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the effect of solar gravitational potential on gps clocks

This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation

  • In Slide Show, click on the right mouse button
  • Select “Meeting Minder”
  • Select the “Action Items” tab
  • Type in action items as they come up
  • Click OK to dismiss this box
  • This will automatically create an Action Item slide at the end of your presentation with your points entered.

The Effect of Solar Gravitational PotentialOn GPS Clocks

Tom Van Flandern & Thomas B. Bahder

Army Research Laboratory

PAWG, Colorado Springs

1998 August 19

(last two slides updated 2002 March 30)

what affects clock rates
What affects clock rates?
  • SR: motion slows clocks by the factor (typically < 10-8)
  • GR: gravitational potential slows clocks by the factor (typically  10-8)
      • N.B.neglected (10-16)
gps satellite clock rates ns day
GPS satellite clock rates (ns/day)
  • Orbital speed slowing: 7,200
  • Gravitational potential slowing at GPS orbital altitude: 14,400
  • Gravitational potential slowing on Earth’s geoid: 60,300
  • Net: GPS satellites run faster than clocks on geoid by: 38,700
question why is solar potential effect not included in gps
Question: Why is solar potential effect not included in GPS?
  • Predicted effect: 12-ns amplitude, 12-hour period
  • GPS raw pseudo-ranges show unexplained 12-hour periods correlated with Sun direction
  • Hoffman (1963): Clocks in “freefall” should show no effect. But counter-examples exist.
what does not affect clock rates
What does not affect clock rates?
  • Cyclotron experiments with meson decay times show that acceleration as such does not affect clock rates even at 1019 g.
  • F = m a and equivalence principle: If acceleration does not affect clocks, gravitational force cannot either.
slide6

Inside a uniform spherical shell, force is zero, potential is constant, clocks slow

Alley experiment: speed & altitude affect clocks, but not acceleration (e.g. when plane circles)

slide7

Fixed and accelerating clocks with same speed and height tick at same rates

Suspension/free fall doesn’t affect clock rates

slide8

Compared to pole, clocks on equator slow due to higher rotation speed, but speed up due to weaker gravitational potential. These effects cancel.

Result: All clocks at sea level tick at the same rate!

slide9

Satellite clocks tick slower than clocks at infinity because speed and potential effects accumulate.

Also, as satellite falls toward perigee, potential gets stronger and speed increases. Again, the two clock-slowing effects accumulate.

slide10

As Earth and satellite fall toward perihelion, all their clocks slow in unison relative to distant pulsar clocks. The two slowing effects accumulate.

slide11

But as the satellite orbits, do the two clock-slowing effects from gravitational potential and velocity in the Sun’s field cancel or accumulate?

predicted amplitude of solar potential effect: 12 ns (3.6m)

To Sun

slide12

Or if Earth is not present but the satellite follows the same path as before using rocket propulsion, do the two solar clock-slowing effects cancel or accumulate?

predicted amplitude of solar potential effect: 12 ns (3.6m)

To Sun

slide13

Alley experiment:

Clocks flown over south pole to New Zealand

South pole in winter was always farther from Sun than Earth center

No effect of Sun’s potential was seen.

solar clock slowing computation
Solar clock-slowing computation
  • Sun’s potential at Earth’s surface is 14 x stronger than Earth’s potential.
  • Mathematica applied to GR metric equation to compute satellite proper time in Sun’s field for any orbit.
  • Lorentz transformation applied to convert from SSB coordinate time to ECI coordinate time.
  • Result: potential and velocity effects from Sun on Earth-satellite cancel!
slide15

A

Explanation: As Earth orbits Sun (center path), aphelion satellite positions must travel at higher speed to get from A to B, and perihelion satellite positions must travel at slower speed to get from C to D.

C

D

B

This “centripetal potential” is speed difference added by Sun’s presence.

summary of clock slowing effects
Summary of clock-slowing effects

Motion free Motion forced

conclusions
Conclusions
  • Solar potential effect does not exist in GPS data; motion is “forced”
  • Unexplained 12-hour periods correlated with Sun direction must have some other explanation
  • No unresolved relativity issues remain at the 1-meter level for GPS