Calculating the Size of an Arbitrary Planet

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SUMMARY

The discussion focuses on calculating the size of an arbitrary planet based on observations of the celestial pole. The user notes a shift from 40 degrees to 30 degrees above the horizon after flying 1000 km south at a speed of 1000 km/hour. Using the Circle Circumference Formula, the user deduces that 10 degrees of the planet corresponds to 1000 km, leading to a calculated circumference of 36,000 km. This method effectively determines the planet's size based on angular displacement and distance traveled.

PREREQUISITES
  • Understanding of celestial navigation and angular measurements
  • Familiarity with the Circle Circumference Formula
  • Basic knowledge of trigonometry related to spherical geometry
  • Concept of angular displacement in relation to distance traveled
NEXT STEPS
  • Study the Circle Circumference Formula in detail
  • Explore spherical geometry and its applications in navigation
  • Learn about celestial navigation techniques
  • Investigate angular displacement calculations in various contexts
USEFUL FOR

Students of physics, astronomy enthusiasts, and anyone interested in celestial navigation and planetary measurements will benefit from this discussion.

Maximil
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Homework Statement


You land on an unknown planet. The first night you note that its celestial pole is 40 degrees above the northern horizon at your current position. Your flight module is able to go 1000 km/hour. You fly an hour due south, and note that the celestial pole is now 30 degrees above the horizon. How big is the planet?

Homework Equations


Circle Circumference Formula

The Attempt at a Solution


What I started off with was that we traveled 10 degrees in 1 hour, right? That means 10 degrees of the planet as a "circle" is 1000km. Using this, we can calculate the circumference as 1000km * 36, right? Am I on the right track? Thank you.
 
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Hi Maximil, Welcome to Physics Forums!

Yes, it looks like you're on the right track.
 
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