In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun but occupying less space than our moon. Suppose that one of these black holes has a mass of \(1 \times 10^{3}\) suns and a radius equal to one-half the radius of our moon. What is its density in grams per cubic centimeter? The mass of the sun is \(2.0 \times 10^{30} \mathrm{~kg}\), and the radius of the moon is \(2.16 \times 10^{3} \mathrm{mi}\). (Volume of a sphere \(=\frac{4}{3} \pi r^{3}\).)

Astrophysics is a branch of astronomy that involves the study of the physical properties of celestial objects, including stars, planets, and galaxies, as well as phenomena that take place in the universe beyond Earth's atmosphere. A significant aspect of astrophysics involves the examination of the characteristics of various celestial bodies, such as their composition, density, and motion through space.

One of the most intriguing objects studied in astrophysics is the black hole, a region in space where the gravitational pull is so strong that nothing, not even light, can escape from it. Black holes are significant not only because of their mysterious nature but also because they impact their surroundings profoundly, influencing galaxy formation and evolution. Calculating properties like the density of black holes helps scientists understand more about these enigmatic entities and the role they play in the cosmos.

Stellar mass refers to the amount of matter contained within a star, typically measured in solar masses (the mass of our Sun). This measurement is crucial because it largely determines the evolution, structure, and eventual fate of the star. For instance, while some stars may end their life cycle as white dwarfs, more massive stars can explode as supernovae or collapse to form black holes.

In the context of the exercise, we're presented with an example of an extraordinary stellar mass condensed within a black hole, which is many times the mass of our Sun but confined within a much smaller space. Understanding the stellar mass of black holes and how it compares to familiar objects, such as our Moon, can offer valuable insights into their formation and ultimate impact on their cosmic surroundings.

In physics and astrophysics, calculating the volume of an object is often necessary to determine its density. The volume of regular solid objects can be calculated using mathematical formulas, and for a sphere, this is expressed as \( \frac{4}{3} \pi r^{3} \), with \( r \) representing the sphere's radius. This formula is derived from the principles of calculus and is a key tool in various fields of study.

For the black hole referenced in the exercise, despite its non-solid state, we can still apply the volume calculation for a sphere because a black hole is defined by a boundary known as the 'event horizon,' beyond which nothing can escape. Thus, the volume within this boundary can be considered for density calculations. The precise volume calculation is essential in our exercise to accurately determine the density of the black hole.

Unit conversion is an integral part of scientific calculations, allowing us to convert measurements from one system of units to another to perform calculations consistently and accurately. In astrophysics and many other sciences, the International System of Units (SI) is often employed, which includes meters for length, kilograms for mass, and seconds for time.

In the provided black hole density calculation exercise, we encounter the need to convert celestial masses into kilograms and distances from miles to centimeters. Such conversions are vital to ensure all measurements are in compatible units before proceeding with further calculations, such as volume and density. This diligence in unit conversion helps prevent errors and ensures that scientific findings are meaningful and can be reliably compared across different studies and disciplines.