To solve this problem, we can use Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution of a planet is directly proportional to the cube of its average distance from the sun.

Let's denote:
- T1 = period of revolution of Earth = 1 year
- R1 = distance of Earth from Sun = 1.5 x 10^6 km
- T2 = period of revolution of the imaginary planet = 2.83 years
- R2 = distance of the imaginary planet from Sun (which we are trying to find)

According to Kepler's Third Law, (T1/T2)^2 = (R1/R2)^3.

We can rearrange this equation to solve for R2: R2 = R1 * (T2/T1)^(2/3).

Substituting the given values into this equation gives us:

R2 = 1.5 x 10^6 km * (2.83/1)^(2/3) = 3 x 10^6 km.

So, the distance of the imaginary planet from the Sun would be 3 x 10^6 km.

Question

To solve this problem, we can use Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution of a planet is directly proportional to the cube of its average distance from the sun.

Let's denote:
- T1 = period of revolution of Earth = 1 year
- R1 = distance of Earth from Sun = 1.5 x 10^6 km
- T2 = period of revolution of the imaginary planet = 2.83 years
- R2 = distance of the imaginary planet from Sun (which we are trying to find)

According to Kepler's Third Law, (T1/T2)^2 = (R1/R2)^3.

We can rearrange this equation to solve for R2: R2 = R1 * (T2/T1)^(2/3).

Substituting the given values into this equation gives us:

R2 = 1.5 x 10^6 km * (2.83/1)^(2/3) = 3 x 10^6 km.

So, the distance of the imaginary planet from the Sun would be 3 x 10^6 km.

Knowee AI · Accepted Answer

To solve this problem, we can use Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution of a planet is directly proportional to the cube of its average distance from the sun.

Let's denote:
- T1 = period of revolution of Earth = 1 year
- R1 = distance of Earth from Sun = 1.5 x 10^6 km
- T2 = period of revolution of the imaginary planet = 2.83 years
- R2 = distance of the imaginary planet from Sun (which we are trying to find)

According to Kepler's Third Law, (T1/T2)^2 = (R1/R2)^3.

We can rearrange this equation to solve for R2: R2 = R1 * (T2/T1)^(2/3).

Substituting the given values into this equation gives us:

R2 = 1.5 x 10^6 km * (2.83/1)^(2/3) = 3 x 10^6 km.

So, the distance of the imaginary planet from the Sun would be 3 x 10^6 km.

If the distance of the earth from Sun is 1.5×106 km, then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is: 6 × 107 km 6 × 106 km3 × 106 km3 × 107 kmMark for Review & NextClear ResponseSave & NextSubmit

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