In a large outburst in 1841 , the \(120-M_{\odot}\) star Eta Carinae was losing mass at the rate of \(0.1 M_{\odot}\) per year. Let's put that into perspective. a. The mass of the Sun is \(2 \times 10^{30}\) kg. How much mass (in kilograms) was Eta Carinae losing each minute? b. The mass of the Moon is \(7.35 \times 10^{22}\) kg. How does Eta Carinae's mass loss per minute compare with the mass of the Moon?

Astronomical calculations often involve very large numbers and complex conversions. For example, when calculating the mass loss of a star like Eta Carinae, it is essential to convert between different units of measurement. This ensures accuracy and consistency in the results. Calculations involving astronomical bodies may include the comparison of masses, distances, and rates of change. These calculations help us understand phenomena on a cosmic scale.

These processes often require the use of scientific notation, which simplifies the manipulation of very large or very small numbers. For instance, instead of writing all the zeros, scientists use powers of ten, such as writing the mass of the Sun as \(2 \times 10^{30} \text{ kg}\). Understanding and performing these conversions is crucial for anyone studying astronomy or astrophysics.

The mass of celestial objects like stars, planets, and moons is often given in kilograms or as a multiple of the mass of known objects like the Sun or Earth. For example, the mass of the Sun is a common reference point in these calculations.

In the given exercise, Eta Carinae has a mass of 120 solar masses, which means it is 120 times more massive than the Sun. Similarly, the mass of the Moon is given as \(7.35 \times 10^{22} \text{ kg}\).

When comparing these masses, it's important to understand the relative scales. For example, even though the Moon seems large to us, its mass is tiny compared to the mass being lost by Eta Carinae every minute during its outburst. This understanding helps put cosmic events into perspective.

Conversion of units is a crucial skill in astronomical calculations. It ensures that measurements are consistent and comparable. In the exercise, converting the mass loss rate of Eta Carinae from solar masses per year to kilograms per year is an example of such a conversion.

To perform this conversion, first multiply the rate by the mass of the Sun to get the mass loss per year in kilograms: \(0.1 M_{\text{Sun}} = 0.1 \times 2 \times 10^{30} \text{ kg} = 2 \times 10^{29} \text{ kg/year}\).

Next, convert the yearly mass loss to a per-minute rate by dividing by the number of minutes in a year: \(525,600 \text{ minutes/year}\). This gives: \( \frac{2 \times 10^{29} \text{ kg/year}}{525,600 \text{ minutes/year}} \text{ kg/min} \approx 3.8 \times 10^{23} \text{ kg/min}\).

These conversions allow us to better understand and compare astronomical events in more manageable terms.