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### Course: NASA > Unit 2

Lesson 2: Measuring the solar system- A flat earth
- Arc length
- Circumference of Earth
- Occultations
- Occultation vs. transit vs. eclipse
- Size of the moon
- Angular measure 1
- Angular measure 1
- Trigonometric ratios in right triangles
- Angular Measure 2
- Angular Measure 2
- Intro to parallax
- Parallax: distance
- Parallax method
- Solar distance
- Solve similar triangles (advanced)
- Size of the sun
- Scale of solar system

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# Size of the moon

## Relative sizes

We previously determined that the diameter of the earth is 12742 km. Now we want to determine the size of the moon relative to the earth.

Let’s start with an even simpler question: Is the moon bigger or smaller than the earth? How could you prove this? Remember this question wouldn’t seem silly to someone standing on the Moon!

This question was tackled over 2300 years ago by Aristarchus of Samos (310-230 BC). His measurement begins with the observation of a

**total lunar eclipse**. He correctly assumed that this was the result of the**earth casting a shadow on the moon.**First Aristarchus timed how long the moon took to travel through the earth’s shadow. As Eratosthenes did, he also made a simplifying assumption that the sun’s light reaches us in perfectly parallel lines. Which we know isn’t exactly true as two cone shaped shadows are produced: umbral and penumbral. Though it was close enough for a nice estimation.

He was actually timing how long between the entry and exit of the darker (umbral) shadow. Which to him appeared to be around 2.6 hours. Next, he compared this with the time it takes the moon to move a distance equal to it’s diameter.

**In the previous article we determined that this was about 1 hour**. So he’s left with two numbers:- time it takes the moon to travel 1 moon diameter =
**1 hour** - time it takes the moon to travel 1 earth diameter =
**2.6 hours**

How could we figure out the size of the moon from this?

**If the times were equal than it would imply that the moon is the same size as the earth.**However the time of a lunar eclipse is much longer, which means the earth must be larger. How much larger? We need to setup a basic proportion:

time #1 / time #2 = moon diameter / earth diameter

**1 / 2.6**= moon diameter / earth diameter

This led him to claim that the earth was about

**8/3**the diameter of the moon. This is pretty close to the actual difference:**the earth is about 3.7 times bigger than the moon**. The main reason he underestimated was because the umbral shadow is narrower than the earth.## Actual size of the moon

We now know the relative size of the moon compared to earth. We also know the actual size of the earth from a previous calculation. Finally we can determine the approximate size of the moon!

moon diameter = earth Diameter / 3.7

moon diameter = 12742/3.7 =

**3444 km**This is very close to the actual diameter of the moon:

**3474.8 km**### We determined the size of the earth and moon using nothing but shadows!

## Want to join the conversation?

- You said the darker (penumbral) shadow, shouldn't it be (umbral) ?(7 votes)
- no because the thing is 1982(1 vote)

- if the lunar eclipse happens how would the shadow be red or would that be light pollution?(3 votes)
- The red comes from the Sun's light passing through the Earth's atmosphere. You are essentially seeing the sunrises and sunsets all around Earth casting their glow onto the Moon.(7 votes)

- why can't we see the other side of the moon(6 votes)
- The moon is tidally locked with the earth, which means we only see one side. Here is a nice video about why it is tidally locked with the earth: https://www.youtube.com/watch?v=6jUpX7J7ySo(4 votes)

- How does the moon get red in a lunar eclipse(4 votes)
- During a lunar eclipse, light from the sun passes through Earth's atmosphere, splitting it into different colors. Of the colors, red reaches the moon, making it look visibly red.(4 votes)

- will the moon always be there?(3 votes)
- It should be, at least until some catastrophic event occurs which spoils everything. The moon is currently moving away from the Earth at about 3.8 cm each year. However, that rate decreases over time until the Earth and the moon are tidal locked (Google it). Eventually the Earth's day will last a whole month and the moon will be fixed in one spot over the Earth (similar to how one side of the moon faces the Earth all the time). Of course, that'll probably take billions of years. The sun may become a red giant before all that happens.(3 votes)

- the sun is so big but the earth is so small why is that?(3 votes)
- the Sun is a star, stars are all ways big there for it is bigger than Earth(2 votes)

- The moon is smaller than the earth beacause if it where bigger then instead of it rotates us then we rotate it.(3 votes)
- Why does the
*moon get red*in a**Lunar Eclipse**?(1 vote)- During a Lunar eclipse, all of the direct Sunlight is blocked by the Earth. But unlike the Moon, the Earth has an atmosphere. The Sun's rays strike our atmosphere at a shallow angle which absorbs all of the blue light and scatters the red light. From the Moon, this would look like a faint red glow forming a circle around the Earth. Since only the red light is getting through is hitting the Moon, it turns a dim red.(3 votes)

- how can the earth and the moon be shadows(0 votes)
- When the earth comes in front of the moon, it casts of shadow on the moon like when you cast of shadow on a wall. This is called a lunar eclipse. In a solar eclipse, the moon comes in front of the earth casting a shadow on the earth.(2 votes)

- I first assumed that the distance that the moon travels in the shadow is: the earth's diameter + the moon's diameter. Isn't that right?(1 vote)