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An object has an average distance of 9.70 ✕ 108 km from the Sun. What is its orbital period (in years)?

1 Answer

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Answer:

16.5 years

Step-by-step explanation:

You want to know the orbital period of an object with an average distance of 9.7×10^8 km from the sun.

Period

The period (P) in years of an object with distance from the sun of A astronomical units is given by the relation ...

P² = A³

Solving for P, we have ...

P = A^(3/2)

An astronomical unit is about 1.496×10^8 km. The orbital period of the object is ...

P = ((9.7×10^8)/(1.496×10^8))^(3/2) ≈ 16.5 . . . . years

The orbital period in years is about 16.5.

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Additional comment

In general, there is a constant of proportionality that will depend on the mass of the sun, and the units of time and distance. As it happens, that constant is 1 for distances in AU and time in years, where the object is orbiting the Sun.

The object described here is between the orbits of Jupiter and Saturn, so has a period between the periods of those planets.

An object has an average distance of 9.70 ✕ 108 km from the Sun. What is its orbital-example-1
User Timo Geusch
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