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# Cosmic distance ladder : To the Moon!
The ancient Greeks were also able to find the distance to the moon, again of course, without physically measuring it. By now they knew the size of the Earth, and using some clever observation about the moon and **lunar eclipses**, they were able to estimate the distance to the moon !
Let us see how this might be done.
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## Lunar eclipse.
The Greeks knew that lunar eclipses are caused by the moon **moving into** Earth's shadow that's blocking out the sun, as shown in the diagram below:
![[1 teaching/summer program 2023/week 1/---files/Cosmic_distance_ladder_2 2023-05-10 11.08.07.excalidraw.svg]]
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![[---images/---assets/---icons/question-icon.svg]] Denote the length of the path in Earth's shadow as $S$ , indicate this on the diagram above.
They estimated that the moon takes **about an hour to enter a total lunar eclipse**, which then **lasts about two hours**, and then it takes **another hour to completely exit the eclipse**.
![[---images/---assets/---icons/question-icon.svg]] Roughly how many hours does the moon need to travel a distance of $S$ ? Let us denote $T$ to be the time for the moon to travel a distance of $S$.
![[---images/---assets/---icons/question-icon.svg]] The **angular speed** $\omega$ of the moon orbiting around the Earth is also known (think about how often the moon cycles). What is this angular speed ? Express $\omega$ in units of revolution per day. Can you also express it in terms of radians per day?
![[---images/---assets/---icons/question-icon.svg]] If we now write $d_\text{moon}$ to denote the distance from the Earth to the moon, write an equation relating $S$, $T$, $\omega$ and $d_\text{moon}$,.
![[---images/---assets/---icons/question-icon.svg]] Express (solve for) $d_\text{moon}$ in terms of the other variables. Do we know every piece of information? For the ones we don't know can we estimate them using what we know ?
![[---images/---assets/---icons/question-icon.svg]] Estimate the distance to the moon $d_\text{moon}$. Make sure your units all work out !
![[---images/---assets/---icons/question-icon.svg]] Compare it with what you found on the internet. What would cause our estimate to be an over or underestimation?
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