Find The Mean Distance Of A Planet From The Sun If Its Period Of Revolution Is 300

Find the mean distance of a planet from the sun if its period of revolution is 300

Answer:

The mean distance is 44.81 AU

Explanation:

Kepplers 3rd Law formula

$T^2 = r^3$

where

T is the orbital period, unit is in Earthly years

r is the mean distance of a planet from the Sun, unit is in AU

Astronomical units (AU) is a unit for length which is the distance of the Earth to the Sun.

Given information

T = 300 revolutions

Take note: that 1 revolution around the sun is equivalent to one (1 ) year, $1rev=1year$ , therefore 300 revolutions = 300 years

Solving the problem

Using Kepplers 3rd Law formula

$T^2 = r^3$

Substitute the given information

$(300)^2=r^3$

$90,000=r^3$

$r=\sqrt3{90,000}$

r = 44.814 AU

Therefore, the mean distance of the planet from the sun is 44.814 AU.

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