If Comet Halley is approximated as a sphere \(5 \mathrm{km}\) in radius, what is its density if it has a mass of \(2.2 \times 10^{14} \mathrm{kg} ?\) How does that density compare to that of water \(\left(1,000 \mathrm{kg} / \mathrm{m}^{3}\right) ?\)

To determine the density of Comet Halley, we use the **density formula**. This formula is essential in physics and many scientific calculations. The formula for density is as follows:
\(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\)
Density is typically measured in kilograms per cubic meter (kg/m³).
Knowing the mass of the object and its volume allows us to use this straightforward formula. For Comet Halley, we already have a mass of \(2.2 \times 10^{14}\ \text{kg}\). The next step involves calculating the volume of Comet Halley. This value will then be used in the denominator of our density formula.

To find Comet Halley's volume, we approximate its shape as a sphere.
The formula for the volume of a sphere is:
\[ V = \frac{4}{3} \times \frac{\text{π}} \times r^3 \]
Here, **V** stands for volume, **π** is a constant approximately equal to 3.14159, and **r** is the radius of the sphere.
The given radius of Comet Halley is 5 km. First, we need to convert this radius into meters, as standard SI units are required for consistency.
Conversion: \(5 \ \text{km} = 5000 \ \text{m}\)
Substituting these values into the volume formula, we get:
\[ V = \frac{4}{3} \times \frac{\text{π}} \times (5000 \ \text{m})^3 \]
Simplifying this, we find the volume of Comet Halley. With this volume, we can now proceed to calculate its density.

After calculating the volume, we use the density formula again:
\[ \text{Density of Comet Halley} = \frac{2.2 \times 10^{14} \ \text{kg}}{\text{Volume obtained from previous section}} \]
Upon calculating, we find Comet Halley's density. The final step is to compare this density to water's density, which is known to be \(1000 \ \text{kg/m}^3\).
If Comet Halley's density is less than water's density, it indicates that Comet Halley is less dense than water.
This ***comparison of densities*** helps us understand the nature of Comet Halley in terms of its composition and internal structure.
The calculation reveals whether Comet Halley would sink or float if placed in water, showcasing a practical perspective of density analysis.