Two satellites, X and Y, orbit a planet in nearly circular orbits. Satellite X takes 20 days to complete one orbit, while satellite Y takes 160 days. If satellite X has orbital radius 1.0r, what is the orbital radius of satellite Y?

B. Satellite X has a greater period and a slower tangential speed than Satellite Y.

To find the orbital radius of satellite Y, we can use Kepler's third law of planetary motion, which states that the square of the orbital period (T) of a satellite is proportional to the cube of its average distance from the planet (r^3).

We are given that satellite X takes 20 days to complete one orbit and has an orbital radius of 1.0r. We can use this information to set up a proportion:

(TX)^2 / (TY)^2 = (RX^3) / (RY^3)

Since we are finding the orbital radius of satellite Y, let's call it RY. The orbital period of satellite X is 20 days and the orbital period of satellite Y is 160 days.

(20)^2 / (160)^2 = (1.0r)^3 / (RY)^3

To solve for RY, we need to rearrange the equation:

(RY)^3 = (1.0r)^3 * (160)^2 / (20)^2

Cancelling out the squares on the right side:

(RY)^3 = (1.0r)^3 * (8)^2

(RY)^3 = (1.0r)^3 * 64

Taking the cube root of both sides:

RY = 1.0r * 4

Finally, we get:

RY = 4.0r

Therefore, the orbital radius of satellite Y is 4.0 times the orbital radius of satellite X.