The cosmos presents scales so immense that our everyday frame of reference fails to grasp them. Astronomical comparisons often pivot on a simple question: how many of a familiar object, like Earth, could physically fit inside an enormous celestial body? To answer this question for a body like “Phoenix A,” we must first establish a precise unit of measure, understand the principles of three-dimensional scaling, and apply that mathematics to a specific, hypothetical scale.
The Baseline: Defining Earth’s Scale
Earth serves as the fundamental unit of measure for planetary volume comparisons. Its physical dimensions provide the necessary baseline for calculating how many times its volume can be contained within a larger object. For practical astronomical calculations, scientists use the mean diameter to represent the planet’s average size. Earth’s mean diameter measures approximately 12,742 kilometers (about 7,918 miles) across. Using this measure, the planet’s total volume is established at approximately \(1.08 \times 10^{12}\) cubic kilometers. This specific volume is the starting point from which all subsequent comparisons must be made.
Diameter vs. Volume: The Cube Factor
Calculating the number of smaller spheres that fit inside a larger one requires an understanding that volume scales dramatically faster than linear dimensions like diameter or radius. The relationship between a sphere’s size and its capacity is governed by the mathematical formula for volume: \(V = \frac{4}{3}\pi r^3\). In this equation, \(V\) represents volume, \(r\) is the radius, and the presence of the exponent three is what drives the vast differences in size. This is commonly referred to as the cube factor.
If we compare two hypothetical spheres, where Sphere B has a radius ten times greater than Sphere A, the volume of Sphere B will not be ten times larger. Because the radius is cubed, the volume ratio is determined by cubing the linear ratio, which is \(10^3\), or 1,000. This means Sphere B holds 1,000 times the volume of Sphere A.
This principle holds true for any spherical objects. A celestial body only twice the width of Earth will possess a volume eight times greater, since \(2^3\) equals 8. This mathematical reality explains why even small differences in diameter lead to astronomical differences in capacity, making linear size a poor predictor of total volume.
The Hypothetical Phoenix A: Calculating the Fit
The object named “Phoenix A” is the central galaxy or its ultramassive black hole in the Phoenix Cluster, making a volume calculation impossible in reality. To answer the question, we must define a clear, hypothetical scale for a spherical “Phoenix A” that reflects the immense size implied by its name. We assume this hypothetical body has a diameter 10,000 times greater than that of our Sun.
Since the Sun’s diameter is approximately 109.24 times greater than Earth’s mean diameter, the hypothetical Phoenix A is 1,092,400 times wider than Earth. This linear ratio is the value we must cube to find the volumetric comparison. Applying the cube factor means raising the linear ratio to the third power: \((1,092,400)^3\). The result reveals that the hypothetical Phoenix A could contain approximately \(1.303\) quintillion Earths. This number, 1,303,000,000,000,000,000, provides a direct answer based on the assumed dimensions and volumetric scaling.
Real-World Context: Placing Phoenix A Among Known Giants
The calculated size for the hypothetical Phoenix A places it far beyond the scale of any known star and into the territory of the largest astronomical structures. For context, our Sun is a medium-sized star, yet it could hold over 1.3 million Earths within its volume. Even the largest known star, the hypergiant UY Scuti, is estimated to have a volume nearly 5 billion times that of the Sun.
If UY Scuti were compared to the hypothetical Phoenix A, the hypergiant star would still be many orders of magnitude smaller. The massive scale assigned to the hypothetical object is more comparable to the scale of a planetary nebula or a large globular cluster. The actual Phoenix A is a central galaxy with a diameter of hundreds of thousands of light-years. The calculation provides a tangible way to comprehend a size that is otherwise abstract, by framing it in terms of our home planet.