Astronomical distances.

Classical Mechanics Level pending

The average distance from Earth to the sun is about $150,000,000$ kilometers. This distance is called an astronomical unit, the $AU$ . The relationship of a planet's distance from the sun and it's orbital period is $a^3=p^2$ where $a$ is the given planet's average distance from the sun in astronomical units and $p$ is the planet's period in Earth years.

Using the given information find the average distance from Jupiter to the sun in kilometers. Round to the nearest kilometer.

$1AU=150,000,000km$
Jupiter's period $=12$ years
$a^3=p^2$

Hint: Solve for $a$ then convert units. Do NOT round until your final answer.

The answer is 786222418.

1 solution

Alex Harman
May 24, 2016

$a^3=p^2$ then $a=\sqrt[3]{p^2}$ . When $p=12$ we get $a=\sqrt[3]{12^2}=\sqrt[3]{144}$ $≈5.24142788$ .
Since $1AU=150,000,000km$ and we have roughly $5.24142788$ $AU$
then $5.24142788 \times 150,000,000=786,222,418.3km$
rounded to the nearest kilometer is $786,222,418km$

Astronomical distances.

The answer is 786222418.

1 solution

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