Question

The full moon has an angular size of about 0.52◦ when viewed with the naked eye.

(a) Given that the moon has a radius of 1, 737 km, how far away is it? Compare this with the tabulated value of d(moon) = 384, 400 km.

(b) You pull out a telescope with an objective focal length of 700mm and an eye-piece focal length of 26 mm. What angle does the moon subtend when viewed through this telescope?

(c) How close would the moon have to be in order for us to see it with our naked eye as good as we saw it through our telescope?

(For trig based physics class)

Answer 1

1. angular size = 0.52◦=0.52 * 3.14/180 radian =0.0090711

radius of 1,737 km,

D = linear size or diameter = 2*r= 2*1,737=3474 km

Formula:

angular size= linear size / distance from moon

distance from moon= linear size / angular size

=3474/0.0090711=382974.50 km

Calculated value(382974.50 km) is lower than tabulated value of d(moon), 384, 400 km.

2. we can use formula of telescope:

Angle from telescope = focal length of eye piece / focal length of objective =26m/700mm=0.037 radian

3. We know , magnification = focal length of objective / focal length of eye piece= 700 /26 =26 .92

So telescope magnifies image 26.92 times

So to see same size of image by naked eye, moon should be close at 384, 400 km / 26.92 =14,279.346 km