Respuesta :
Kepler's third law is used to determine the relationship between the orbital period of a planet and the radius of the planet.
The distance of the earth from the sun is [tex]1.50 \times 10^{11}\;\rm m[/tex].
What is Kepler's third law?
Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the radius of their orbits. It means that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
[tex]T^2 \propto R^3[/tex]
Given that Mars’s orbital period T is 687 days, and Mars’s distance from the Sun R is 2.279 × 10^11 m.
By using Kepler's third law, this can be written as,
[tex]T^2 \propto R^3[/tex]
[tex]T^2 = kR^3[/tex]
Substituting the values, we get the value of constant k for mars.
[tex]687^2 = k\times (2.279 \times 10^{11})^3[/tex]
[tex]k = 3.92 \times 10^{-29}[/tex]
The value of constant k is the same for Earth as well, also we know that the orbital period for Earth is 365 days. So the R is calculated as given below.
[tex]365^3 = 3.92\times 10^{-29} R^3[/tex]
[tex]R^3 = 3.39 \times 10^{33}[/tex]
[tex]R= 1.50 \times 10^{11}\;\rm m[/tex]
Hence we can conclude that the distance of the earth from the sun is [tex]1.50 \times 10^{11}\;\rm m[/tex].
To know more about Kepler's third law, follow the link given below.
https://brainly.com/question/7783290.
