Polar Coordinates: Apollo 13 Reentry: Calculating Theta

In summary, when determining theta in the polar coordinate system for velocity during Apollo 13's reentry into the atmosphere, it is important to note that theta represents the angle between the radius at the current position and the radius at the starting position. The unit vector eθ points in the tangential direction, while gamma represents the angle between the velocity and eθ. This explains why gamma is labeled as such and not theta.
  • #1
Ry122
565
2
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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  • #2
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:
 

FAQ: Polar Coordinates: Apollo 13 Reentry: Calculating Theta

What are polar coordinates and how are they used?

Polar coordinates are a mathematical system used to locate points on a two-dimensional plane. They consist of a distance from the origin (r) and an angle from a reference direction (theta). They are often used in physics and engineering to describe the position of objects or to calculate trajectories.

How do polar coordinates relate to the Apollo 13 reentry?

During the Apollo 13 mission, polar coordinates were used to calculate the angle (theta) at which the spacecraft needed to reenter the Earth's atmosphere. This was essential for determining the correct trajectory and ensuring a safe return to Earth.

How is theta calculated for the Apollo 13 reentry?

Theta for the Apollo 13 reentry was calculated by using a combination of data from the spacecraft's instruments and mathematical equations. The angle was constantly adjusted to ensure the spacecraft stayed on the correct path for reentry.

Why were polar coordinates used instead of Cartesian coordinates for the Apollo 13 reentry?

Polar coordinates were used for the Apollo 13 reentry because they are better suited for describing circular motion, which is what the spacecraft was experiencing during reentry. This made it easier to calculate the appropriate angle for a safe return.

What other applications do polar coordinates have in science and engineering?

Polar coordinates are commonly used in fields such as physics, engineering, and astronomy. They are used to describe the position and movement of objects, calculate trajectories, and solve complex equations involving circular motion. They also have practical applications in navigation, mapping, and GPS systems.

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