Respuesta :
Answer:
1200 days
Explanation:
- Time/Year on Planet X = [tex]T_{x} = 150[/tex] earth days
- Radius of Planet X = [tex]r_{x}[/tex]
- Radius of Planet Y = [tex]r_{y}[/tex] = [tex]4r_{x}[/tex]
- Time/Year on Planet Y = [tex]T_{y}[/tex] = ?
According to the Kepler's Third Law: "The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.”
Using above statement we get,
Tx^2/rx^3 = Ty^2/ry^3
Rearranging the above terms for [tex]T_{y}[/tex] we get,
[tex]T_{y} =[/tex][tex]\sqrt{\frac{Tx^{2}ry^{3} }{rx^{3}}}[/tex]
[tex]T_{y} =\sqrt{150^{2}4^{3}}[/tex]
[tex]T_{y} = \sqrt{22500*64}[/tex]
[tex]T_{y} = 1200[/tex] days
Kepler's third law shows the relationship between a planet's orbital period and the size of its orbit.
The orbital period of the planet Y is 1200 earth days.
What is Kepler's Third Law?
Kepler's third law states that the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axis of their orbits.
Given that time Tx on the planet X is 150 earth days.
Let's consider that rx is the radius of planet X and ry is the radius of planet y. The time period on planet Y is given by Kepler's Third Law.
[tex]\dfrac {T_x^2}{r_x^3} = \dfrac {T_y^2}{r_y^3}[/tex]
[tex]T_y^2 = \dfrac {T_x^2 r_y^3}{r_x^3}[/tex]
Given that ry = 4rx
[tex]T_y^2 = \dfrac {T_x^2 \times 64 r_x^3 }{r_x^3}[/tex]
[tex]T_y^2 = T_x^2 \times 64[/tex]
[tex]T_y = \sqrt{64 \times 150^2}[/tex]
[tex]T_y = 1200[/tex]
Hence we can conclude that the orbital period of the planet Y is 1200 earth days.
To know more about Kepler's third law, follow the link given below.
https://brainly.com/question/7783290.
