Understanding Angular Size Calculation: Europa and Jupiter

[blink_1992]

i have a list of problems dealing with angular size that i have to complete, but I am a little confused on how exactly to solve them. if anyone could help me with this first example, it would be greatly appreciated. thank you (:

europa is about 1.7 times more distant from Jupiter than the moon is from earth, and jupiters diameter is 41 times larger than that of the moon. how large would Jupiter appear to you as standing on europa compared to the way a full moon looks as viewed from earth? finally, express this angular size in degrees considering the moons angular size is 0.5^0

 

[zhermes]

The problem is more about similar triangles and geometry than angular-size in particular. Try drawing a picture of the relative situations.

 

[granpa]

for very small angles the angular size in radians is approximately
diameter/distance

 

[armin.hodaie]

assume that angular size of moon is "a" :
tan (a)=(R1/D1)
R1 : diameter of moon
D1 : distance of moon-earth
and for Jupiter that angular size is "b" :
tan (b)=(R2/D2)
R2 : diameter of jupiter----> R2=41R1
D2 : distance of jupiter-europa ----> D2=1.7D1
so we have:
tan (b)=(41/1.7)(R1/D1)------> tan(b)=(41/1.7)tan (a)
so -----> b=11.88 degrees