Estimate Diameter of Moon Using Pencil Measurements

[k_yup]

im new to the physics world and know this is probably an easy problem but i don't know where to start

Hold a pencil in front of your eye at a position where its end just blocks out the moon. Make approprite measurements to estimate the diameter of the moon, given that the earth-moon distance is 3.8x10^5km.

i figured that you prob had to measure the end of a pencil which i measured about 1.5 cm which is 1.5x10^-5km but i don't really know what to do from there.

 

[jimvoit]

Your also need to also estimate the distance from your eye to the pencil.
Draw a picture...there are two similar triangles involved

 

[sir-pinski]

No problem, estimating the diameter of the moon using pencil measurements can be a fun and easy problem to solve. First, let's review the steps you have already taken. You correctly measured the end of your pencil to be 1.5 cm, which is equivalent to 1.5x10^-5km. This is a great start!

Next, we need to use some basic geometry to estimate the diameter of the moon. We can create a simple triangle with the moon, the earth, and the end of your pencil. The distance from the moon to the earth is given as 3.8x10^5km. Now, since we know the distance from your eye to the end of the pencil (1.5x10^-5km) and the distance from the moon to the earth, we can use the concept of similar triangles to estimate the diameter of the moon.

Using the formula for similar triangles, we know that the ratio of the corresponding sides of two similar triangles is equal. So, we can set up the following equation:

(1.5x10^-5km)/(3.8x10^5km) = (diameter of pencil)/(diameter of moon)

Solving for the diameter of the moon, we get:

Diameter of moon = (1.5x10^-5km)*(diameter of pencil)/(3.8x10^5km)

Plugging in the value for the diameter of the pencil that you measured (1.5x10^-5km), we get:

Diameter of moon = (1.5x10^-5km)*(1.5x10^-5km)/(3.8x10^5km) = 5.625x10^-11km

This is an estimate of the diameter of the moon using pencil measurements! Keep in mind that this is just an approximation and the actual diameter of the moon is about 3,474 km. However, this is a great way to practice using basic geometry and estimation skills. Keep exploring and learning in the exciting world of physics!