RELATIVISTIC DOPPLER EFFECT AND GPS SATELLITES
PHYSICS LAB-1 | 15B17PH171
SUBMITTED BY:
SUHANI RANA 2401020160
KARTIKEYA RAI 2401020173
SAYLI MOGHE 2401020161
ACKNOWLEDGEMENT
First and foremost, we would like to express my deepest gratitude to our physics lab faculty, MR ANURAG
PANWAR for invaluable guidance, feedback and constant encouragement throughout the duration of this
project.
We are extremely grateful to our institution JAYPEE INSTITUTE OF INFORMATION TECHNOLOGY, for granting
me access to the physics lab, library management team for providing us the platform to work upon our
ideas and also, would like to thank our lab assistants faculties for their guidance.
We would like to acknowledge my group members for their assistance during this project.
Finally, we must thank my parents for providing their unwavering support and encouragement without
which we could not have completed our project. We learned new things from this project.
INTRODUCTION
This project report examines the Doppler Effect, its principles, and its application in GPS (Global Positioning
System) technology. GPS relies heavily on signals from satellites and, crucially, on the understanding of Doppler
shifts to calculate the position, speed, and direction of objects on Earth. Through this report, we will understand
the science behind the Doppler Effect and its role in GPS technology.
1. The Doppler Effect
• The Doppler Effect refers to the change in observed frequency of a wave due to the relative motion between
the wave source and the observer.
• For GPS, which relies on electromagnetic waves (radio signals), the Doppler Effect occurs when there is
relative motion between a GPS satellite and a receiver on Earth.
• The observed frequency of the GPS signal changes based on the velocity of the satellite relative to the receiver.
APPLICATIONS OF DOPPLER EFFECT
• 1. Astrophysics and Cosmology
• Determining the Motion of Celestial Bodies: The Doppler Effect is crucial in observing red and blue
shifts in the light from stars and galaxies. When a celestial object is moving away from Earth, the light
waves stretch, leading to a redshift (lower frequency). Conversely, if an object is moving toward Earth, it
experiences a blueshift (higher frequency). This helps astronomers measure not only the speed and
direction of a celestial body’s movement but also to infer its distance.
• 2. Medical Imaging and Diagnostics
• Doppler Ultrasound for Blood Flow Measurement: Doppler ultrasound technology utilizes high-
frequency sound waves to measure the speed and direction of blood flow within vessels. It is widely
used in cardiology to assess the health of arteries and veins, detecting blockages, blood clots, or
reduced blood flow due to cardiovascular conditions. The Doppler Effect allows visualization and
quantification of blood flow in real-time.
3. Wireless Communication and Radar Technology
• Frequency Hopping in Mobile Communication: Doppler shift can affect signal quality in mobile
communication, especially in fast-moving environments (like trains or cars). Mobile networks account
for these Doppler shifts through adaptive algorithms that maintain signal stability and reduce errors in
data transmission. For 5G networks and beyond, Doppler shifts will be even more critical to manage due
to the higher frequency bands in use.
4. Satellite and Space Communication
• Satellite Navigation and Positioning Systems (GPS): Doppler shifts in signals from GPS satellites are
used to calculate the speed and position of objects on Earth. The relative movement between a GPS
satellite and a receiver causes shifts in signal frequency, which can be used to determine the receiver's
speed and direction, aiding in accurate navigation for aviation, maritime, and road transport.
MATHEMATICAL EXPLANATION
• The formula for the Doppler shift in sound is given by:
• f′=f(v+vo)/(v+vs)
• Where:
• f′ is the observed frequency,
• f is the emitted frequency,
• v is the speed of the wave in the medium,
• vo is the velocity of the observer relative to the medium,
• vs is the velocity of the source relative to the medium.
INTRODUCTION
2. GPS Satellite System
• Overview of GPS Technology
• The Global Positioning System is a satellite-based navigation system consisting of at least 24 satellites. It
provides geolocation and time information to a GPS receiver anywhere on Earth, as long as it has a clear line
of sight to at least four satellites.
• Components of the GPS System
1. Space Segment: The satellites orbit Earth at an altitude of about 20,200 km and transmit signals to Earth.
2. Control Segment: The ground control stations monitor and maintain the satellites' operations and orbit.
3. User Segment: Receivers on the ground capture the signals from multiple satellites and compute their exact
position.
ROLE OF DOPPLER EFFECT IN GPS
SATELLITES
• Importance in Determining Speed and Direction
• The Doppler Effect is critical in GPS because it allows the system to determine not only the position of
the receiver but also the speed and direction. When a GPS receiver is moving, the frequency of the
signal from each satellite will experience a Doppler shift. By analyzing these shifts, the GPS system can
calculate the velocity of the receiver.
• Doppler Shifts in Satellite Signals
• GPS satellites broadcast signals at a fixed frequency. Due to their high orbital speed and the movement
of the GPS receiver, a Doppler shift occurs in the frequency that the receiver detects. GPS receivers use
these shifts to determine their relative speed and direction in real-time, which is essential for
applications like navigation in moving vehicles.
EXPERIMENT AND OBSERVATIONS
• For a practical experiment, one could use a GPS receiver in a moving vehicle, such as a car. The
objectives would be:
1. To measure the GPS-calculated speed and compare it with the vehicle’s actual speed.
2. To analyze the frequency of the received signals in real-time and observe how they change with changes
in speed and direction.
• Procedure:
• Use a GPS receiver in a car, logging the speed calculated by the GPS over time.
• Record the data at regular intervals.
• Analyze any deviations in speed calculations when moving in different directions (e.g., moving towards
or away from a satellite).
• Observations:
• The GPS speed aligns closely with the actual speed when moving at constant velocity.
• Variations in frequency are noted when changing directions or speeds, reflecting the Doppler shifts due
to relative movement.
SIMULATION OF DOPPLER EFFECT IN GPS:
• Simulation of Doppler Effect in GPS:
• A simulation was developed in Python (or other computational software) to model the Doppler shift
observed in GPS signals as they travel between a moving satellite and a stationary receiver on Earth.
• The following parameters were used:
• Satellite speed relative to Earth: ≈3.87 km/s
• Orbital altitude: ≈20,200 km
• Signal frequency: GPS L1 frequency at 1575.42 MHz
• The relativistic Doppler formula was applied to calculate the expected frequency shifts based on
satellite approach and recession phases relative to the receiver.
• Analysis of Time Dilation:
• Time dilation due to both velocity and gravitational field strength was calculated using:
• Δt′=Δt root(1−v2/c2)(1−2GM/rc2)
These values were compared to demonstrate the cumulative effect on time discrepancy.
CONCLUSION
• The Doppler effect is an essential factor in the operation of GPS systems. By understanding and
accounting for this effect, GPS systems can achieve accurate positioning and velocity calculations. As
GPS technology continues to evolve, further advancements in Doppler correction techniques and
algorithms will enhance navigation accuracy in high-speed environments. The ability to compensate for
Doppler-induced errors is critical for applications such as aviation, space missions, and autonomous
vehicles.
REFERENCES
•Einstein, A. (1905). On the Electrodynamics of Moving Bodies. Annalen der Physik.
•Hofmann-Wellenhof, B., Lichtenegger, H., & Collins, J. (2008).
•Global Positioning System: Theory and Practice. Springer.
•Parkinson, B. W., & Spilker, J. J. (1996). Global Positioning System: Theory and Applications.
• Volume 1 and 2. American Institute of Aeronautics and Astronautics.
