# Apparent semimajor axis

#### arcTomato

Problem 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.

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#### gneill

Mentor
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

Mentor
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!!
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

Mentor
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.

#### gneill

Mentor
Happy to help!

"Apparent semimajor axis"

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