Mars revolves around the sun in 687 Earth days, which represents a Martian year. How far is Mars from the sun? Express your answer in astronomical units.
The average distance between Mars and the Sun is 1.52 astronomical units (AU).
Mars is on average about 1.52 astronomical units (AU) away from the sun. An astronomical unit is the average distance from Earth to the sun, which is approximately 93 million miles or 150 million kilometers.
To determine the distance between Mars and the Sun in astronomical units (AU), we can use Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period of a planet is proportional to the cube of the average distance between the planet and the Sun.
Given that Mars has an orbital period of 687 Earth days, we can set up the following equation:
(Period of Mars / Period of Earth)^2 = (Average Distance of Mars from Sun / Average Distance of Earth from Sun)^3
Substituting in the values, we have:
(687 days / 365.25 days)^2 = (Average Distance of Mars from Sun / 1 AU)^3
Simplifying further:
(1.8809)^2 = (Average Distance of Mars from Sun / 1 AU)^3
3.5363 = (Average Distance of Mars from Sun / 1 AU)^3
Taking the cube root of both sides:
Cube Root (3.5363) = (Average Distance of Mars from Sun / 1 AU)
0.637 = (Average Distance of Mars from Sun / 1 AU)
Therefore, the average distance of Mars from the Sun is approximately 0.637 AU.