Respuesta :
Saturn’s distance from the Sun is 9.54 AU and this can be determined by using Kepler's third law and the given data.
Given :
Saturn orbits every 29.5 years.
The following steps can be used in order to determine Saturn’s Distance from the Sun:
Step 1 - Kepler's third law is used in order to determine Saturn’s Distance from the Sun.
[tex]T^2\;\alpha \;r^3[/tex]
Step 2 - The above expression becomes:
[tex]\dfrac{T^2_1}{T^2_2}=\dfrac{r^3_1}{r^3_2}[/tex]
where [tex]T_1[/tex] and [tex]T_2[/tex] is the time in years and [tex]r_1[/tex] and [tex]r_2[/tex] is the radius.
Step 3 - The value of [tex]T_1[/tex] for Earth is 1 year, [tex]T_2[/tex] for Saturn is 29.5 years, and [tex]r_1[/tex] of Earth is 1 AU.
Step 4 - Substitute the values of [tex]T_1[/tex], [tex]T_2[/tex], and [tex]r_1[/tex] in the above formula.
[tex]\dfrac{(1)^2}{(29.5)^2}=\dfrac{(1)^3}{r^3_2}[/tex]
Step 5 - Simplify the above expression.
[tex]r_2 = 9.54 \;{\rm AU}[/tex]
Saturn’s distance from the Sun is 9.54 AU.
For more information, refer to the link given below:
https://brainly.com/question/25900771
