Author: Alexia Beale

Author: 🇳🇵 Rabin Thapa, Dolpo Buddha Rural municipality, Dolpa

Rabin has shared his experiences of being a Science teacher in a mountainous region of Nepal with jIAPS:

After completing my Master’s degree in physics, I applied for the post of teacher of mathematics and science in Crystal Mountain School (CMS) which is located in upper Dolpa at an altitude of 4300 meters. Inside me, the answer to the question: ‘why did I apply for this professional vacancy as a late twenties Nepalese citizen , is still an unanswered conflict or chaos tumbling in a wave of thought whenever I close my eyes.

Passing through the physical interview process and orientation, I was ready for an hour flight from Kathmandu to Nepaljung, followed by two days road travel and three days uphill trek to the school. However, my plans were disrupted by a domestic flight cancellation. 

Vision Dolpo, an organization managing the seven months academic terms during summer with an ambition to uplift the local literacy potential, can be highly praised. During the six days’ journey, the pressure related to finance and socio economic fluctuation was clearly visible. Meanwhile, we reached our destination on 17th April. A day’s rest was scheduled to face altitude sickness before starting regular teaching on 19th April.

Considering the harsh geographical navigation of CMS coupled with the local living standard, the encounter of limited stationary, student’s uniforms, teaching resources, regular food and IT access was inevitable. In this context, everything apart from basic requirements had to be brought from the capital, to be able to conduct regular academic activity. These supplies were  transported from Dolpa’s district headquarters to the school’s location by mules and donkeys. In April, around hundred shacks of school material were on the way to our location. During dinnertime a few days after I arrived, I heard that Dolpo Buddha Rural Municipality was facing official blockage due to political turbulence, which resulted due to per-planned local elections announced by the government. Due to this blockage, whatever its cause, CMS’s administration had to face the scarcity of food for the staff. Most prominently, the 250 students who come to school here are struggling with availability of stationary, learning material, laboratory tools and uniforms. The stark reality, the real image of public education as experienced by me, is really heartbreaking. I can remember wishing that my heartache could be consoled and thinking of the passenger’s song entitled, “Survivor”.

After a long wait of three months, the supplies, including the stationary for the students, finally arrived. However, the staff, along with the administration team, had to overcome the challenge of continuing regular academic activities with limited resources. At a general meeting, I was assigned to initiate the lead in STEAM activities and upgrade the science laboratory. Selecting extracurricular projects was pivotal because I found that very few students in the school were interested in classical or analog projects. Consequently, to motivate interest in modern science and technology, we established a ‘Makers’ Club’. The annual projects selected were: the construction and installation of electric bell, execution of robotics design and designing a smart dustbin. Fifteen students initially enrolled in the ‘Makers’ Club’. In the ‘Maker’s Space’, we came to a mutual agreement with the students that all the members had to contribute two hours to the club every day after their regular class. 

These two hours of the school day are the most precious time for the students. They can explore a variety of engineering tools, through regular workshops where they are instructed in practical electronics, magnetism, wiring, working principle of switches, AC, DC, transformers, software coding, hardware and basic design principles, to name a few activities. Sometimes, the students became so enthused by their projects that we used to work for hours, even without sleeping. When all our annual projects were accomplished, after four months of hard work, we showed our finished products to the other students and we were able to attract more students to join the ‘Makers’ Club’. Now, at the altitude of 4100 m, in a remote mountainous region of Nepal, we have a self-made electric bell in operation; an inter-house robotic battle; and smart dustbins with software and hardware developed by the students. In our corner of the world, we are introducing modern science and technology to children in their regular learning environment, in a region where these scientific advances were unknown. 

Photo Credits: Rabin Thapa

Implications of Relativistic Effects on the Global Positioning System (GPS)

Raghav Sharma, BSc Physical Science with Electronics, University of Delhi

Abstract

Relativity has no obvious consequences in daily life, but one close look at the working of a GPS device is sufficient to highlight the enormous implications of relativistic effects on situations where velocity, gravity, and accuracy are involved. Clocks on a moving satellite do not appear to tick at the same intervals as clocks on Earth. This is especially problematic in high-accuracy systems like the GPS. Understanding the mathematical principles behind these effects allows for a derivation of precise offset values- adjustments that need to be made to satellite clocks to correct any time difference caused by relativity.

Introduction

The Global Positioning System (GPS) is a highly accurate, satellite-based positioning and navigation system.^[1] To maintain that accuracy, time-dilating relativistic effects arising from both the general and special theory of relativity need to be taken into account. This is achieved by adjusting the rates of onboard satellite clocks and incorporating mathematical corrections. This article explores time dilation effects on GPS and describes some calculations and adjustments that are made to account for them. The correction for special relativistic time dilation is derived in detail.

1. An Overview of Time-Dilation Effects

A handheld GPS receiver can determine the absolute position on the surface of the Earth to within 5 to 10 metres.^[1] Achieving a navigational accuracy of 5 metres requires knowing the onboard GPS satellite time to an accuracy of about 17 nanoseconds, which is the time taken by light to travel 5 metres. Because satellites are constantly moving with respect to the Earth-centred (approximately inertial) frame and are further away from the Earth’s gravitational well, one must consider time dilation caused by both special and general relativistic effects. If these effects were left uncompensated, navigational errors would accumulate at a rate in excess of 10 kilometres per day, rendering the system unusable within about 2 minutes.^[2] 

2. Special Relativity

GPS Satellites are not geosynchronous because that would limit coverage. They have a time period of about 12 hours (so that any satellite passes over the same location each day) and a corresponding orbital velocity of about 3874 m/s relative to the centre of the Earth.^[3]

According to the Special Theory of Relativity, moving clocks run slower.^[2] The time dilation amount is determined by Lorentz transformations. The time measured on-board the satellite is reduced by the Lorentz factor γ:

where τ_{Ground} and τ_{GPS} are time intervals measured on the Earth’s surface and by the satellite clock, respectively.

The derivation of the time by which satellite clocks lag behind surface clocks, Δτ, is given below: 

Using binomial expansion for small values of (v/c):

Taking v=3874 m/s and c=2.998×108m/s:

 For a time-interval of 1 day (86,400s) on the Earth’s surface:

Therefore, GPS clocks lose about 7μs a day due to special relativistic time dilation.

3. General Relativity

GPS satellites have an orbital altitude of 20,184 km measured from the surface.^[3] According to the General Theory of Relativity, a clock in a gravitational field runs slower. This effect is given by:

Where τ_0 is the time interval measured near a mass (i.e., in a gravitational well), and is the time interval measured far away from the mass. 

For small values of (M/r):

The clocks on the Earth’s surface are a distance of R_Earth=6378.1 km from the gravitational centre, so the time dilation with respect to GPS satellites is twofold. It is stated without proof that due to general relativistic time dilation effects, clocks onboard the satellites gain about 45μs per day, with respect to ground-based clocks.^[1]

4. Error Correction

The combination of general and special relativistic time dilation means that GPS clocks gain about 38μs a day. As stated before, the desired accuracy can be as high as 17 nanoseconds. Thus, it is crucial to correct any time difference. 

A time offset of 38μs corresponds with a fractional change of +4.465×10^-10, i.e. the satellite clocks need to be slowed down by this fraction. The fundamental L-band frequency produced by the atomic clocks on-board is 10.23 MHz. This needs to be offset by the aforementioned fraction. Therefore, the actual frequency of the GPS clocks is set to 10.22999999543 MHz before launch.^[3-4]

The variation in these changes due to the eccentricity (deviation from circularity) of the satellite orbit also needs to be taken care of. Built-in microcomputers used in GPS receivers help in any additional timing calculations required using satellite-provided data.^[1]

Conclusion

Relativity dictates that clocks aboard GPS satellites do not tick at the same rate as those on the Earth. Both general and special relativistic time dilation effects are at play. Neglecting to adjust for these would render GPS useless in a few minutes. Correcting them involves giving the onboard atomic clocks a slight offset in frequency, so that they may appear to run at the same rate as ground-based clocks. This correction is one of many needed to maintain a navigational accuracy of up to a few metres.

References:

1. Pogge, Richard W. (2017): Real-World Relativity: The GPS Navigation System
2. Will, Clifford M.: Einstein’s Relativity and Everyday Life
3. Nelson, Robert A. (1999): The Global Positioning System- A National Resource
4. Oxley, Alan (2017): Uncertainties in GPS Positioning- A Mathematical Discourse, Pages 71-80