QuestionJune 13, 2025

47. Referring to Figure 2.18, estimate when Vega the fifth-brightest star in our sky (excluding the Sun), will once again be the northern pole star. 48. The apparent diameter of the Moon is approximately 1/20 How long does it take the moon to move 3600? About how long does it take the Moon to move a distance equal to its own diameter across the sky (starfield)? 50. Earth has an average radius of 6,371 km. If you were standing on the Moon how much larger would Earth appear in the lunar sky than the Moon appears in our shy?

47. Referring to Figure 2.18, estimate when Vega the fifth-brightest star in our sky (excluding the Sun), will once again be the northern pole star. 48. The apparent diameter of the Moon is approximately 1/20 How long does it take the moon to move 3600? About how long does it take the Moon to move a distance equal to its own diameter across the sky (starfield)? 50. Earth has an average radius of 6,371 km. If you were standing on the Moon how much larger would Earth appear in the lunar sky than the Moon appears in our shy?
47. Referring to Figure 2.18, estimate when Vega the fifth-brightest star in our sky (excluding the Sun), will once again be the northern pole star. 48. The apparent diameter of the Moon is approximately 1/20 How long does it take the moon to move 3600? About how long does it take the Moon to move a distance equal to its own diameter across the sky (starfield)? 50. Earth has an average radius of 6,371 km. If you were standing on the Moon how much larger would Earth appear in the lunar sky than the Moon appears in our shy?

Solution
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Answer

48. It takes approximately 2 hours for the Moon to move 3600 arcseconds. ### About 1 hour for the Moon to move a distance equal to its own diameter across the sky. ### 50. Earth appears about 3.67 times larger in the lunar sky than the Moon appears in our sky. Explanation 1. Calculate the Moon's movement speed The Moon moves approximately 360^\circ in about 27.3 days (one sidereal month). Therefore, its speed is \frac{360}{27.3} degrees per day. 2. Calculate time to move 3600 arcseconds Convert 3600 arcseconds to degrees: 3600 \text{ arcseconds} = 1 \text{ degree}. Using the speed from Step 1, calculate the time to move 1^\circ: \frac{27.3}{360} days. 3. Calculate time to move its own diameter The apparent diameter of the Moon is 1/20 of a degree. Time to move this distance: \frac{27.3}{360} \times \frac{1}{20} days. 4. Calculate Earth's apparent size from the Moon The Earth-Moon distance is about 384,400 km. The angular diameter formula is \theta = 2 \arctan\left(\frac{R}{d}\right), where R is the radius and d is the distance. Calculate for both Earth and Moon, then find the ratio.

Explanation

1. Calculate the Moon's movement speed<br /> The Moon moves approximately $360^\circ$ in about 27.3 days (one sidereal month). Therefore, its speed is $\frac{360}{27.3}$ degrees per day.<br /><br />2. Calculate time to move 3600 arcseconds<br /> Convert $3600$ arcseconds to degrees: $3600 \text{ arcseconds} = 1 \text{ degree}$. Using the speed from Step 1, calculate the time to move $1^\circ$: $\frac{27.3}{360}$ days.<br /><br />3. Calculate time to move its own diameter<br /> The apparent diameter of the Moon is $1/20$ of a degree. Time to move this distance: $\frac{27.3}{360} \times \frac{1}{20}$ days.<br /><br />4. Calculate Earth's apparent size from the Moon<br /> The Earth-Moon distance is about 384,400 km. The angular diameter formula is $\theta = 2 \arctan\left(\frac{R}{d}\right)$, where $R$ is the radius and $d$ is the distance. Calculate for both Earth and Moon, then find the ratio.
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