Question

earth is at an average distance of 93 million miles (1 au) from the sun. the period of earth is one year. planet x is at a distance of 10 au from the sun. what is the period of planet x

Answer 1

Using Kepler's Third Law and the fact that Earth's orbital period is 1 year at a distance of 1 AU from the Sun, the orbital period of Planet X, which is 10 AU away from the Sun, can be calculated to be approximately 31.62 Earth years.

Step-by-step explanation:

The orbital period of a planet in the solar system can be estimated using Kepler's Third Law of Planetary Motion, which states that the square of the period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit. In simpler terms, there is a relationship between the time a planet takes to orbit the Sun and its distance from the Sun.

In the case of Planet X, which is 10 AU from the Sun, we can use the information we have from Earth's orbit as a reference. Since Earth is 1 AU from the Sun and has an orbital period of 1 year, we can setup a proportion:

(Period of Earth)^2 / (Distance of Earth from Sun)^3 = (Period of Planet X)^2 / (Distance of Planet X from Sun)^3

Plugging in the values we get:

1^2 / 1^3 = T^2 / 10^3

Simplifying further:

1= T^2 / 1000

T^2 = 1000

T = sqrt(1000)

T ≈ 31.62 years

Therefore, the orbital period of Planet X is approximately 31.62 Earth years.

Answer 2

The period of planet X can be determined using Kepler's third law, which states that the square of the period is directly proportional to the cube of the orbital distance. Plugging in the values, we find that the period of planet X is 10 years.

Step-by-step explanation:

The period of a planet is determined by its orbital distance from the Sun. In this case, planet X is 10 AU away from the Sun, while Earth is 1 AU away. The period of planet X can be determined using Kepler's third law, which states that the square of the period is directly proportional to the cube of the orbital distance.

To calculate the period of planet X, we can use the equation:

TX2 = (RX3 / RE3) * TE2

Where TX is the period of planet X, RX is the distance of planet X from the Sun in AU, RE is the distance of Earth from the Sun in AU, and TE is the period of Earth. Plugging in the values, we get:

TX2 = (103 / 13) * 12

TX2 = 100

TX = 10

Therefore, the period of planet X is 10 years.