What is the angular size of the moon as viewed from Earth's surface?

[monke]

Homework Statement

a) what is the angular size of the moon as viewed from the Earth's surface?
b) The objective and eyepiece of a refracting telescope have focal lenghts 80cm and 2.0cm. What is the angular size of the moon as viewed though this telescope?

mean radius of the moon- 1.737x10^6m
mean distance from earth- 3.854x10^8m

Homework Equations

Im not sure what equations to use or why the answer from the book is in radians

The Attempt at a Solution

i tried using the equation m=near point/ object distace, with the near point being 25cm and object distace being the distance from the earth. HOwever the anwer from the book is in radians.


Thanks in advanced!

 

[cepheid]

Im not sure what equations to use or why the answer from the book is in radians

Of course the answer is in radians. It's asking you for the angular size. The angular size is defined as the angle subtended (spanned) by the object as seen by the observer. In other words, how big does it look? How much of your field of view does it take up?

What is the equation for an angle in terms of of the radius and the arc length (which you can equate to physical size)?

 

[monke]

would that be theata= h (size of object)/N ( near point =25cm)?

 

[cepheid]

No, I was just talking about the equation that gives you the definition of an angle (in the radian system)

 

[monke]

i think i found it
theata = 2(radius)/disatance from the sun?

 

[monke]

angle in terms of radians is
theta= s/r
(size of arc)/ radius

 

[monke]

how should i have applied that to this particular question?

 

[monke]

for the second part of the question, if a refracting telescope functions like a compound microscope does that mean that you would use the same angular equation?

M= -L/foX N/Fe

 

[cepheid]

angle in terms of radians is
theta= s/r
(size of arc)/ radius

how should i have applied that to this particular question?

Well, how big is the object? How far away is it? Therefore, what angle does it span? This is its angular (or apparent) size. That will get you the answer to part a.