**Understanding the Angular Diameter of an Astronaut from Above the Moon**When an astronaut in a spacesuit with a linear diameter of 0.8 meters is viewed from a distance of 800 kilometers above the surface of the Moon, the angular diameter can be calculated using the small-angle formula. This formula is expressed as:\[ \text{angular diameter (in arc seconds)} = \left( \frac{\text{linear diameter}}{\text{distance}} \right) \times 2.06 \times 10^5 \]**Estimating Visibility from the Command Module**The unaided human eye can resolve details down to about 100 arc seconds in bright lighting conditions. Thus, the question arises: could someone looking out of the command module window have seen the astronauts on the Moon based on the calculated angular diameter?- **Yes** - **No**Use these calculations to understand whether the astronauts would be discernible to the human eye at this distance.

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From a distance of 800 km above the surface of the Moon, what is the angular diameter of an astronaut in a spacesuit who has a linear diameter of 0.8 m viewed from above? (Hoe Use the small-angle formula, (Hint angular diameter (in arc seconds) linear diameter 2.06 x 105 distance arc seconds The unaided human eye has a resolution of about 100 arc seconds in bright lighting conditions. Could someone looking out the command module window have seen the astronauts on the Moon? Yes No

From a distance of 800 km above the surface of the Moon, what is the angular diameter of an astronaut in a spacesuit who has a linear diameter of 0.8 m viewed from above? (Hoe Use the small-angle formula, (Hint angular diameter (in arc seconds) linear diameter 2.06 x 105 distance arc seconds The unaided human eye has a resolution of about 100 arc seconds in bright lighting conditions. Could someone looking out the command module window have seen the astronauts on the Moon? Yes No

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Understanding the Angular Diameter of an Astronaut from Above the Moon**

When an astronaut in a spacesuit with a linear diameter of 0.8 meters is viewed from a distance of 800 kilometers above the surface of the Moon, the angular diameter can be calculated using the small-angle formula. This formula is expressed as:

\[ \text{angular diameter (in arc seconds)} = \left( \frac{\text{linear diameter}}{\text{distance}} \right) \times 2.06 \times 10^5 \]

**Estimating Visibility from the Command Module**

The unaided human eye can resolve details down to about 100 arc seconds in bright lighting conditions. Thus, the question arises: could someone looking out of the command module window have seen the astronauts on the Moon based on the calculated angular diameter?

- **Yes**
- **No**

Use these calculations to understand whether the astronauts would be discernible to the human eye at this distance.

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