A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2.0 10^26 kg.

Moon X km
Moon Y km

To find the distance of each satellite moon from the planet's center, we can use Kepler's third law, which states that the square of the period of an orbit is proportional to the cube of the semi-major axis of the orbit.

First, let's find the orbital radius of Moon X.
Since Moon X has an orbital period of 2.13 days, we can convert it to seconds:
2.13 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 183,888 seconds

Now we can use Kepler's third law, which states that:
(T1^2 / T2^2) = (R1^3 / R2^3)

Let's assign the following variables:
T1 = orbital period of Moon X in seconds = 183,888 seconds
R1 = orbital radius of Moon X

The planet's mass is given as 2.0 * 10^26 kg.

Let's substitute these values into the equation:
(T1^2 / T2^2) = (R1^3 / R2^3)

(183,888^2 / 3.53^2) = (R1^3 / R2^3)

Simplifying this equation, we get:
(R1^3 / R2^3) = (183,888^2 / 3.53^2)

Now we can solve for R1. Taking the cube root of both sides:
(R1 / R2) = (183,888^2 / 3.53^2)^(1/3)

Rearranging this equation, we get:
R1 = R2 * (183,888^2 / 3.53^2)^(1/3)

Next, let's find the orbital radius of Moon Y.
Using the same process, we can substitute the values:
T2 = orbital period of Moon Y in seconds = 3.53 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 305,712 seconds
R2 = orbital radius of Moon Y

(R1 / R2) = (T1^2 / T2^2)

Substituting the values:
(R1 / R2) = (183,888^2 / 305,712^2)

Rearranging to solve for R2:
R2 = R1 * (305,712^2 / 183,888^2)^(1/3)

Now we can solve for R1 and R2 by plugging in the values into the equations above. Using a calculator, you can calculate the values of R1 and R2 as follows:

R1 = (R2 * (183,888^2 / 3.53^2)^(1/3))
R2 = (R1 * (305,712^2 / 183,888^2)^(1/3))

Keep in mind that the distances will be in the same unit as the orbital radius used (e.g., kilometers, meters, etc.).