Question

Which planet is more massive: Earth or Saturn? Which planet is more dense: Earth or Saturn?

Short answer

Saturn is more massive, but Earth is more dense.

Step-by-step solution

Determine the Mass of Each Planet

First, we need to find the mass of Earth and Saturn. The mass of Earth is approximately \(5.97 \times 10^{24}\) kilograms, while the mass of Saturn is approximately \(5.68 \times 10^{26}\) kilograms.

Compare the Mass of Earth and Saturn

Now, compare these two values. The mass of Saturn is significantly larger than the mass of Earth. Therefore, Saturn is more massive than Earth.

Determine the Volume of Each Planet

To find the density, we need the volume of each planet. The average radius of Earth is about 6,371 kilometers, and that of Saturn is approximately 58,232 kilometers. Using the formula for the volume of a sphere, \( V = \frac{4}{3} \pi r^3 \), calculate the volumes:- Volume of Earth: \( V_{Earth} \approx \frac{4}{3} \pi (6,371 \times 10^3)^3 \approx 1.08 \times 10^{21} \text{m}^3 \)- Volume of Saturn: \( V_{Saturn} \approx \frac{4}{3} \pi (58,232 \times 10^3)^3 \approx 8.27 \times 10^{23} \text{m}^3 \)

Calculate the Density of Each Planet

Density is mass divided by volume, \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).- Density of Earth: \( \text{Density}_{Earth} = \frac{5.97 \times 10^{24} \text{kg}}{1.08 \times 10^{21} \text{m}^3} \approx 5,517 \, \text{kg/m}^3 \)- Density of Saturn: \( \text{Density}_{Saturn} = \frac{5.68 \times 10^{26} \text{kg}}{8.27 \times 10^{23} \text{m}^3} \approx 687 \, \text{kg/m}^3 \)

Compare the Density of Earth and Saturn

Compare the densities calculated. Earth has a much higher density than Saturn. Therefore, Earth is more dense than Saturn.

Key concepts

Mass Comparison

In planetary science, mass comparison between planets can reveal fascinating differences. Mass is essentially the amount of matter contained in each planet, and it is measured in kilograms. For example, Earth, our home planet, has a mass of approximately \(5.97 \times 10^{24}\) kg. However, when we look at Saturn, a giant gas planet, its mass is about \(5.68 \times 10^{26}\) kg, which is a substantial amount more.

Saturn's massive value suggests that it is composed of much more matter than Earth. But remember, it does not mean Saturn is denser, as density involves volume too. Mass does not necessarily equate to size, but rather reflects the total material present. This is why two celestial bodies can significantly differ in mass despite differences in composition.

In conclusion, Saturn is more massive than Earth, highlighting its prominent stature in our solar system.

Density Calculation

Density is calculated as mass divided by volume and provides insight into how tightly matter is packed within a planet. When we calculate Earth's density, we take its mass, \(5.97 \times 10^{24}\) kg, and divide by its volume, \(1.08 \times 10^{21}\) m\(^3\). This gives us a density of about \(5,517 \, \text{kg/m}^3\).

Saturn, on the other hand, has a much larger volume, \(8.27 \times 10^{23}\) m\(^3\), due to its gaseous nature. When dividing its mass, \(5.68 \times 10^{26}\) kg, by this volume, we find a much lower density of \(687 \, \text{kg/m}^3\).

Key points to remember:

• Earth's higher density is attributed to its solid and metallic core, whereas Saturn's predominantly gaseous composition leads to a lower density.
• Planets with higher density are generally rock-based, while those with lower densities often have a larger percentage of gases or ices.

Hence, even though Saturn is more massive, Earth is considerably denser due to its compact structure.

Volume of Planets

The volume of a planet is determined using the formula for the volume of a sphere, \( V = \frac{4}{3} \pi r^3 \). This formula helps us calculate the space that the planet occupies. For Earth, which has a radius of about 6,371 kilometers, its volume turns out to be approximately \(1.08 \times 10^{21}\) cubic meters.

Saturn, conversely, boasts a much larger radius of around 58,232 kilometers. By employing the same formula, we discover that Saturn's volume is a staggering \(8.27 \times 10^{23}\) cubic meters.

A few takeaways regarding planet volume:

• A larger radius results in a significantly increased volume; thus, size plays a crucial role in volume calculation.
• Volume doesn't directly tell us about a planet's mass or density but is essential for finding out its density.

Therefore, although Saturn has a much larger volume than Earth, it does not mean it is denser. It's the combination of volume and mass which sheds light on the planet's composition and density characteristics.