The Earth's distance from the Sun and orbital periods are proportional to that of Jupiter's, due to _____
the conservation of angular momentum.
The Earth's distance from the Sun and orbital periods are proportional to that of Jupiter's, due to Kepler's Third Law of Planetary Motion.
The Earth's distance from the Sun and orbital periods being proportional to that of Jupiter's is due to Kepler's third law of planetary motion. Kepler's third law states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the Sun. This means that if a planet has a longer orbital period, it will also have a greater average distance from the Sun.
To understand why this is the case, we can look at the gravitational force between the Sun and a planet. The strength of the gravitational force depends on the masses of the two objects and the distance between them. In the case of the Sun and planets, the mass of the Sun is much larger than the mass of any planet, so we can consider the Sun to be stationary at the center of the solar system.
As a planet orbits the Sun, it experiences a gravitational force that pulls it inward towards the Sun. This force causes the planet to accelerate towards the Sun, which keeps it in its orbit. The strength of this gravitational force decreases with increasing distance from the Sun. Thus, a planet that is farther from the Sun will experience a weaker gravitational force compared to a planet that is closer.
For example, Jupiter is much farther from the Sun than Earth, so it experiences a weaker gravitational force from the Sun. This weaker force means that Jupiter requires a longer orbital period to stay in its orbit compared to Earth. In other words, Jupiter takes a longer time to complete one orbit around the Sun.
Therefore, the Earth's distance from the Sun and orbital period being proportional to Jupiter's is a natural consequence of the gravitational forces between the Sun and the planets, as described by Kepler's third law.