Satellite tracking - Dynamics, Angular velocity, Circular motion

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SUMMARY

The discussion centers on calculating the time a satellite in a circular orbit 1600 km above Earth will pass through the beam of a tracking antenna aimed 30 degrees above the horizon. The satellite completes one orbit in two hours, and the Earth's radius is 6400 km. Key equations discussed include angular velocity (w = dx/dt), period (T = 2π/w), and the sine rule for determining angles in triangles. Participants emphasize the importance of trigonometry in solving the problem, particularly in finding the angle at the center of the Earth and the arc length traveled by the satellite.

PREREQUISITES
  • Understanding of basic trigonometry, including sine and cosine rules.
  • Familiarity with angular velocity and circular motion concepts.
  • Knowledge of the Universal Law of Gravitation.
  • Ability to apply geometric principles to solve problems involving triangles.
NEXT STEPS
  • Study the Law of Sines for solving non-right triangles.
  • Learn about angular velocity calculations in circular motion.
  • Explore arc length formulas in circular geometry.
  • Review the Universal Law of Gravitation and its applications in orbital mechanics.
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on dynamics, circular motion, and trigonometry. This discussion is also beneficial for educators seeking to enhance their teaching methods in these subjects.

  • #31
Coto said:
Overkill :). And this only finds a velocity which can be found using the data of the problem in a more direct manner.

What can I say other than I'm a nerd and yes I'm proud of it :)
 

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