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

 

[rwisz]

First, it's important to understand the concept of angular size. Angular size refers to the apparent size of an object as seen from a particular point of view. It is measured in degrees and is affected by both the distance and the physical size of the object.

In this example, we are comparing the angular size of Jupiter as seen from Europa to the angular size of the full moon as seen from Earth. To solve this problem, we can use the formula:

Angular size = (physical size of object / distance to object) x (180/pi)

Let's break down the information given in the problem:

- Europa is 1.7 times more distant from Jupiter than the moon is from Earth.
- Jupiter's diameter is 41 times larger than that of the moon.
- The moon's angular size is 0.5^0.

Using the first two pieces of information, we can calculate the distance between Europa and Jupiter. Since we know that the moon is about 384,400 km from Earth, we can use this as our reference point. So, the distance between Europa and Jupiter would be 1.7 x 384,400 km = 653,480 km.

Next, we can calculate the physical size of Jupiter compared to the moon. Since Jupiter's diameter is 41 times larger than that of the moon, we can calculate its diameter as 41 x 3,474.8 km (the diameter of the moon) = 142,686.8 km.

Now, we can plug these values into the formula to calculate the angular size of Jupiter as seen from Europa:

Angular size = (142,686.8 km / 653,480 km) x (180/pi)
= 0.219^0

This means that Jupiter would appear to be about 0.219 degrees in size when viewed from Europa. To put this into perspective, the full moon appears to be 0.5 degrees in size when viewed from Earth. So, Jupiter would appear to be about half the size of the full moon when viewed from Europa.

I hope this explanation helps you understand how to approach and solve problems related to angular size. Remember to always use the appropriate formula and to carefully consider the given information. Good luck with the rest of your problems!