Yes, according to Kepler's third law of Planetary Motion.
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Not totally true.
AUs
The greater the distance, the longer is the orbital period and the slower the velocity. "Kepler's Laws of Planetary Motion" contain mathematical details. Further explanation is given by the work of Isaac Newton and his theory of gravitation. For example, one version of Kepler's 3rd law is : The square of the orbital period (in Earth years) equals the cube of the average distance from the Sun (in Astronomical Units). <<>> The second half of the question can be answered from the above formula. For example, a planet at four times the distance of Earth from the Sun would go round the Sun in eight years. The length of that orbit would be (almost exactly) four times as far as Earth's. So, the planet would travel at half the speed of Earth. In this example, and also generally, the orbital speed is inversely proportional to the square root of the average distance from the Sun.
It would depend on the star it was orbiting. If it were in our solar system, its orbital period would be little more than 30 years. (Saturn is approximately 9.5 AU from the Sun.)
The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Not totally true.
AUs
No it is not true. The second variable is the cube of the semi-major axis.
Yes, spot on, good guess . .
At what distance from the Sun would a planet's orbital period be 3 million years?
The greater the distance, the longer is the orbital period and the slower the velocity. "Kepler's Laws of Planetary Motion" contain mathematical details. Further explanation is given by the work of Isaac Newton and his theory of gravitation. For example, one version of Kepler's 3rd law is : The square of the orbital period (in Earth years) equals the cube of the average distance from the Sun (in Astronomical Units). <<>> The second half of the question can be answered from the above formula. For example, a planet at four times the distance of Earth from the Sun would go round the Sun in eight years. The length of that orbit would be (almost exactly) four times as far as Earth's. So, the planet would travel at half the speed of Earth. In this example, and also generally, the orbital speed is inversely proportional to the square root of the average distance from the Sun.
To calculate the orbital period of a planet with an average distance from the Sun of 9.1 Astronomical Units (AU), we use Kepler's Third Law of Planetary Motion: P^2 = a^3. Given: a = 9.1 AU Substitute the value of 'a' into Kepler's Third Law to find the orbital period, P: P^2 = (9.1)^3 P^2 = 753.571 AU^3 To find the orbital period P, take the square root of both sides of the equation: P = √753.571 P ≈ 27.45 years Conclusion: A planet with an average distance of 9.1 AU from the Sun has an estimated orbital period of approximately 27.45 Earth years.
you are chicken
Use Kepler's Third Law, and compare with Earth's orbit.
Yes, the equation p2 = a3, where p is a planet's orbital period in years and a is the planet's average distance from the Sun in AU. This equation allows us to calculate the mass of a distance object if we can observe another object orbiting it and measure the orbiting object's orbital period and distance.
It would depend on the star it was orbiting. If it were in our solar system, its orbital period would be little more than 30 years. (Saturn is approximately 9.5 AU from the Sun.)