How does Kepler’s third law compare the periods and orbital radii of two planets within a solar system?(1 point)
Kepler's third law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis, or orbital radius.
In other words, if we have two planets within a solar system, one with a longer orbital period and a larger orbital radius than the other, the ratio of their orbital periods squared will be equal to the ratio of their orbital radii cubed.
For example, if Planet A has a period 2 times longer than Planet B, then the ratio of the orbital periods squared would be (2)^2 = 4. If Planet A also has an orbital radius 3 times larger than Planet B, then the ratio of the orbital radii cubed would be (3)^3 = 27.
Therefore, the comparison between the periods and orbital radii of the two planets is that the ratio of the orbital periods squared is equal to the ratio of the orbital radii cubed.
Kepler's third law, also known as the law of harmonies, compares the periods and orbital radii of two planets within a solar system. It states that the ratio of the square of the period of revolution (T) of a planet to the cube of the semi-major axis (r) of its orbit is constant (k), regardless of the mass of the planet or star. Mathematically, the relationship can be expressed as:
(T1/T2)^2 = (r1/r2)^3
This equation shows that the ratio of the periods to the square of the orbital radii of two planets is constant. Therefore, if you know the period of one planet and the semi-major axis of its orbit, you can use Kepler's third law to determine the period or orbital radius of another planet within the same solar system.
Kepler's third law, also known as the law of harmonies, relates the periods and orbital radii of two planets within a solar system. The law states that the square of the period of revolution (T) of a planet is directly proportional to the cube of its semi-major axis (r) of its orbit.
To understand how to compare the periods and orbital radii of two planets using Kepler's third law, you can follow these steps:
1. Determine the period of revolution (T) for each planet. The period is the time it takes for a planet to complete one orbit around its star, usually measured in Earth years.
2. Measure the semi-major axis (r) of each planet's orbit. The semi-major axis is the average distance between the planet and its star, usually measured in astronomical units (AU), where 1 AU is the average distance between the Earth and the Sun.
3. Square the periods of each planet. To do this, multiply the period of each planet by itself. For example:
- Planet 1: T1 * T1 = T1^2
- Planet 2: T2 * T2 = T2^2
4. Cube the semi-major axes of each planet. To do this, multiply the semi-major axis of each planet by itself two times. For example:
- Planet 1: r1 * r1 * r1 = r1^3
- Planet 2: r2 * r2 * r2 = r2^3
5. Compare the ratios. According to Kepler's third law, the ratio of the squared periods is equal to the ratio of the cubed semi-major axes:
- T1^2 / T2^2 = r1^3 / r2^3
6. Simplify the equation. You can solve for one unknown value by cross-multiplying:
- T1^2 * r2^3 = T2^2 * r1^3
By using Kepler's third law and following these steps, you can compare the periods and orbital radii of two planets within a solar system. Remember that this law is applicable for planets orbiting the same star.