Question

Find the average distance of the orbit from the Sun to the nearest whole number. Use the Cube Root table provided
Quaoar is an object orbiting in an outer area of the solar system called the Kuiper belt. It is estimated to orbit the Sun once every 285 years.
O = 87 AU
O - 43 AU
O - 34 AU
O = 83 AU
*60 AU

Answer 1

We can estimate that the average distance is 43 AU, so the correct option is the second one.

How to find the average distance?

For an object orbiting the sun, the average distance of the orbit is:

$r =\sqrt[3]{ (\frac{T }{2*3.14})^2*G*M }$

Where:

• T is the period of the orbit, in this case, 285 years = 285*(3.154*10^7 s)
• G is the gravitational constant = 6.7*10^(-11) N*m/kg
• M is the mass of the sun = 1.989*10^30

Replacing all that in the average distance equation we get:

$r =\sqrt[3]{ (\frac{285*(3.154*10^7 s) }{2*3.14})^2*6.7*10^{-11} N*m/kg* 1.989*10^{30} \\}\\\\r = 6.387*10^{12}m$

Now, we know that:

1 AU = 1.49*10^(11) m

Then:

$r = (6.487*10^{12}/1.49*10^{11}}) AU = 43.5 AU$

Rounding to the whole number below, we get 43 ua, so the correct option is the second one.

If you want to learn more about orbits, you can read:

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