The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula mc023-1.jpg. If Saturn’s orbital period is 29.5 years, what is its distance from the sun?
9.5 AU , 19.7 AU, 44.3 AU, or 160.2 AU
we know that
Given the orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula [tex] P = a^\frac{3}{2} [/tex]
So
In this problem
[tex] P=29.5 years [/tex]
[tex] P = a^\frac{3}{2} [/tex]
solve for a
[tex] 29.5=a^\frac{3}{2}\\ \\ a^{3} =29.5^{2} \\ \\ a=\sqrt[3]{29.5^{2}} \\ \\ a=9.54AU [/tex]
therefore
the answer is
Saturn's distance from the sun is [tex] 9.5 AU [/tex]
The measurement of the distance between planet and sun is 160.2 AU. The correct option is D.
The process of associating numbers with physical quantity and phenomenon. Distance is the length that is measured between the two ends.
Given
[tex]\rm P = a^{\frac{3}{2} }[/tex]
a = 29.5 years
To find
Distance between sun and planet.
Distance between sun and planet is given by
[tex]\rm P = a^{\frac{3}{2} }[/tex]
where, a = 29.5
Distance between sun and planet will be
[tex]\rm P = a^{\frac{3}{2} }\\\\P = 29.5^{\frac{3}{2} } \\\\P = 160.2[/tex]
Hence, the distance between planet and sun is 160.2 AU.
Thus, the correct option is D.
More about the measurement link is given below.
https://brainly.com/question/5014603
