# Practical Exercise 12: THE MOON IN ACTION FOR THE THIRD TIME

a) Figure 6 shows the total Lunar eclipse. With the help of Figure 6 and times, estimate how many times the radius of the Earth’s shadow is larger than the radius of the Moon.

b) If the angular magnitude of the Sun is θ =  32', the radius of the Earth equals R = 6 378 km and the radius of the circular orbit is θ =32‘, the radius of the Earth equals R = 6 378 km and the radius of the circular orbit is a2 = 384 400 km, calculate with the help of the result in point a) the radius of the Moon. Figure 7 can help. Figure 6 Lunar Eclipse Figure 7 Lunar Eclipse - situation analysis b) The sketch shows the following: Since , it is possible to write the left side of the first equation as , it is possible to write the left side of the first equation as , which is equal to , it is possible to write the left side of the first equation as , which is equal to . From the first equation we can simply express ,it is possible to write the left side of the first equation as , which is equal to . From the first equation we can easily express . From the second equation we get it is possible to write the left side of the first equation as , which is equal to . From the first equation we can easily express . From the second equation we get .
We get the radius of the Moon as follows: , it is possible to write the left side of the first equation as , which is equal to . From the first equation we can easily express . From the second equation we get . We get the radius of the Moon as follows: . The actual radius of the Moon is 1737 km, so the result gives a reasonable estimate.