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Introduction

Satellites move at high speed far above Earth, where gravity is weaker. According to Einstein's general theory of relativity, weaker gravity makes clocks run faster. According to his special theory of relativity, fast motion makes clocks run slower. It is hard to imagine, but time passes at a different rate aboard a satellite than on Earth.

The difference is big enough that, without correcting for it, satellite navigation systems could not provide accurate positions. This site shows live GPS or GLONASS satellites, depending on the receiver's current mode, and presents representative relativity calculations for those two systems.

The receiver supplies live observation data. The relativistic clock effects are calculated from representative orbit models; the receiver does not directly measure the difference between satellite and Earth-based clock rates.

Why relativity matters to satellite navigation

Satellite navigation works largely by timing radio signals. A satellite transmits precisely timed information, and the receiver uses differences in signal arrival times to estimate its distance from several satellites and calculate a position.

Light travels about 30 centimeters in one nanosecond. A nanosecond is one billionth of a second. Very small clock errors can therefore become meaningful distance errors.

GNSS satellite clocks are affected by both gravity and motion. For example, in the representative GPS MEO orbit model, the combined effect is about +38.6 microseconds per day. A microsecond is one millionth of a second.

For that GPS MEO example, if the clock-rate difference were left uncompensated, the equivalent accumulated signal-ranging error would grow by roughly 7.2 miles (11.6 kilometers) per day. This does not mean that a displayed position would simply move by exactly that distance after one day. It means that the modeled clock-rate difference corresponds to that much signal-travel distance over a day.

Two effects compete

Two physical effects push the satellite clock in opposite directions.

• Higher altitude means weaker gravity. Compared with a clock near sea level, this makes the satellite clock run faster.
• Rapid orbital motion makes the satellite clock run slower.
• For the representative GNSS orbit models implemented by this site, the gravity effect is larger, so the combined result is a net clock gain.

Representative values for the GPS MEO orbit model:

In this documentation, geopotential refers to gravity together with the sea-level terrestrial reference convention used for timekeeping near Earth.

What is live and what is calculated

The dashboard combines live receiver observations with calculations based on representative orbit models.

Receiver data available to the application

These values come from the GNSS data source:

• receiver status;
• receiver-provided time and position-solution information;
• satellite constellation and identifier;
• azimuth;
• elevation, shown as height in the sky;
• signal strength;
• whether a satellite is used in the current position solution.

The dashboard's Time at receiver is the current civil time at the receiver location in the town of Bladel, The Netherlands. It is displayed in the Europe/Amsterdam time zone and automatically follows CET/CEST; it is not the time aboard the selected satellite or the time on the visitor's computer.

Calculated using representative orbit models

For GPS or GLONASS satellites, the dashboard uses the corresponding representative MEO orbit model and calculates:

• representative orbit class;
• representative orbital altitude;
• representative orbital speed;
• gravitational acceleration at the representative orbit;
• gravity-related clock effect;
• motion-related clock effect;
• combined clock effect;
• equivalent daily signal-ranging error;
• approximate distance from the receiver.

Selecting a satellite connects that live observation to the appropriate scientific model. It does not mean that the receiver measured that satellite's orbit, speed, distance, gravitational field, or relativistic clock offset.

Spacecraft identity

NMEA-style receiver data identifies a satellite signal by its constellation and a numeric identifier. For GPS, this identifier is commonly described as the PRN, or pseudo-random noise code, used by receivers to distinguish GPS signals.

The dashboard can map a known receiver identifier through a separate spacecraft catalogue. That catalogue supplies verified physical-spacecraft details such as launch date, manufacturer, SVN, NORAD catalogue number, and COSPAR international designator.

Receiver identifiers denote navigation signals or constellation slots, and assignments can change over time. A catalogue mapping must therefore be checked for the date and context being shown.

When an exact identity is verified, 'GPS Relativity' shows verified catalogue metadata. Otherwise, it shows representative constellation or orbit-class information, such as operator, orbit class, and representative altitude, without inventing launch dates or catalogue numbers.

Images in the spacecraft section may represent the satellite generation or constellation rather than the exact individual spacecraft. The USB receiver does not provide manufacturer, launch date, spacecraft age, catalogue numbers, or image information.

Reading the sky plot

The sky plot shows where satellites appear in the local sky.

• The outer circle is the horizon.
• The center points straight up, toward the zenith.
• The displayed sky-view direction is placed at the top of the plot. A dotted radial line marks that direction, and its bearing is shown just outside the circle.
• Compass labels show true geographic directions, and azimuth values remain true compass bearings.
• A satellite moves toward the center as its elevation increases.
• The red marker is the selected satellite.
• Satellites used in the current position solution have an additional visual cue.
• Signal strength is shown subtly through marker appearance. It is not a measurement of distance.

The sky plot represents observed direction only. It does not show the satellite's orbital position around Earth.

A satellite can be selected directly on the sky plot or from the list below it.

Orbit and observation values

The selected-satellite panel combines representative orbit information with live receiver observations.

Height above Earth is the representative MEO orbital altitude above Earth's surface for the selected GPS or GLONASS satellite. For the GPS MEO model, it is about 20,189 kilometers.

Approximate distance from receiver is the estimated straight-line distance from the GNSS receiver to the satellite. It changes as the satellite appears higher or lower in the sky. The estimate uses the observed elevation angle, the selected representative orbital radius, and a spherical-Earth geometry model. It is not a range measurement reported by the receiver.

Gravity at orbit is calculated from Earth's gravitational parameter and the representative orbital radius. The dashboard shows it as a percentage of the modeled gravitational acceleration at Earth's surface, followed by the value in m/s². This is gravitational acceleration at that radius, not weight felt aboard the freely falling satellite.

Orbital speed is the speed of a circular orbit at the representative orbital radius. In English, the dashboard shows miles per hour followed by kilometers per second in parentheses.

Height in sky, Azimuth, and Signal come from the receiver observation. Used for positioning indicates whether the receiver currently includes that satellite in its position solution.

Dashboard behavior

The dashboard shows the local civil time at the receiver location in Bladel and orients the sky plot to match the receiver's physical sky view. The top of the plot corresponds to the displayed sky-view direction, while compass labels and azimuth values retain their true geographic meanings.

The dashboard updates automatically as receiver data changes. Selecting another satellite updates the observation values, representative orbit model, relativity calculations, and spacecraft information for that satellite.

Supported satellite systems

GNSS means Global Navigation Satellite System. On this site, the supported live receiver modes are GPS and GLONASS.

The installed VK-162 uses a u-blox 7 receiver that can operate in GPS mode or GLONASS mode, one at a time. It does not report simultaneous GPS and GLONASS observations. The dashboard applies representative MEO orbit models to the currently active GPS or GLONASS observations.

Visitors can switch the live receiver with the Satellite type controls above the receiver-status panel. The button for the currently active type is disabled. If another visitor is controlling the receiver, both buttons are disabled and "(locked)" is shown; control is released when possible after that visitor leaves, with a 10-minute timeout as fallback. Switching briefly interrupts live data while the receiver acquires satellites in the newly selected system, after which the displayed satellites and calculations correspond to the newly active GPS or GLONASS system.

MEO means medium Earth orbit. The dashboard links this orbit-class abbreviation to its entry in the Glossary.

What the receiver provides

The VK-162 is a USB GNSS receiver connected to the webserver. It sends standardized NMEA text messages to the computer through a serial connection.

Those messages can contain receiver-provided time, position and position-solution information, satellite identifiers, azimuth, elevation, signal strength, and information about which satellites are used for positioning. The exact messages reported depend on the receiver's current GPS or GLONASS mode, current reception conditions, and the satellites visible at that location and time.

The receiver does not supply the representative orbit models, relativistic calculations, spacecraft catalogue information, or spacecraft images shown by 'GPS Relativity'.

Current limitations

The dashboard is educational. It is not a precision navigation or surveying instrument.

• The displayed calculations use nominal representative circular orbits.
• Actual satellite altitude and speed vary.
• No broadcast ephemeris is currently used. An ephemeris is the detailed orbital data broadcast by navigation satellites.
• The calculations are not instantaneous satellite-specific clock corrections.
• The small periodic eccentric-orbit relativistic correction is therefore not displayed.
• The distance estimate ignores fine details such as Earth's ellipsoidal shape, receiver altitude, atmospheric propagation, and the satellite's exact orbital state.
• The gravitational acceleration display uses the same spherical-Earth representative model and is not a measurement made by the receiver.