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EastStroudsburg13 wrote:

y_utsumi wrote:What is the difference among the 3 variants of Kepler's Law? They all produce different answers..

1. p^2 = a^3

2. p^2 = (4 pi^2 a^3) / (GM_total)

3. M_total = a^3 / p^2

3 only works if M_total is in solar masses, p is in earth years, and a is in AU.

If the system has a solar mass of 1 (i.e. our solar system), then 3 simplifies to 1.

2 is the true full form of the law, and the units can be anything as long as they cancel correctly. So for example, if your G is in Nm^2/kg^2, then your a has to be in meters and your p has to be in seconds.

Something I haven't been able to figure out; how does one get from #2 to #3? It seems too convenient for G and 4pi^2 to just cancel like that, so I think I'm missing something.

Unome wrote:

EastStroudsburg13 wrote:

y_utsumi wrote:What is the difference among the 3 variants of Kepler's Law? They all produce different answers..

1. p^2 = a^3

2. p^2 = (4 pi^2 a^3) / (GM_total)

3. M_total = a^3 / p^2

3 only works if M_total is in solar masses, p is in earth years, and a is in AU.

If the system has a solar mass of 1 (i.e. our solar system), then 3 simplifies to 1.

2 is the true full form of the law, and the units can be anything as long as they cancel correctly. So for example, if your G is in Nm^2/kg^2, then your a has to be in meters and your p has to be in seconds.

Something I haven't been able to figure out; how does one get from #2 to #3? It seems too convenient for G and 4pi^2 to just cancel like that, so I think I'm missing something.

It has to do with the fact that G/4pi^2 is a constant, so one can say that a^3 is proportional to p^2*M_total (rearranging the equation to avoid fractions ). So we can express each variable as a ratio of values from two systems: (a1/a2)^3 = (p1/p2)^2 * (M1/M2). We know that if M2 is 1 solar mass and a2 is 1 AU, then p2 must be 1 earth year. So as long as we carry those units through, a2, p2, and M2 can all be dropped because they all equal 1, and we're left with #3.

Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

choiireneus wrote:Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

You must have wikipedia articles or just know them. Many test supervisors will just take their question from the 3-10th paragraphs, or even the first on a wikipedia page, so the info is actually super valuable. Have all the DSOs, a lot of reference stuff, math resources and then ace the test.

Ashernoel wrote:

choiireneus wrote:Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

You must have wikipedia articles or just know them. Many test supervisors will just take their question from the 3-10th paragraphs, or even the first on a wikipedia page, so the info is actually super valuable. Have all the DSOs, a lot of reference stuff, math resources and then ace the test.

This holds especially true for objects- a lot of event supervisors will pull all questions on objects from the respective Wikipedia page, even moreso than some of the concepts. Also make sure to have a whole lot of images, since a lot of tests will just have you straight matching it with the picture.

choiireneus wrote:Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

Stellar evolution in ridiculous detail.

antoine_ego wrote:

choiireneus wrote:Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

Stellar evolution in ridiculous detail.

Know all the stuff about the hr diagram.

Ashernoel wrote:

antoine_ego wrote:

choiireneus wrote:Hi Science Olympians!

I am looking to hear some tips for this year's astro tests! What specific things do you think is a MUST HAVE for my notes?? Any information would be awesome!

Good luck to everyone

Stellar evolution in ridiculous detail.

Know all the stuff about the hr diagram.

These two things, to a ridiculous degree.

Like, really, after I'm done with the event this year I'm not going to want to look at another HR diagram for several months or I may rip my eyes out.

Avogadro wrote:

Ashernoel wrote:

antoine_ego wrote:
Stellar evolution in ridiculous detail.

Know all the stuff about the hr diagram.

These two things, to a ridiculous degree.

Like, really, after I'm done with the event this year I'm not going to want to look at another HR diagram for several months or I may rip my eyes out.

You don't like the smooth curves? It's quite a beautiful representation of stars...

Ashernoel wrote:

Avogadro wrote:

Ashernoel wrote: Know all the stuff about the hr diagram.

These two things, to a ridiculous degree.

Like, really, after I'm done with the event this year I'm not going to want to look at another HR diagram for several months or I may rip my eyes out.

You don't like the smooth curves? It's quite a beautiful representation of stars...

I don't like answering repeated questions on what each of the axes is and where to find certain types of stars on the diagram, more accurately. Actual representations of things (i.e. HR for M15) isn't so bad.