Final answer:
The unit 'a*' signifies the radius of a circular orbit and is equivalent to the semi-major axis of an elliptical orbit. It is equal to an AU, the average radius of Earth's orbit around the Sun, and facilitates calculations involving Kepler's third law as well as communication between astronomers.
Step-by-step explanation:
The unit 'a*' relates specifically to the radius of a circular orbit. Its importance lies in astrophysics and celestial mechanics, often in connection with Kepler's laws of planetary motion. When we refer to the unit 'a*' in astrophysical contexts, it represents the semi-major axis of an elliptical orbit, which, for a circle, is simply the orbit's radius.
An Astronomical Unit (AU), which is the average radius of Earth's orbit around the Sun, corresponds to 1 AU = 1.50 × 10¹¹ meters. In many cases, orbits in our solar system can be approximated as circular, using this convenient scale. The radius of such an orbit in 'a*' is a dimensionless number describing how many times larger or smaller an orbit is compared to Earth's orbit around the Sun. Consequently, this unit is widely used in describing distances within our solar system or in calculations involving Kepler's third law, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Using 'a*' as a unit offers several advantages: it simplifies calculations by providing a scale relative to Earth's orbit, aids conceptual understanding by creating a reference point, and improves communication among astronomers by using a standardized measurement.