Here's how to calculate the orbital period of an object 4 AU from the sun, using Kepler's Third Law:

Kepler's Third Law:

The square of the orbital period (P) of a planet is proportional to the cube of its average distance (a) from the Sun. Mathematically:

P² = a³

Units:

* P: Orbital period in Earth years

* a: Average distance from the Sun in Astronomical Units (AU)

Calculation:

1. Given: a = 4 AU

2. Substitute into Kepler's Third Law:

P² = 4³ = 64

3. Solve for P:

P = √64 = 8 years

Therefore, an object at a distance of 4 AU from the sun would have an orbital period of 8 years.