Satellite geometry physics problem

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SUMMARY

The discussion focuses on calculating the angle above the horizon required to communicate with a geosynchronous satellite positioned directly above the equator at the same longitude as Seattle, Washington. The Earth's radius is specified as 6.38×106 m, while the radius of the geosynchronous satellite is 3.58×107 m. The law of sines and the law of cosines are essential for solving the problem. The user attempts to derive the angle using the equation sin(90+x)/3.58e7=sin(42.4)/6.38e6, indicating a need for clarity on the correct approach to find the angle x.

PREREQUISITES
  • Understanding of trigonometric functions, specifically the law of sines and the law of cosines.
  • Familiarity with geosynchronous satellite mechanics.
  • Basic knowledge of geometry, particularly in relation to triangles.
  • Proficiency in using a scientific calculator for trigonometric calculations.
NEXT STEPS
  • Study the law of sines and the law of cosines in detail.
  • Learn how to apply trigonometric identities to solve for unknown angles.
  • Research the mechanics of geosynchronous satellites and their positioning.
  • Practice solving similar problems involving angles and distances in satellite communication.
USEFUL FOR

Students studying physics, particularly those focusing on satellite communications, as well as educators and professionals involved in aerospace engineering and telecommunications.

linnus
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Homework Statement



A geosynchronous satellite is stationary over a point on the equator (zero degrees latitude) at the same longitude as Seattle, Washington. Seattle's latitude is 47.6°. If you want to communicate with the satellite, at what angle above the horizon must you point your communication device? The Earth's radius is 6.38×10^6 m. Hint: You will also need the law of sines and the law of cosines.

Homework Equations



Sin angleA/A=sin angleB/B
radius of a geosynchronous satellite= 3.58e7 meters

The Attempt at a Solution


I drew a triangle- a quick question would the angle at which the line tangent to the surface and the radius of the Earth be a right angle?

I got
sin(90+x)/3.58e7=sin(42.4)/6.38e6
I'm not sure how to solve for x here...and I don't think this equation is right...
 
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well I don't know if the equation is correct or not, but for finding x,

sin(90+x)=cos x ...This is an identity. You will need a scientific calculator to find cos inverse.
 

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