finding a linear diameter

[buc4933]

how do you find the linear diameter of something.<br /><br />for example the great galaxy in andromeda has an angular diameter along its long axis of about 5 degrees. Its distance is about 2.2 million light-years. What is its linear diameter?<br /><br /><br />Object’s diameter = angle between lines (over)<br />Circumference 360 <br /><br />Is this the right formula ? <br />

 

[buc4933]

anybody know??

 

[bobw]

2.2x10^6 light years would be the length of the vertical line in the center of the triangle below.<br /><br />5 degrees is the angle at the top.<br /><br />The diameter of your galaxy would be the length of the line on the bottom.<br /><br />The only way I can think to do it is trigonometry. Galaxy diameter = 2x(distance to galaxy x tan 2.5 degrees) <br /><br /><br /><pre><br /> /|<br /> / | <br /> / | <br />/ | <br />--------- <br /></pre> <div class="Discussion_UserSignature"> </div>

 

[buc4933]

I got 192,108.1488 does that seem right ??

 

[bobw]

Yes.<br /><br />I guess if you took 5/360 of the circumference of the circle, that would be close. The actual distance would be a bit shorter because your circumference is an arc and the diameter is a straight line. I wouldn't have thought to do it that way. <div class="Discussion_UserSignature"> </div>

 

[buc4933]

thanks

 

[bobw]

You are welcome.<br /><br />Don't forget the units in your answer.... 190000 LIGHT YEARS <div class="Discussion_UserSignature"> </div>

 

[buc4933]

I think this next question goes along with this last one. <br /><br />The question is a shell of gas blown out of a star has an angular diameter of .1 degree and a linear diameter of 1 light year. How far away is it? <br /><br />now for this one I think I would just divide right ?

 

[bobw]

Sorry I'm late...went to the store.<br /><br />It does seem like the backwards version of the last one. On that one you knew you needed 5/360 of a circle. What part of a circle do you need this time? <div class="Discussion_UserSignature"> </div>

 

[buc4933]

it asks how far away is it

 

[bobw]

The last time its distance was the radius of a circle, wasn't it? <div class="Discussion_UserSignature"> </div>

 

[buc4933]

ya

 

[buc4933]

this one is a shell of gas blown out of a star has an angular diameter of .1 degrees and a linear diameter of 1 light year. How far away is it?

 

[bobw]

Last time your angular size was 5/360 of a circle so your circle was 72 times bigger than your galaxy. How many times bigger than your nova is the circle for this problem? <div class="Discussion_UserSignature"> </div>

 

[buc4933]

I dont know my last post is all the information that I have... thats why i'm a little confused

 

[bobw]

Well, your linear diameter is part of the circumference of a circle. If you figgure out how big the whole circle is you can find it's radius. To do that you need to know how many tenths of a degree are in a circle. Then you know that each tenth of a degree is 1 light year so you multiply how many parts times how big each part is to give you the circumference of the whole circle. <div class="Discussion_UserSignature"> </div>

 

[buc4933]

so 3,600 x 1 ly = 3,600 right?

 

[bobw]

Right. Your star shell is 1/3600 of a circle. So what is the radius of the circle? That's how far away it is. <div class="Discussion_UserSignature"> </div>

 

[buc4933]

2.77777x10^-4 or am I totally off on this

 

[bobw]

Way off.<br /><br />What is the formula for the circumference of a circle? <div class="Discussion_UserSignature"> </div>

 

[buc4933]

c = pie <br />over <br />d

 

[buc4933]

where do I go from here

 

[bobw]

nope <div class="Discussion_UserSignature"> </div>

 

[buc4933]

I dont Know then.... I'm confused

 

[bobw]

circumference is not pi over d. You need the right formula. <div class="Discussion_UserSignature"> </div>