Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units. years.
Kepler's third law states that for any object in a gravitational orbit,
P2∝a3P2∝a3
where PP is the orbital period of the object and aa is the average distance between the object and what it is orbiting.
In our Solar System, the natural units are distances measured in astronomical units (A.U.) and orbital periods measured in years. This can be seen for the Earth-Sun system which has an orbital period P=1P=1 year and an average distance a=1a=1 AU. Using these natural units in the Solar System, the proportionality becomes an equality, so for our Solar System:
(Pyears)2=(aA.U.)3(Pyears)2=(aA.U.)3 .
Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units.
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