Need formula to relate distance to arcsec in the sky

[leonne]

Homework Statement

I need to find how long it will take a supernova explosion to be a size of one arc sec here on earth, the distance to this explosion is 50 kilparsec

Homework Equations

The Attempt at a Solution

Any clue on what the formula is?
thanks

 

[AC130Nav]

Homework Statement

I need to find how long it will take a supernova explosion to be a size of one arc sec here on earth, the distance to this explosion is 50 kilparsec

Wiki defines the kiloparsec at http://en.wikipedia.org/wiki/Parsec so you can get the circumference at 50 kpc using Pi*d. Then divide by 360 to get degrees, 60 to get minutes, and 60 again to get seconds.

 

[leonne]

hmm, don't think that will help me I need to find how big the explosion needs to be to see 1 arc sec. With the radius, than i can calculate the time. I found this formula D=H/2tan(a) , but don't think it will work. either hmm. Well if I solve for H would that be the true diameter of the explosion?
Well thanks for the help

 

[gneill]

Have you tried drawing a diagram to see what the geometry of the situation is?

Things to keep in mind for very small angles: θ ≈ sin(θ) ≈ tan(θ).

You're looking for the time it takes "a supernova explosion to be a size of one arc sec [as seen] here on earth". What were you planning on using for the expansion rate of the supernova debris?

 

[leonne]

hey,
well i remembered using a formula last semester to find something similar, but forgot what the formula was. I found what the velocity was in part 1.

 

[AC130Nav]

hey,
well i remembered using a formula last semester to find something similar, but forgot what the formula was. I found what the velocity was in part 1.

The shockwave of a supernova propagates at approximately the speed of light. I would suspect that's visible.

 

[leonne]

well we where told that ...ejected mass of 20 solar mass.