Astronomy Olympiad: Questions & Discussion

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Discussion Overview

The discussion revolves around questions from the Astronomy Olympiad, focusing on descriptive problems related to satellite positioning, light behavior with mirrors, and buoyancy principles in fluid mechanics. The scope includes conceptual understanding and mathematical reasoning.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant poses a question about the maximum latitude from which a satellite, located 36000 km from the equator, can be viewed, suggesting a geometric approach to find the angle.
  • Another participant questions the stability of the satellite at that altitude, indicating a shift from the original geometric focus.
  • A subsequent question involves light passing through a box of mirrors, with one participant suggesting multiple arrangements are possible and proposing that the sum of angles of incidence and reflection is constant.
  • Another participant agrees with the possibility of multiple arrangements but challenges the claim about the sum of angles, stating it can vary between 180° and 720°.
  • A third question addresses the buoyancy of a spherical iron shell floating in water, with a participant seeking validation for their assumptions regarding the shell's shape and internal conditions.

Areas of Agreement / Disagreement

Participants generally express differing views on the sum of angles in the mirror arrangement, indicating a lack of consensus. The discussion on the satellite's stability also reflects differing perspectives, while the buoyancy question remains open for exploration.

Contextual Notes

Participants have not fully resolved the implications of satellite stability or the conditions affecting the angles of incidence and reflection in the mirror arrangement. Assumptions regarding the spherical shell and vacuum conditions are also not universally accepted.

ritwik06
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Recently I gave my Astronomy Olympiad. There were some questions of descriptive type. If you all don't mind I would like to discuss them here. :rolleyes:
 
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russ_watters said:
Shoot...

Here goes the first...
A satellite is 36000 Km away from the equator. What will be the maximum latitude from which the satellite can be viewed.

Well, if it had been a question of geometry, I would have just calculated the angle for cos-1 (6400/42400). My answer would come 81.1...

But what I wrote is about the stability of the satellite. Will the satellite be stable at an altitude of 36000 Kilometres. What do you think??
 
It doesn't matter if it is stable or not - it is at 36000km right now.
 
russ_watters said:
It doesn't matter if it is stable or not - it is at 36000km right now.

OK :D It means I was foolish to prove that the satellite was unstable. anyways, here goes the second question:
Light passes through a box containing an arrangement of 4 plane mirrors. If the box is removed, even then light doesn't change its path. Is there more than 1 arrangments possible? What will be the sum of all the angles of incidence and reflection.
I think that more than 1 arrangement is possible. And the sum should always be a constant. Probably 360 degree. Whadda say? :-p
 
ritwik06 said:
I think that more than 1 arrangement is possible. And the sum should always be a constant. Probably 360 degree.
I agree on the first but disagree with the second. I can make any sum from 180* to 720*.
 
Gokul43201 said:
I agree on the first but disagree with the second. I can make any sum from 180* to 720*.

Oh very well! thanks for that :D The third question.
If a shell of iron just floats inside water. Find the ratio of the outer radius to the inner radius. (Density of iron: 7.87 g/cc)
I have assumed that the shell is spherical. And the the space inside the shell is vacuum. Am I going in the right direction?
 

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