Calculating the Year Length of Planet Y Around Alpha

[jnimagine]

Planet X orbits the star Alpha with a 'year' that is 200 Earth days long. Planet Y circles Alpha at nine times the distance of planet X. How long is a year on planet Y?

I know that I have to use the kepler's law : T^2 = (4pi^2/GM)r^3
but I'm not too sure how to do solve this...
Please help!
Thanks.

 

[LowlyPion]

Planet X orbits the star Alpha with a 'year' that is 200 Earth days long. Planet Y circles Alpha at nine times the distance of planet X. How long is a year on planet Y?

I know that I have to use the kepler's law : T^2 = (4pi^2/GM)r^3
but I'm not too sure how to do solve this...
Please help!
Thanks.

The third law : "The squares of the orbital periods of planets are directly proportional to the cubes of the axes of the orbits."

So T1²/r1³ = T2²/r2³

 

[baba89]

Based on the information provided, we can calculate the year length of planet Y using Kepler's Third Law of Planetary Motion. This law states that the square of a planet's orbital period (T) is proportional to the cube of its semi-major axis (r). In other words, T^2 is directly proportional to r^3.

Since planet X has a year length of 200 Earth days, we can calculate its semi-major axis (r) using the equation T^2 = (4pi^2/GM)r^3. Rearranging the equation, we get r = (T^2GM/4pi^2)^(1/3). Plugging in the values for planet X (T = 200 days, GM = gravitational constant x mass of Alpha), we get r = 0.000079 AU.

Since planet Y orbits at nine times the distance of planet X, its semi-major axis would be nine times larger, giving us a value of r = 0.000711 AU. Now, we can use this value to calculate the year length of planet Y by rearranging the equation T^2 = (4pi^2/GM)r^3 to solve for T. Plugging in the values for planet Y (r = 0.000711 AU, GM = gravitational constant x mass of Alpha), we get T = 1.2 Earth years or approximately 437 Earth days.

Therefore, the year length of planet Y around Alpha is approximately 437 Earth days. However, it is important to note that this is an estimate and may vary slightly due to factors such as the eccentricity of planet Y's orbit and the gravitational influence of other celestial bodies in the system.