Polar Coordinates: Apollo 13 Reentry: Calculating Theta

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SUMMARY

The discussion focuses on calculating the angle theta (θ) in the polar coordinate system during the Apollo 13 reentry. It clarifies that θ represents the angle at the center of the Earth between the current radius and the initial radius. Additionally, the angle gamma (γ) is defined as the angle between the velocity vector and the tangential unit vector (eθ). This distinction is crucial for understanding the dynamics of reentry trajectories.

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  • Understanding of polar coordinate systems
  • Familiarity with vector mathematics
  • Knowledge of basic physics principles related to reentry dynamics
  • Concept of unit vectors in polar coordinates
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  • Explore the mathematics of vector angles and their applications
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Ry122
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in this situation where apollo 13 is reentering the atmosphere, how would you determine what theta is in the polar coordinate system for velocity?

[PLAIN]http://img37.imageshack.us/img37/7366/shuttlek.jpg

Wouldn't the angle gamma be equal to theta since gamma is equal to the angle of the shuttle with the horizontal if you use the geometry postulate for opposite adjacent angles? But if this is the case then why is it labeled gamma and not theta?
 
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Hi Ry122! :smile:

(have a theta: θ and a gamma: γ :wink:)

θ is the angle (at the centre of the Earth) between the radius where it is now and the radius where it started.

eθ is the unit vector in the θ (ie tangential) direction.

γ is just the angle between the velocity and eθ :wink:
 

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