General Relativity and The Global Positioning System

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General Relativity andThe Global Positioning
System

• Cheyene Creaser
• Benji Wales

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Outline

• What is GPS?
• GR in GPS
• Coordinate definitions
• Corrections

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GPS in a nutshell

• Space segment
• 24 satellites in 12h orbits 20000km above Earth
• Transmit time and orbit parameters (ephemerides)
• Control segment
• Base stations record satellite positions
• Update satellites with correct times and orbit
  parameters
• User segment
• Devices receive 4 satellite signals and compute
  position time

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GPS in a nutshell
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GPS in a nutshell

• 4 satellites in 6 orbital planes inclined at 55O
  above equator
• At least 4 visible everywhere
• cesium atomic clocks (1014 precision)

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Where am I?

• Using satellite time and orbital parameters
  calculate Keplerian orbit and solve for position
  and time

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GR in GPS

• Require 2 frames of reference
• ECI
• ECEF
• Need proper time definition
• Account for GR effects

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GR Corrections in GPS

• Sagnac Effect (SV and EB)
• Clock frequency shift
• Signal Delay
• Orbit perturbations (negligible)
• Other potentials (negligible)

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Metric in a rotating frame
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Effective Potential on Earth
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Time at Infinity
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Earth Centered Inertial Metric
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Proper Time Differences
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Relativistic Effects on GPS
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In Closing

• GPS requires GR to keep consistent
• Many corrections, frequency shift the largest
• Next largest 2cm
• At the end of day, GPS stays within 100ns of UTC

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End, boi!
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