Suppose a new dwarf planet is discovered orbiting the Sun with a semimajor axis of 50 AU. What would be the orbital period of this new dwarf planet?

The term 'orbital period' refers to the time it takes for an object to complete one full orbit around another object. In our solar system, planets, dwarf planets, and other celestial bodies revolve around the Sun.

The concept is central to understanding Kepler's Third Law, which provides a relationship between the orbital period and the semimajor axis of an orbit. When we say that a planet has an orbital period of 1 year, like Earth, it means that it takes one Earth year to make a complete trip around the Sun.

To find the orbital period of any other object orbiting the Sun, Kepler's Third Law comes into play. In mathematical terms, the law states that the square of the orbital period (T) is proportional to the cube of the semimajor axis (a), or \( T^2 = a^3 \). This formula is incredibly useful because if we know the distance of a planet to the Sun (the semimajor axis), we can easily find out how long it takes for that planet to orbit the Sun (the orbital period).

The semimajor axis is a key parameter in understanding orbits. It represents half of the longest diameter of an elliptical orbit. In simpler terms, if you imagine an orbit as an elongated circle, the semimajor axis is the longest distance from the center to the edge.

In our problem, the semimajor axis of the dwarf planet's orbit is given as 50 Astronomical Units (AU). An Astronomical Unit is the average distance between the Earth and the Sun, about 93 million miles or 150 million kilometers.

Therefore, a semimajor axis of 50 AU means that the distance from the center of the planet's elliptical orbit to its furthest edge is about 50 times the average distance from the Earth to the Sun. This large distance plays a crucial role in determining the orbital period of the celestial body, as illustrated by Kepler's Third Law.

A dwarf planet is a celestial body that shares some characteristics with regular planets but differs in important ways. According to the International Astronomical Union (IAU), a dwarf planet:

• Orbits the Sun
• Has sufficient mass for its self-gravity to overcome rigid body forces so that it achieves hydrostatic equilibrium (a nearly round shape)
• Has not cleared its neighboring region of other objects
• Is not a satellite

Famous examples of dwarf planets include Pluto, Eris, Haumea, and Makemake. In this exercise, the newly discovered dwarf planet has a semimajor axis of 50 AU, much farther from the Sun than Pluto.

Understanding the characteristics and orbits of dwarf planets helps scientists gain insights into the formation and evolution of our solar system. These distant worlds can provide hints about processes that took place billions of years ago.