In the year 8000 (Y8K) the mass of the Earth has increased (due to excessive space mining). As a result, the moon has moved further from the earth (the distance between the earth and the moon in the year 8000 is 4.06x108 m) and is now in a circular orbit. A lunar month remains at 29.5 days. ▼ Part A Calculate the mass of the earth in the year 8000 (Y8K) mearth = Submit IVE ΑΣΦ Request Answer ? kg

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In the year 8000 (Y8K) the mass of the Earth has increased (due to excessive space mining). As a result, the moon has moved further from the earth (the distance between the earth and the moon in the year 8000 is 4.06×108 mm ) and is now in a circular orbit. A lunar month remains at 29.5 days.

Calculate the mass of the earth in the year 8000 (Y8K)

M earth = ?kg

**Educational Context: Earth and Moon Dynamics in the Year 8000 (Y8K)**

In the hypothetical scenario for the year 8000 (Y8K), the Earth's mass has increased due to extensive space mining activities. This increase in mass has led to changes in the Earth-Moon dynamic system. Consequently, the Moon has drifted further away from the Earth, resulting in an increased distance of \(4.06 \times 10^8 \, \text{m}\). Despite these changes, the duration of a lunar month remains constant at 29.5 days.

**Diagram Explanation:**

The accompanying diagram illustrates the Moon's orbit around the Earth. The orbit is depicted as a circular path, with various phases of the Moon shown along the trajectory. This image visually represents the Moon's consistent orbital cycle as it revolves around the Earth.

**Part A: Calculation Task**

You are tasked with calculating the Earth's mass in the year 8000 (Y8K). 

**Input Box and Buttons:**

- The input box allows you to enter the calculated mass of the Earth in kilograms.
- Several functional buttons are available: a calculator icon for input formatting, a recentering icon, and an option to clear the entry.
- Once you've entered an answer, use the "Submit" button to confirm your response, or choose "Request Answer" for guidance.

---

This exercise serves as a theoretical exploration of space resource utilization and its potential impact on celestial mechanics.
Transcribed Image Text:**Educational Context: Earth and Moon Dynamics in the Year 8000 (Y8K)** In the hypothetical scenario for the year 8000 (Y8K), the Earth's mass has increased due to extensive space mining activities. This increase in mass has led to changes in the Earth-Moon dynamic system. Consequently, the Moon has drifted further away from the Earth, resulting in an increased distance of \(4.06 \times 10^8 \, \text{m}\). Despite these changes, the duration of a lunar month remains constant at 29.5 days. **Diagram Explanation:** The accompanying diagram illustrates the Moon's orbit around the Earth. The orbit is depicted as a circular path, with various phases of the Moon shown along the trajectory. This image visually represents the Moon's consistent orbital cycle as it revolves around the Earth. **Part A: Calculation Task** You are tasked with calculating the Earth's mass in the year 8000 (Y8K). **Input Box and Buttons:** - The input box allows you to enter the calculated mass of the Earth in kilograms. - Several functional buttons are available: a calculator icon for input formatting, a recentering icon, and an option to clear the entry. - Once you've entered an answer, use the "Submit" button to confirm your response, or choose "Request Answer" for guidance. --- This exercise serves as a theoretical exploration of space resource utilization and its potential impact on celestial mechanics.
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