The radius of planet X is 5.0 bleems. It takes 4 earth years to complete it's orbit. Another planet, Z, orbits the same sun and has an orbit with the radius of 12 bleems.
How long does it take for planet Z to complete an orbit?
kepplers third law: the square of the orbital period is proportional to the cube of mean radius.
4^2/T^2=5^3/12^3
solve for period T
To find out how long it takes for planet Z to complete an orbit, we can use the concept of Kepler's Third Law, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of its average distance from the sun (r), or T² = k * r³, where k is a constant.
In this case, we have the radius of planet X's orbit (5.0 bleems) and its orbital period (4 earth years). Let's call the orbital period of planet Z 'Tz' and its radius 'rz' to solve for this unknown value.
Since both planet X and planet Z orbit the same sun, we can set up the following proportion:
(Tz²) / (4²) = (rz³) / (5.0³)
Simplifying the equation:
(Tz²) / 16 = (rz³) / 125
To find Tz, we need to find the value of rz. Given that the radius of planet X's orbit is 5.0 bleems and the radius of planet Z's orbit is 12 bleems, we can set up the following ratio:
5.0 / 12 = 4 / Tz
Now we can solve for Tz:
(5.0 / 12) * Tz = 4
Tz = (12 * 4) / 5.0
Tz = 48 / 5.0
Tz ≈ 9.6 earth years
Therefore, it takes approximately 9.6 earth years for planet Z to complete an orbit around the sun.