Geostationary Orbits: Benefits & Challenges

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    Geostationary Orbit
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Discussion Overview

The discussion revolves around the calculations related to geostationary orbits, specifically focusing on determining distances and angles associated with orbital mechanics. Participants engage in mathematical reasoning and problem-solving related to the geometry of orbits.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks for help with a calculation involving the length of AC in the context of geostationary orbits.
  • Another participant provides a formula for the circumference of a circle and suggests using it to find the diameter AC.
  • Further calculations are proposed, including the use of the Pythagorean theorem to find BC and the cosine function to determine angle BAC.
  • A participant confirms a calculated distance of 84,300 km, explaining the components of this distance based on the altitude of the orbit and the radius of the Earth.

Areas of Agreement / Disagreement

Participants appear to agree on the calculations and the method used to arrive at the distance of 84,300 km, but there is no explicit consensus on the correctness of the initial assumptions or calculations presented.

Contextual Notes

Some assumptions regarding the definitions of distances and the geometry of the orbit may not be fully articulated, and the discussion does not resolve potential ambiguities in the calculations.

Pasha
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Hi, everyone can you help me with this question, please?
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(i) This calculation is straightforward ... what do you get for the length of AC?

(ii) recall $C = \pi \cdot d$, where $d$ is the length of the orbital diameter AC.

(iii) $BC = \sqrt{|AC|^2-|AB|^2}$

(iv) note ... $\cos(\angle{BAC}) = \dfrac{|AB|}{|AC|}$. Use inverse cosine on your calculator to determine the angle measure.
 
skeeter said:
(i) This calculation is straightforward ... what do you get for the length of AC?

(ii) recall $C = \pi \cdot d$, where $d$ is the length of the orbital diameter AC.

(iii) $BC = \sqrt{|AC|^2-|AB|^2}$

(iv) note ... $\cos(\angle{BAC}) = \dfrac{|AB|}{|AC|}$. Use inverse cosine on your calculator to determine the angle measure.

(i) for this one i got 84.300 is it right ?
 
Yes. Since the orbit is 35,800 km above the Earth surface, the distance from the Earth's surfacr to C, although it is not shown in the picture is also 35,800 km so the distance from A to C is 35,800+ 12,700+ 35,800= 84,300 km.
 

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