Geostationary Orbits: Benefits & Challenges

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    Geostationary Orbit
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SUMMARY

The discussion focuses on the calculations involved in determining the length of AC in geostationary orbits, specifically at an altitude of 35,800 km above Earth's surface. The formula used for circumference, C = π · d, is applied to find the diameter, while the Pythagorean theorem is utilized to calculate BC. The final calculated distance from point A to point C is confirmed to be 84,300 km, which includes Earth's radius and the altitude of the orbit.

PREREQUISITES
  • Understanding of basic trigonometry, including the use of inverse cosine.
  • Familiarity with the Pythagorean theorem.
  • Knowledge of orbital mechanics, specifically geostationary orbits.
  • Basic understanding of geometry related to circles and diameters.
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  • Research the mathematical principles behind geostationary orbit calculations.
  • Learn about the implications of altitude on satellite positioning and communication.
  • Explore the physics of orbital mechanics and satellite dynamics.
  • Study the applications of trigonometry in real-world engineering problems.
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Students in physics or engineering, satellite communication engineers, and anyone interested in the mathematics of orbital mechanics.

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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