The abbreviation "a.u." stands for "astronomical unit" and is a unit of measurement used to describe distances in the solar system. 1 a.u. is equal to the average distance between the Earth and the Sun, which is about 93 million miles.
The formula for calculating the period (P) of a planet with a given eccentricity (e) and distance from the sun (a) is P = (2π√(a^3))/√(1-e^2), where a is measured in a.u. and e is unitless. In this case, the period would be P = (2π√(2^3))/√(1-0.5^2) = 3.82 years.
Eccentricity refers to the shape of a planet's orbit, with a value of 0 representing a perfectly circular orbit and a value of 1 representing a highly elliptical orbit. The higher the eccentricity, the more elongated and less predictable the orbit becomes. In this case, the planet's orbit would be more elongated and take longer to complete one full revolution around the sun compared to a planet with a lower eccentricity.
Yes, there is a direct relationship between a planet's period and its distance from the sun. The farther a planet is from the sun, the longer its period will be. This can be seen in Kepler's third law, which states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun.
A planet's eccentricity can change over time due to various factors, such as gravitational interactions with other planets or external forces like comets or asteroids. However, these changes are usually very small and occur over long periods of time, so for practical purposes, the eccentricity of a planet can be considered constant.