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A Simple Flight Mill for the Study of Tethered Flight in Insects
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Flying through polytropes.

W Dean Pesnell1

  • 1NASA, Goddard Space Flight Center, Greenbelt, Maryland, 20771.

American Journal of Physics
|September 20, 2019
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Summary
This summary is machine-generated.

Objects dropped through a tunnel bored through Earth demonstrate simple harmonic motion. This study calculates fall-through times for polytropic models, revealing how central condensation affects travel time and velocity, with implications for planets and stars.

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Area of Science:

  • Physics
  • Astrophysics
  • Geophysics

Background:

  • The classic "tunnel through Earth" problem visualizes simple harmonic motion.
  • Previous models assumed a uniform Earth density, limiting applicability.

Purpose of the Study:

  • To calculate the fall-through time of objects through Earth using polytropic models.
  • To explore how varying central condensation impacts travel time and velocity.
  • To analyze brachistochrone tunnels and compare Earth models with degenerate objects.

Main Methods:

  • Numerical integration of polytrope and degenerate object equations.
  • Analytic solutions and numerical integration for fall-through time calculations.
  • Numerical integration with analytic approximations for brachistochrone calculations.

Main Results:

  • Fall-through time and velocity approach free-fall limits as central condensation increases.
  • More condensed models yield higher maximum velocities but are less Earth-like.
  • Degenerate objects have Earth-like sizes but shorter fall-through times due to higher mass.

Conclusions:

  • Polytropic models provide a more realistic approach to Earth's interior for fall-through calculations.
  • Central condensation is a key factor influencing object dynamics in planetary tunnels.
  • The study offers scaling relationships for applying results to other celestial bodies.