Calculating Apparent Semimajor Axis: A Unit Conversion Challenge

[arcTomato]

Homework Statement

Lead linear size of the semi-major axis by using precision parallax

Relevant Equations

precision parallax

Hello

I think this image's calculation is wrong.
I cannot convert units(What is arcsec??How convert to pc??)

How do you think ??I would like to see your calculation process.

I'm so grad if you show.

 

[gneill]

What do you know about the parallax method of distance determination?

An arcsec (arcsecond) is one sixtieth of one sixtieth of one degree. That is:
$$arcsec = \frac{1°}{60 \times 60} = \frac{1°}{3600}$$

 

[arcTomato]

What do you know about the parallax method of distance determination?

An arcsec (arcsecond) is one sixtieth of one sixtieth of one degree. That is:
$$arcsec = \frac{1°}{60 \times 60} = \frac{1°}{3600}$$

Thank you !
I think I know,But I cannot lead 14AU again.( I lead 10455AU)
Could you show me a process?

 

[gneill]

Thank you !
I think I know,But I cannot lead 14AU again.( I lead 10455AU)
Could you show me a process?

Helpers can only give hints and suggestions, we cannot do the work for you. If you show your calculation attempts in detail then we can point out where you might have gone wrong.

I suspect that there was more to the question that you haven't shown, since there's no apparent place that the 4.1 arcsec in question B came from. I imagine that the original problem statement gave the parallax reading for Procyon and the apparent angular measure of some body orbiting it.

The calculation shown in your image looks simple enough: $4.1 \times 3.50 = 14.3 \text{(in AU)}$

 

[lomidrevo]

I think this image's calculation is wrong.

To me, both calculations in the picture looks correct. Although, there is no complete explanation provided, where the parallax in the second questions comes from, it apparently points to the fact that Procyon is binary star system and it refers to the semi-major axis of this binary (Although wiki mentions value $4.3''$ instead, but this is not important - use the value you are given).

If you are not sure why the sheer multiplication of the values in $arcsec$ and $pc$ works, you can convert the values to $rad$ and $AU$ respectively, before the multiplication.

 

[arcTomato]

Helpers can only give hints and suggestions, we cannot do the work for you. If you show your calculation attempts in detail then we can point out where you might have gone wrong.

I suspect that there was more to the question that you haven't shown, since there's no apparent place that the 4.1 arcsec in question B came from. I imagine that the original problem statement gave the parallax reading for Procyon and the apparent angular measure of some body orbiting it.

The calculation shown in your image looks simple enough: $4.1 \times 3.50 = 14.3 \text{(in AU)}$

Wow,this is so simple!
Finally I lead 14AU.
I realize my mistake about convertion.

I'm sorry for my bad English, and I appreciate for your help!

 

[arcTomato]

Whan I convert all units to $rad$ and $AU$, I can lead right answer! thank you!

But,,,,

If you are not sure why the sheer multiplication of the values in $arcsec$ and $pc$ works,

Yes, exactly!
My pic shows that we should use $degree$ and $maters$?? It also works??

 

[gneill]

Yes, exactly!
My pic shows that we should use degreedegreedegree and matersmatersmaters?? It also works??

Yes, because of the way that parsecs are defined in terms of radius of the Earth's orbit (1 AU by definition : look up the definition).

 

[arcTomato]

Yes, because of the way that parsecs are defined in terms of radius of the Earth's orbit (1 AU by definition : look up the definition).

I got it.
I have lead right answer again (in degrees) !
Thanks for your kindness!

 

[gneill]

Happy to help!