My calculs are wrong!!

[Hatan]

Ok, My first real good night to watch the sky, yeah!! I get out and setup everything and prepare to watch MARS.

According to Skymap, Mars is around 16 arc second diameter right now and 90 millions km from earth. So with these maths I tried to determine what would be the size of mars if I use 150X (around the maximum of my 3 inch refractor). Here are my calculs:

I create a right triangle so I can use the Tan to determine the angle and so on. so:
I divide 16" by 2 = 8" (angle that form a right triangle)
3500 km = radius of Mars
90 millions km = distance

Tan 8/3600 = 3500km/90 millions (this works)

So with a 150X zoom I could consider that Mars is actually 150 times bigger so 3500km X 150 = 525 000 km

If I use that and try to retreive the new arc sec I could see:

Tan X = 525 000 / 90 000 000

So X = 1200"

Multiply by 2 to get the diameter = 2400"

Considering that moon without zoom is 2000" I was impressed that I could see Mars about the size (in diameter) of the moon. But..... the reality was kinda different. What I saw (at 180X) was actually a small spot probably 20x smaller (in diameter) than the moon with naked eyes.

So my question is.... where am I wrong in these calculs? :)

[Dave Mitsky]

I believe that the answer may be that when you look through an eyepiece you're comparing, either consciously or unconsciously, the apparent size of Mars to the diameter of the field of view, which is readily noticeable. Try comparing the size of the naked-eye Moon to the whole dome (actually the half-dome) of the sky. If you were able to simultaneously compare the naked-eye Moon with one eye and the telescopic view of Mars (at the appropriate magnification) with the other, the two bodies should be about the same size.

Dave Mitsky

[hhEb09'1]

According to Skymap, Mars is around 16 arc second diameter right now and 90 millions km from earth. So with these maths I tried to determine what would be the size of mars if I use 150X (around the maximum of my 3 inch refractor). Here are my calculs:

I create a right triangle so I can use the Tan to determine the angle and so on. so:
I divide 16" by 2 = 8" (angle that form a right triangle)
3500 km = radius of Mars
90 millions km = distance

Tan 8/3600 = 3500km/90 millions (this works)

So with a 150X zoom I could consider that Mars is actually 150 times bigger so 3500km X 150 = 525 000 km

If I use that and try to retreive the new arc sec I could see:

Tan X = 525 000 / 90 000 000

So X = 1200"

Multiply by 2 to get the diameter = 2400"Just a note: you get the same answer just by multiplying 16 arcseconds by 150 :)

[Hatan]

Well, actually you are right, but only because the angle is soooooo small. But since planet will only be small angle, I might have complicated things for nothing. But strictly mathematicly talking, the result is a bit different. If I had this monster telescope and able to multiply by 10 000 or more, the 2 answer would be a lot different :)

But anyway, according to Dave the 2 should looks exactly the same in size(naked Moon and telescopic Mars). I will re-check and try to recompare then.

But just to be sure I understand, with a million dollar telescope I would be able to see as much detail on Mars (at 150x) that I can see on the moon with naked eyes (Considering the eye can resolve 1'-3' arc no matter if it is in a telescope or without)?

I guess my telescope does not worth 1 million because I can see quite a lot of details on the moon without telescope, but mars was only a small blurry point :)

[hhEb09'1]

Were you looking at the moon when it was near the horizon? :)

BTW, welcome to the BAUT, Hatan

[Romanus]

<<I guess my telescope does not worth 1 million because I can see quite a lot of details on the moon without telescope, but mars was only a small blurry point >>

Keep in mind that the Moon is so large that it's not noticeably affected by atmospheric seeing to the naked eye, while the Martian disk (which is small) is very strongly affected by it.