The immense scale of the cosmos often challenges human comprehension, but even within our own solar system, the size difference between the planets and our star is staggering. The Sun is a colossal body, dominating the system by its sheer physical volume. Understanding the magnitude of this difference requires a comparison of their fundamental dimensions and a precise calculation of capacity.
Comparing the Dimensions of Earth and the Sun
The comparison begins with the diameter of each celestial body. Earth has an equatorial diameter of approximately 12,742 kilometers. The Sun, by contrast, has a diameter of roughly 1.39 million kilometers. This ratio means that approximately 109 Earths could be lined up side-by-side to span the diameter of the Sun.
This ratio of linear dimensions forms the mathematical basis for determining the relative volume. Since both the Sun and Earth are approximately spherical, the difference in their radii directly influences the difference in their total volume. The fact that the Sun’s diameter is 109 times greater than Earth’s means the volume difference will be a much larger, three-dimensional figure.
Calculating the Theoretical Volume Capacity
To find the theoretical number of Earths that could fit inside the Sun, scientists compare their respective volumes. The volume of a sphere is calculated using the formula \(V = \frac{4}{3}\pi r^3\), where \(r\) is the radius. Since the Sun’s radius is about 109 times that of Earth, the volume ratio is found by cubing the radius ratio (\(109^3\)). This calculation yields a figure of approximately 1,295,000.
Based on pure volume, the Sun is large enough to contain roughly 1.3 million Earths if it were a hollow shell. This number represents the absolute maximum capacity, assuming the volume is completely filled. This theoretical calculation is purely mathematical and ignores the physical impossibility of perfectly packing solid, spherical objects. This volume-based number is the one most often cited when discussing the relative sizes of the two bodies.
The Geometry of Packing Spheres
The physical reality of fitting spheres inside a much larger spherical container is governed by the principles of packing efficiency. When spheres of equal size are packed together, there will always be empty spaces, or voids, between them, regardless of the arrangement. This phenomenon prevents the complete utilization of the container’s volume, meaning the theoretical 1.3 million figure cannot be physically achieved.
In three-dimensional space, the maximum theoretical packing density for equal spheres is approximately 74% of the total volume. Applying this geometric constraint means that only about 74% of the calculated capacity would be filled by whole Earths. By multiplying the theoretical volume capacity of 1.3 million by the maximum packing efficiency of 0.74, the practical number of Earths that could fit within the Sun is reduced significantly. This more realistic estimate is closer to 962,000 Earths.
Scale Comparison to the Solar System
The Sun’s dominance extends beyond its comparison with Earth, encompassing the entire solar system. The star accounts for 99.86% of the total mass of the system. This gravitational dominance ensures all other bodies remain in orbit around the Sun.
Even the gas giants, which are immense on their own, are dwarfed by the Sun’s volume. Jupiter, the largest planet, could hold approximately 1,000 Earths inside it, yet the Sun could still contain about 1,000 Jupiters.