle P = \sqrt{50 \times 50 \times 50} = \sqrt{125,000} = 353.6 \,\, years $

Therefore, the orbital period of the object is about $350$ years. This would place our hypothetical object beyond the orbit of Pluto.

Check Your Learning

What would be the orbital period of an asteroid (a rocky chunk between Mars and Jupiter) with a semimajor axis of $3$ AU?

Answer

$\displaystyle P = \sqrt{3 \times 3 \times 3 } = \sqrt{27} = 5.2 \,\, years $

This article is a derivative work of the creative commons share alike with attribution in [1].

Bibliography

[1] Fraknoi, Andrew, David Morrison, and Sidney Wolff. The Sky Above. In Astronomy 2e. Houston, Texas : OpenStax, 2022. The Sky Above



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Cross-references: work, square, Kepler's third law of planetary motion, object

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Physics Classification: 45.50.Pk (Celestial mechanics )
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