Hi,
Can someone who understands basic trig help me please?
For kicks, I thought I'd try to calculate the sizes of the comet & galaxy in APOD 10/19/06 based on apparent diameters and distances. But I'm clearly doing someting wrong:
I thought the tangent of half the apparent diameter (angle) would be qual to half of the true diameter divided by the distance.
I was thinking: right triangle ABC with the Earth at A and the right angle and center of the comet at C. tan = opposite over adjacent.
If the galaxy is 6.5' in diameter, then the comet (not including tail) is maybe 8', right?
So I did: tan(8/(60*2)) = (x / 2) / 9 light minutes
I used excel so converting the angle to radians:
Tan(Radians(1/15)) = x / 9*2
x = 0.001164 * 18 = 0.020944 light minutes
and then
0.020944 * 60sec/min * 186,000mi/sec = 234,735 miles!
... which seems way too big.
Thanks,
B
My math is wrong (APOD 19 Oct 2006)
Your math is correct, and although the idea and thought process is simple, I think the error lies in resolution.
First off, I thought NGC 5005 was 5.8' x 2.8'.
This arc angle is probably measured by a much more finer detail image, therefore making the one we see not as accurate. I.e, blur/glow can be misinterpreted as actual arc length of the galaxy.
Then, the bigger thing is what you are considering to be the comet. The seemingly 6-8 arc minute image must be a reflection of ice and dust and distortion well outside the radius of the actual comet body.
Comet tails can be quite long.
First off, I thought NGC 5005 was 5.8' x 2.8'.
This arc angle is probably measured by a much more finer detail image, therefore making the one we see not as accurate. I.e, blur/glow can be misinterpreted as actual arc length of the galaxy.
Then, the bigger thing is what you are considering to be the comet. The seemingly 6-8 arc minute image must be a reflection of ice and dust and distortion well outside the radius of the actual comet body.
Comet tails can be quite long.