Astronomy C

[syo_astro]

Internet is not helping.I think it has to do with Kepler's third law, but I can't figure out how to get the distance.

Questions/comments for your question:
What is the distance in question? Is it the distance away from us? Well, that was given. Is it the size of the system? Ah, well for that we are given...
"This image of a system 490 parsecs distant...and an angular separation of 1.02*10^-6 arcseconds."
Now what is the formula that connects distance away, angular sizes, and physical sizes?

With that in hand, indeed you just need to do Kepler's Laws (with some appropriate unit conversions of course).

[Unome]

Now what is the formula that connects distance away, angular sizes, and physical sizes?

Regarding this, how do the units work out here? Do they even matter? (since angles are just ratios anyway)

[Magikarpmaster629]

Internet is not helping.I think it has to do with Kepler's third law, but I can't figure out how to get the distance.

This image of a system 490 parsecs distant depicts...

Sorry, it's kinda hidden.

EDIT: Whoops, didn't see syo_astro already pointed it out.

Also yeah, units are ratios:

Small angle formula:

Where theta is the angle of separation in radians (because that's how ratios work), d is distance of separation, D is distance to the object. d and D are in the same units because it needs to be ratios.

Now for something really cool. Since the ratio of an AU to a parsec is the same as the ratio of an arcsecond to a radian (1:206265) the units can work out to be: theta in arcseconds, d in AU, D in parsecs.

[syo_astro]

Regarding this, how do the units work out here? Do they even matter? (since angles are just ratios anyway)

Units always matter! It's what separates us from mathematicians (...unless you're a theorist or something I guess...anyway).

The two distances should have the same units, and it is for the reason you say that angles are inherently defined as dimensionless. That is, say we want a convenient angle to measure with, then we can easily make it a ratio of distances (eg. or better seen as ). The essential point here is that radians are defined as ratios of lengths for a circle, so radians are natural for measuring arclength or relating distances on circles.

It is important to note that degrees or arcseconds are NOT defined in the same way as say degrees just split any circle up 360 times. This introduces a factor of (2pi)/360 into these calculations then (or extra 60s if we go to arcsecs). Note the conversion comes from the fact that 2pi*r = 360 deg * r -> 1 deg = 2pi/360.

Why do we bother with degrees or arcseconds or even milliarcseconds? That's a good question, and I'm not fully sure! My suspicion is it has to do with what was useful with observations/navigation/woodworking, and 360 was a good number based on observations (eg. days in a year, or something to do with time). At the very least, I think it's probably easier to divide something up 360 times or some even number than it is to make divisions with pi, so that's why some might consider pi to be the pesky one and not the degrees.

Edit: OK, fine there's also the AU/pc thing, but whatever I don't feel like editing out my explanation .

[Adi1008]

Why do we bother with degrees or arcseconds or even milliarcseconds? That's a good question, and I'm not fully sure! My suspicion is it has to do with what was useful with observations/navigation/woodworking, and 360 was a good number based on observations (eg. days in a year, or something to do with time). At the very least, I think it's probably easier to divide something up 360 times or some even number than it is to make divisions with pi, so that's why some might consider pi to be the pesky one and not the degrees.

I think the prevalence of 60 and 360 might be because of how earlier number systems were sexagesimal (base-60), which is the same reason there's 60 seconds in a minute and 60 minutes in an hour. Wikipedia, for example, says this on the topic:

These units [arcminutes and arcseconds] originated in Babylonian astronomy as sexagesimal subdivisions of the degree...

Now for something really cool. Since the ratio of an AU to a parsec is the same as the ratio of an arcsecond to a radian (1:206265) the units can work out to be: theta in arcseconds, d in AU, D in parsecs.

Just to add on, in case anyone's wondering how this works: it's because the number of arcseconds in a radian (3600*180/pi = 206264.81) is almost the same as the number of AU in a parsec (206265)

[syo_astro]

To Karp/Adi: I will find it hilarious if our combined effort managed to not answer the question somewhere XD. Also, you two still need to work on the onward blog cough cough.

[Unome]

Why do we bother with degrees or arcseconds or even milliarcseconds? That's a good question, and I'm not fully sure! My suspicion is it has to do with what was useful with observations/navigation/woodworking, and 360 was a good number based on observations (eg. days in a year, or something to do with time). At the very least, I think it's probably easier to divide something up 360 times or some even number than it is to make divisions with pi, so that's why some might consider pi to be the pesky one and not the degrees.

I think the prevalence of 60 and 360 might be because of how earlier number systems were sexagesimal (base-60), which is the same reason there's 60 seconds in a minute and 60 minutes in an hour. Wikipedia, for example, says this on the topic:

These units [arcminutes and arcseconds] originated in Babylonian astronomy as sexagesimal subdivisions of the degree...

Now for something really cool. Since the ratio of an AU to a parsec is the same as the ratio of an arcsecond to a radian (1:206265) the units can work out to be: theta in arcseconds, d in AU, D in parsecs.

Just to add on, in case anyone's wondering how this works: it's because the number of arcseconds in a radian (3600*180/pi = 206264.81) is almost the same as the number of AU in a parsec (206265)

(because this quotes all of you at the same time)

Ok, I think I understand it now. The two measurements are the same because of how the parsec is defined from parallax using Earth's orbit, right?

Similar(ish) question: in Kepler's third law, what causes the constant to cancel with certain units? (AU, solar masses? can't remember)

[UnprunedShrub]

Ok, I think I understand it now. The two measurements are the same because of how the parsec is defined from parallax using Earth's orbit, right?

Similar(ish) question: in Kepler's third law, what causes the constant to cancel with certain units? (AU, solar masses? can't remember)

It is similar to how the arcsecond/parsec thing works. Our year is defined as the time it takes Earth (which by definition has a semimajor axis of 1 AU) around the sun (which is by definition 1 solar mass). Therefore, if we want to measure another body's orbital period in years, and if we measure the systems mass in solar masses and the semimajor axis in AU, we have no need for the 4 or the G. Another way to think about it is that you are really doing so all the constants cancel out. For this same reason, when you are using the stefan boltzmann law to calculate another star's luminosity in stellar luminosities you dont need or .

[raxu]

On a practice test, where a question was

An exoplanet orbits a host star at an orbital radius of 2.01 AU in 3.6 years. What is its orbital velocity in km/s?

I thought of using 2pi*r/T, but it gave an answer 1/2 of the official answer... Am I missing something?

[carboxylofthebells]

Hi guys, I'm not sure if this has been posted yet in the forum, so please forgive me for bringing this up again.

Concerning the practice test posted under 2017 (user rwayzataso), of the math question #71 (Given that Type Ia supernova BrightBurst exploded with an apparent magnitude of +14.8, calculate the distance to the remnants. Give your answer in lightyears.),

For the distance modulus equation, I have ݀ d = 10^(m-M+5)/5, but for the answer it has eliminated that 5.

Solution the user posted:
Using the distance modulus, d = 10
(14.8+19.3)/5 =6.61*10^6 pc
1 pc = 3.26 ly
d = 2.16*10^7 ly

So, is this an error in the solution itself or is it a special case for Type 1a Supernovae to eliminate the "5"?

Thanks~!