I think this whole thread highlights the reason why it’s not a very good challenge question. I doubt the v7 curriculum will include anything similar however.
I did not say earth was not at F1 or F2. You’re clearly not reading my post.
I said C is the center of the earth. The circle IS the earth. C->F1 (aka a) is the radius of the earth. And the avgAlt is the distance from the circle to another imaginary circle around the earth (which is the orbit of the satellite).
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I read your post. I’m sorry, but it’s incorrect.
In an elliptical orbit, the body being orbited is centered at one of the two foci of the ellipse. Note that all orbits are ellipses. There is no circular approximation used in this problem.
Without loss of generality, we say the body being orbited, Earth, is at F1. There is nothing important to this discussion of orbital mechanics located at point C.
Kepler’s Third law requires the semi-major axis, or the distance from C to the far points on the ellipse. Recall, there is nothing at this point C. However, looking at our diagram, we can see that the semi-major axis can be computed by taking the average of the minimum distance from F1 to the ellipse and the maximum distance from F1 to the ellipse.
The average of these two values is in fact the average distance from the center of the Earth to the object in orbit. To proceed, we simply add the raidus of the Earth to average orbital altitude and use this value in Kepler’s third law.
So, in short, your statement that the problem relies upon an assumption of a circular orbit and that the Earth is at point C on the ellipse are both incorrect. You used the correct formula but your description is inaccurate.
If this doesnt relay it then you’re a lost cause. Feel free to go to the #physics room in freenode and have them explain it to you.
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This is a fascinating discussion, and I would like to see it continue. Please keep the conversation polite and civil so that it may.
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I agree that it’s not a great challenge in its current form. I like the idea of challenges that require independent research and synthesis from the student, but this challenge has lots of subtle pieces that can trip students up.
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May be for my background, but this one I had no difficulty whatsoever
Someone that is not used to applying formulas (maths, chemistry, physics…) instead may totally feel a fish out of water.
It could be a nice one to have in the Interview Prep section, just to threw something new at people (and that section is there to give a challenge, so it would totally be fine), I hope it is not discarded completely,
I agree that some of the difficulty people have is an unfamiliarity with plugging values into formulas.
The semiMajor = radiusEarth + avgAlt is I think the next tricky part after that. As we’ ve seen in this thread with a few different people over the years, understanding an orbit and the where everything lies is easy to mix up.
Keeping it at least in the interview prep or clarifying some pieces would be great, IMHO.
Yeah, I had to google that, but considering that weird formulas are thrown at me pretty often, it wasn’t much different than usual (and how many different symbols are used for the same thing!?!)
But, yeah, having no experience on that it is pretty confusing
It is probably not the best place for an impromptu astronomy lesson, but as an Interview Prep thing could be great, even as it is now (I bet it happens pretty often to be asked to implement something never heard before, not necessarily in an interview, but during the job…)
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Duh! I should have mentioned Keplar’s First Law in the first place! That’s the source to cite when talking about the fact that the host body in an orbit is at the focus on the ellipse that marks the orbit.
Keplar’s First Law:
The orbit of every planet is an ellipse with the Sun at one of the two foci.
(Note, there is nothing special about the Sun-planet system. Any pair of orbiting bodies follow the same laws, to include Earth-moon, Earth-satellite, Mars-Phoebe, etc. More complex systems, such as three body problems, are completely different and totally awesome.)
As usual, Wikipedia has a good diagram:
The average between r_max and r_min is the length of the semi-major axis.
Thanks for the correction! It’s been a while since I’ve done any orbital dynamics work, and I forgot that the body being orbited is not at the center of an elliptical orbit, but at one of the foci.
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Happy to help. Teenage me wishing to be a rocket scientist would be proud 
This first screenshot is true and from the first link I posted.
The Earth is not centered on point C like you have repeatedly said. The sentence above the one you highlighted points that out. Your description is not fully accurate. The description from my link that you have screen shot-ed is correct.
The phrase ‘average orbital altitude’ is silly with a circular orbit. The challenge is talking about an elliptical orbit, so the Earth is at a focal point of the ellipse. The average altitude was used as a very good approximation to the semi-major axis by Kepler himself.
This is the wrong description:
Edit: I suppose that I could have added for full correctness “Without an eccentricity provided, the only computation we can do for the semi major axis from the average altitude assumes that the altitude is averaged over the eccentric anomaly. Fortunately, if the altitude was averaged over a different quantity, this calculation will still be very close to the true semi major axis length. This calculation was used by Kepler himself as he created this orbital mechanics framework that we continue to use to this day.”
The formula is still not given 4 years later.
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This is true. Do you have a question about the challenge?
This indeed seems more like a Physics question! But perhaps some consolation could be found in the fact that this is one of the few challenges that push our usage of the Math object to a sound limit.
Just thinking 