The distance of a planet from the Sun can be determined using Kepler's Third Law, which states that the square of the period of a planet's orbit (its year) is proportional to the cube of its average distance from the Sun.

If a planet's year is 4 Earth years, then the square of its period is 4^2 = 16.

Since the square of the period is proportional to the cube of the distance, we can set up the following equation to solve for the distance:

16 = d^3

Taking the cube root of both sides gives us d = 2.5.

However, the options provided do not include 2.5. This suggests that the question may be based on a simplified version of Kepler's Third Law, where the period squared is equal to the distance cubed (without the constant of proportionality).

In this simplified version, if a planet's year is 4 Earth years, then the cube root of 4 gives us the distance. The cube root of 4 is approximately 1.587, which is closest to option d. 2 times further than Earth.

So, the answer is d. 2 times further than Earth.

Question

The distance of a planet from the Sun can be determined using Kepler's Third Law, which states that the square of the period of a planet's orbit (its year) is proportional to the cube of its average distance from the Sun.

If a planet's year is 4 Earth years, then the square of its period is 4^2 = 16.

Since the square of the period is proportional to the cube of the distance, we can set up the following equation to solve for the distance:

16 = d^3

Taking the cube root of both sides gives us d = 2.5.

However, the options provided do not include 2.5. This suggests that the question may be based on a simplified version of Kepler's Third Law, where the period squared is equal to the distance cubed (without the constant of proportionality).

In this simplified version, if a planet's year is 4 Earth years, then the cube root of 4 gives us the distance. The cube root of 4 is approximately 1.587, which is closest to option d. 2 times further than Earth.

So, the answer is d. 2 times further than Earth.

Knowee AI · Accepted Answer

The distance of a planet from the Sun can be determined using Kepler's Third Law, which states that the square of the period of a planet's orbit (its year) is proportional to the cube of its average distance from the Sun.

If a planet's year is 4 Earth years, then the square of its period is 4^2 = 16.

Since the square of the period is proportional to the cube of the distance, we can set up the following equation to solve for the distance:

16 = d^3

Taking the cube root of both sides gives us d = 2.5.

However, the options provided do not include 2.5. This suggests that the question may be based on a simplified version of Kepler's Third Law, where the period squared is equal to the distance cubed (without the constant of proportionality).

In this simplified version, if a planet's year is 4 Earth years, then the cube root of 4 gives us the distance. The cube root of 4 is approximately 1.587, which is closest to option d. 2 times further than Earth.

So, the answer is d. 2 times further than Earth.

A planet's year (the time it takes to orbit the Sun) is 4 Earth years. How far is the planet from the Sun compared to Earth?Select one:a.4 times further than Earthb.The same distance as Earthc.8 times further than Earthd.2 times further than Earth

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