Unit Conversion: Astronomical Units, Parsecs and Light Years

[iwantpi]

Hi everyone,
It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem:


Question

"The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is the radius of a circle for which a central angle of 1s intercepts an arc of length 1AU. The light year is the distance that light travels in 1 year. (a) How many parsecs are there in one AU?

The attempt at a solution

I can do simple conversions of units, but I'm having trouble figuring out the connection between AUs and parsecs. I know that Arc length = r * angle (in rad) which leaves me with 1 AU = 1 parsec * 1s. But then again s is seconds, not radians...
Another way I attempted the problem was to assume that the arc of a circle whose radian is 1 parsec is so large that I can assume that the arc is a straight line, is that a fair assumption?

I'd really appreciate any corrections or just a hint in the right direction, not the full answer, and then hopefully I can work out the other parts of the problem myself. Thank you in advance!

 

[gneill]

Hi everyone,
It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem:


Question

"The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is the radius of a circle for which a central angle of 1s intercepts an arc of length 1AU. The light year is the distance that light travels in 1 year. (a) How many parsecs are there in one AU?

The attempt at a solution

I can do simple conversions of units, but I'm having trouble figuring out the connection between AUs and parsecs. I know that Arc length = r * angle (in rad) which leaves me with 1 AU = 1 parsec * 1s. But then again s is seconds, not radians...
Another way I attempted the problem was to assume that the arc of a circle whose radian is 1 parsec is so large that I can assume that the arc is a straight line, is that a fair assumption?

I'd really appreciate any corrections or just a hint in the right direction, not the full answer, and then hopefully I can work out the other parts of the problem myself. Thank you in advance!

Hi iwantpi, Welcome to Physics Forums.

The '1s' above is 1 arc second, an angle. Remember that degrees are divided up into 60 arcminutes, which are in turn divided into 60 arcseconds.

 

[physicsee]

1 parsec = 206264.984626 au
I got it from aconverter.net, which I usually used. hope this help.

 

[iwantpi]

Thanks for all the help you two and sorry bout the late reply. I figured it out. It wasn't so hard once you guys told me about the arc second thing. Thanks again.

 

[Nickie]

Hi there,

I can see that you are struggling with the connection between astronomical units (AU) and parsecs. Let me try to clarify it for you.

Firstly, it is important to understand that both AU and parsecs are units of distance used in astronomy. However, they are different in terms of their definitions and the scale at which they are used.

As you mentioned, AU is the mean distance from Earth to the Sun, which is approximately 149.6 million kilometers or 93 million miles. This unit is primarily used to measure distances within our solar system.

On the other hand, parsecs are much larger units of distance used to measure the vast distances between stars and galaxies. One parsec is equivalent to 3.26 light years or 30.86 trillion kilometers.

Now, to answer your question, one AU is equal to 1 parsec * 1 second. This means that if you were to draw a circle with a radius of 1 parsec, the arc length of that circle would be equal to 1 AU if the central angle intercepts an arc of 1 second. This is because 1 parsec is defined as the distance at which an object would have a parallax angle of 1 arcsecond when viewed from two different points in Earth's orbit.

To put it simply, 1 AU is a smaller unit of distance compared to 1 parsec. Therefore, there are many parsecs in one AU. I hope this helps in understanding the relationship between these units. Good luck with your problem!