The earth is not flat an analysis of a sunset photo

Robert J. Vanderbei

Research output: Contribution to specialist publicationArticle

1 Scopus citations


A method of measuring the diameter of the Earth with the help of a photograph of a sunset over lake Michigan and the effect of water waves roughening up the earth's surface is presented. Pythagorean theorem is used to evaluate that the sun is 69 pixels above the horizon, and the bottom of the reflection is 29 pixels below the horizon. The vector from the center of the Earth to the camera can be decomposed into a sum of two vectors, one from the center of the Earth to the horizon and the other from the horizon to the camera. An analysis of the effect of waves on the water is done by assuming that the maximum slope of the waves is greater than the angle of the sun ray. The incoming light beam is found to illuminate all parts of the wave, even down to the bottom of the troughs, while reflection coming off at the steepest angle is the one that hits the wave where its angle is steepest.

Original languageEnglish (US)
Number of pages6
Specialist publicationOptics and Photonics News
StatePublished - Nov 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


Dive into the research topics of 'The earth is not flat an analysis of a sunset photo'. Together they form a unique fingerprint.

Cite this