## Astronomy C

astro124
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### Re: Astronomy C

Hey everyone! It's been awhile since I've last been on here but I'm glad to see a lot of familiar names still around.

Anyways, I'm having a little bit of trouble with the Union County 2016 practice test (number 25a)

How would we go about solving the tangential velocity. For part b, I figured that we would use Newton's equation for gravitational force. Would the orbital radius be given based on our answer for tangential velocity in part A?

Thanks!
2012 Season: Reach for the Stars-3rd (State) / Keep the Heat-19th (State)
2013 Season: Astronomy-2nd (State) / Disease Detectives-15th (State)
2014 Season: Astronomy-1st (State) / Experimental Design-20th (State)/ Anatomy and Physiology-16th (State)
2015 Season: Astronomy

Thunder

andrewwski
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### Re: Astronomy C

That question cannot actually be answered as written.

You are given the masses of the two bodies and the mean separation between them. The mean separation is equal to the semimajor axis of an ellipse. In order to determine the tangential velocity, though, you need to know the position along the ellipse (or the distance "r" between the masses at the time in question).

IF and only if the orbit is circular, then the separation is constant and equal to "r", in which case all velocity is tangential and you can use the Vis-Viva equation, which would reduce to:

$v=\sqrt{\frac{GM}{r}}$

But the answer in the key (to part a) makes no sense in this case. Intuitively it doesn't make any sense - it says 0.119 m/s. This isn't even near the right order of magnitude! Consider that the earth orbits the sun at ~30 km/s, and in this problem the star is twice as massive and the separation is half!

Likewise, if (and only if) you were to assume the orbit is circular, then you can solve part (b) with the given information. But even then, the answer in the key is wrong (it's off by 6 orders of magnitude, should be $5.637 x 10^{23} N$).

But since it was not stated to assume that the orbit is circular, there is not enough information to answer the question.

Skink
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### Re: Astronomy C

I'm back; this of this as part one of two, as I still have a list of National test images to ask about. This is higher priority, though. If anyone can help, my team and I would really appreciate it!

National Site NY Test #27
We've had difficulty locating the phrase "inclination derived" and are unclear how inclination, itself, relates to the rest, particularly what we're looking for.

National Site MIT Test #24(e)
There's clearly some relation we don't know about in order to find this ratio.

Thanks.

syo_astro
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### Re: Astronomy C

I'm back; this of this as part one of two, as I still have a list of National test images to ask about. This is higher priority, though. If anyone can help, my team and I would really appreciate it!

National Site NY Test #27
We've had difficulty locating the phrase "inclination derived" and are unclear how inclination, itself, relates to the rest, particularly what we're looking for.

National Site MIT Test #24(e)
There's clearly some relation we don't know about in order to find this ratio.

Thanks.
Hey, I wrote that first test, and sorry about the bad wording in retrospect. Most of the questions were meant to be straight-forward. Typically, though, I try to make the questions have some sense that they are coming from somewhere (eg. the inclination was derived or modeled somehow working with data and theory) rather than just saying the value is blah (and in retrospect again I failed at that considering how I just gave other values in those problems, but again this wasn't meant to be the most impossible questions >.>). The other thing I phrased admittedly badly was the ratio of velocities. This one I meant (but didn't express well) to write that the ratio of velocities were determined assuming no inclination. Accounting for inclination modifies it slightly because then we are actually viewing a component of the star's radial velocity in reality, so you have to multiply it by a factor of sin(i).

But the basis of this question relates well to your other problem in 24e on the MIT test. To summarize, it is based around conserving momentum (m1 * v1 = m2 * v2). It takes an extra step, but it's nothing too bad. Let's do it twice!
m_a * v_a = m_planet * v_planet_a; m_b * v_b = m_planet * v_planet_b

Dividing one equation by the other gets us that
(m_a / m_b) * (v_a / v_b) = (v_planet_a / v_planet_b)

Still confused how to get the velocities within the question? I think it should be clear at least you need the masses (given) and the velocities of the planets (I assume these aren't the same if you were to calculate them). It's not a relation that gives the answer outright, but it certainly involves fundamentals! Any questions about this?
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

Skink
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### Re: Astronomy C

Thank you. I solved your problem now and followed your algebra for the second. I'm not sure how to calculate the velocities of the planet for each star (the only things I need to get the requested ratio), but I'll see if the team can figure it out.

And, as a side note: that effort doesn't go unnoticed. We all strive to write questions and scenarios that have purpose (or, at least, more color) to them versus saying "27. Mass is this. Volume is that. Calculate density.". Riveting problem there.

astro124
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### Re: Astronomy C

I just got back from my state's Astro test and was probably the weirdest test I've taken in Science Olympiad.

Instead of an actual test we were given a computer simulation to find habitable planets. The program, which was sponsored by ASU and NASA Astrobiology, was the final for the college's Astronomy 106 class. When we started, there was a screen of over 600 'stars'. You click on one and you're given some data like parallax, apparent magnitude, peak wavelength, etc. From there you're supposed to calculate distance (easy), luminosity, and Temperature. Now came the tricky part. You click on the second screen and start imputing data for the planet. At first I thought, the gave you some background data, but nope. Nothing. After 20 minutes I was completely lost. The proctor told me that you have to use some of your 'funds' (we started with 50,000 USD) to purchase analysis on planets.

Anyways, it didn't go very well. Points were awarded for finding certain planets correctly and supposedly, there was one habitable planet among all ~600 stars.

Has anyone else had a test like this? I'm still trying to find it online but with no luck.
2012 Season: Reach for the Stars-3rd (State) / Keep the Heat-19th (State)
2013 Season: Astronomy-2nd (State) / Disease Detectives-15th (State)
2014 Season: Astronomy-1st (State) / Experimental Design-20th (State)/ Anatomy and Physiology-16th (State)
2015 Season: Astronomy

Thunder

syo_astro
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### Re: Astronomy C

Well, weird tests like that make me feel slightly better about my tests, but I do wish people tried to cover the whole rules...and no, I haven't quite heard of a test like that astro124. I guess if I find anything I'll say.

Also glad to hear that Skink, if they can't figure out how to get the velocities, Tad posted a bit back (on March 1st) about it. As a reminder, just remember that speed is distance divided by time, planets orbit in circles (in simplified cases, so what's the distance around a circle? Parts a and b relate to this), and time is defined by orbital period (look to part c).
B: Crave the Wave, Environmental Chemistry, Robo-Cross, Meteorology, Physical Science Lab, Solar System, DyPlan (E and V), Shock Value
C: Microbe Mission, DyPlan (Earth's Fresh Waters), Fermi Questions, GeoMaps, Gravity Vehicle, Scrambler, Rocks, Astronomy

AlphaTauri
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### Re: Astronomy C

Just uploaded the test I wrote for MI Region 8 to the test exchange.

Based on the score distribution, it was probably a little too hard for a typical Regionals, but it's still good practice :)
Hershey Science Olympiad 2009 - 2014
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asdfqwerzzz2
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### Re: Astronomy C

Just uploaded the test I wrote for MI Region 8 to the test exchange.

Based on the score distribution, it was probably a little too hard for a typical Regionals, but it's still good practice
Just for reference when I take it, what were the top raw scores?

AlphaTauri
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### Re: Astronomy C

Top was just under 40%. I was aiming for ~70%, but uh, that didn't happen...
Hershey Science Olympiad 2009 - 2014
Volunteer for Michigan SO 2015 - 2018

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