Question

If the planet is largely composed of a magnesium alloy with a constant density of 1836kg/m3, calculate the ratio of the total mass of the atmosphere to the total mass of the planet (including the atmosphere).

Answer 1

The ratio of the total mass of the atmosphere to the total mass of the planet, including the atmosphere, can be calculated by considering the density of the magnesium alloy that makes up the planet. Given a constant density of 1836 kg/m³ for the magnesium alloy, the ratio is approximately [1 / (1 - (density of atmosphere / density of planet))].

Step-by-step explanation:

To calculate the ratio, we use the formula:

`\[ \text{Ratio} = \frac{1}{1 - (\frac{\text{Density of Atmosphere}}{\text{Density of Planet}})} \]`

The density of the planet is given as 1836 kg/m³, and assuming the atmosphere has a different density, the ratio provides a measure of how much the atmosphere contributes to the overall mass. For instance, if the atmosphere is negligible compared to the planet, the ratio approaches 1. On the other hand, if the atmosphere is substantial, the ratio will be greater than 1.

In the calculation, it is crucial to convert all units to a consistent measure, typically kilograms per cubic meter (kg/m³). This ensures that the density values are compatible for accurate computations. By plugging in the given values and performing the calculation, the ratio gives a clear indication of the relative contribution of the atmosphere to the total mass of the planet. This approach is fundamental in planetary science, where understanding the distribution of mass is crucial for comprehending planetary dynamics and behavior.

Complete Question:

How do you calculate the ratio of the total mass of the atmosphere to the total mass of the planet (including the atmosphere) if the planet is largely composed of a magnesium alloy with a constant density of 1836 kg/m³?