D. Gravitational, Electric, and Magnetic Fields · Gravitational, Electric and Magnetic FieldsFields, Technology and Society
D1.2 D1.1About 75 minutes
Learning goals- I can explain how GPS uses timing, orbits and relativity to find a position.
- I can describe how satellites are used for weather and storm tracking, sea-ice and ship monitoring, and surveillance, and weigh their benefits against privacy and security concerns.
- I can explain the space-debris problem and the costs and benefits of large satellite constellations.
- I can assess the social, health and environmental impacts of particle accelerators and other field technologies using a clear decision-making process.
Words to know
trilateration
Finding a position from distances to known points. A GPS receiver finds its distance to each satellite from the signal's travel time, d = ct.
remote sensing
Gathering information about Earth's surface from a distance, for example with cameras or radar on satellites.
synthetic aperture radar (SAR)
A satellite radar that sends microwave pulses and builds images from the echoes. It works day and night and sees through cloud.
space debris
Human-made objects in orbit that no longer serve a purpose: dead satellites, spent rocket stages and fragments from collisions and explosions.
Kessler syndrome
A possible chain reaction in which collisions between objects in orbit create debris that causes more collisions, making some orbits unusable.
medical isotope
A radioactive isotope used to diagnose or treat disease, such as fluorine-18 for PET scans. Many are made with cyclotrons.
From equations to everyday life
This morning, a weather forecast used satellite images. A bank transfer was time-stamped with a signal from a GPS satellite. Somewhere in Canada, a patient had a PET scan with a tracer made in a cyclotron that morning. All of these depend on the fields in this unit.
In the last lesson about technology, Field Technologies: Mass Spectrometers, Accelerators and MRI, you analysed how machines work (D1.1). This lesson asks a different question (D1.2): what are their effects on society and the environment, and are the benefits worth the costs? There is rarely one right answer, but there are better and worse arguments. Good arguments use evidence, consider everyone affected and compare alternatives.
GPS: gravity, timing and relativity
The US Global Positioning System has about 31 operational satellites (the count changes as satellites are launched and retired) in six orbital planes, about 20 200 km up, each circling Earth about twice a day (see Satellites and Circular Orbits). Every satellite carries atomic clocks and broadcasts its position and the exact time.
- Your receiver measures how long each signal took to arrive, t, and finds the distance d = ct (light travels about 30 cm in a nanosecond).
- Each distance puts you somewhere on a sphere around that satellite. Three spheres meet at one point (trilateration).
- A cheap receiver clock is not accurate enough, so it needs a fourth satellite to solve for its own clock error as well as its three coordinates.
Because light is so fast, tiny timing errors matter: an error of just 1 μs gives a position error of about 300 m.
Trilateration. Each measured travel time gives a distance, so the receiver lies on a circle (really a sphere) around each satellite. Where all three meet is the receiver.Why GPS needs Einstein
Two effects from relativity change the rate of the satellite clocks:
- General relativity: clocks run faster where gravity is weaker. At 20 200 km, Earth's field is much weaker than at the surface (g = GM/r²), so the satellite clocks gain about 45 μs per day.
- Special relativity: moving clocks run slower. At about 3.9 km/s, the satellite clocks lose about 7 μs per day (see Special Relativity).
The net gain is about 38 μs per day. Engineers set the satellite clocks to tick slightly slow before launch, and receivers apply further small corrections. Without them, GPS positions would drift by kilometres each day. GPS is one of the most direct everyday tests of general relativity.
The relativity budget for a GPS satellite clock. Weaker gravity makes it run fast; its speed makes it run slow. The net effect is corrected before launch.Worked exampleExample 1: How fast would GPS fail without relativity?
A GPS satellite clock gains 38 μs per day relative to ground clocks. If no correction were made, how large a distance error would build up in (a) one day and (b) one hour? (c = 3.00 × 10⁸ m/s)
- The distance error is the speed of light times the timing error: Δd = cΔt.
- (a) Δd = (3.00 × 10⁸)(38 × 10⁻⁶) = 1.14 × 10⁴ m.
- (b) In one hour the clock gains 38/24 = 1.583 μs. Δd = (3.00 × 10⁸)(1.583 × 10⁻⁶) = 475 m.
(a) About 11 km per day; (b) about 480 m after just one hour. Far too much for navigation, farming or emergency services.
GPS in society
Benefits: navigation for drivers, pilots, ships and hikers; faster emergency response; precision agriculture (tractors that steer within centimetres, using less fertilizer and fuel); surveying; earthquake and ice-sheet monitoring. Less obvious, GPS time signals help synchronize cellphone networks, power grids and financial transactions.
Concerns:
- Dependence: many systems would struggle if GPS were jammed, spoofed (faked) or knocked out by a severe solar storm. Other systems exist (Europe's Galileo, Russia's GLONASS, China's BeiDou), and many receivers use several.
- Privacy: phones and apps can record where you go. Who stores that data, and who can see it?
- Military origins: GPS was built and is run by the US military. Countries that rely on it depend on another country's decisions.
Watching Earth: storm tracking, sea ice and surveillance
Weather satellites in geostationary orbit (about 35 800 km up) watch the same part of Earth all day, so forecasters can follow a hurricane or a line of thunderstorms in near real time. Satellites in low polar orbits pass over the whole planet and measure temperatures and moisture through the atmosphere. Better forecasts and earlier storm warnings save lives and money.
Canada's RADARSAT Constellation Mission (RCM), three satellites launched in 2019 about 600 km up, carries synthetic aperture radar. Radar sees through cloud and darkness, which matters in a northern country with long polar nights. RCM data help:
- the Canadian Ice Service map sea ice for ships and northern communities,
- track ships in Canada's waters, including vessels that switch off their location transponders (for example, to fish illegally),
- map floods and wildfire damage for emergency crews,
- monitor crops, forests and changes in Arctic ice.
The same ability that helps a search-and-rescue team can be used for surveillance. Satellite images can show military activity and protect borders, but they also raise questions: Who may photograph whose land? How sharp should images sold to the public be? How should images of people's homes be stored and shared? Laws such as Canada's Remote Sensing Space Systems Act license and limit Canadian commercial imaging satellites.
Space debris: a tragedy of the commons
Every satellite eventually stops working. Low orbits clean themselves slowly, as thin air drags objects down, but higher orbits can stay cluttered for centuries. Space agencies now track tens of thousands of objects larger than a softball, and estimate that there are more than a million pieces larger than 1 cm, too small to track but fast enough to destroy a satellite.
At orbital speeds (about 7 to 8 km/s, and closing speeds up to about 15 km/s in a head-on crossing), even a small fragment carries an enormous kinetic energy. In 1978, NASA scientist Donald Kessler warned that collisions could start a cascade: each collision makes more fragments, which make more collisions.
The number of active satellites has grown very quickly in the 2020s, mostly from large constellations of thousands of small internet satellites in low orbit. They bring fast internet to remote communities, including in the Canadian North, and lower latency than geostationary satellites. They also crowd low orbit, leave streaks across telescope images and release combustion products and metal particles into the upper atmosphere when launched and when they burn up on re-entry, effects scientists are still measuring. Responses include designing satellites to de-orbit within a few years after their missions end, tracking and collision-avoidance manoeuvres, darker satellite coatings and research into debris removal.
Worked exampleExample 2: Why a 1 cm fragment is dangerous
A 1.4 g aluminium fragment (about 1 cm across) hits a satellite at a relative speed of 10 km/s. (a) Find its kinetic energy. (b) At what speed would a 1000 kg car have the same kinetic energy?
- (a) Ek = ½mv² = ½(1.4 × 10⁻³ kg)(1.0 × 10⁴ m/s)².
- Ek = ½(1.4 × 10⁻³)(1.0 × 10⁸) = 7.0 × 10⁴ J.
- (b) Set ½(1000)v² = 7.0 × 10⁴ J, so v² = 140 and v = 11.8 m/s.
- 11.8 m/s × 3.6 = 43 km/h.
(a) 7.0 × 10⁴ J; (b) about 43 km/h. A 1 cm fragment hits like a car in a city street, concentrated on a spot the size of a fingertip.
Worked exampleExample 3: Low orbit versus geostationary internet
A signal goes from a user up to a satellite and straight back down to a ground station. Estimate the travel time for (a) a geostationary satellite 3.58 × 10⁷ m up and (b) a low-orbit satellite 5.5 × 10⁵ m up. Assume both are directly overhead.
- The signal travels up and down: distance = 2h. Time t = 2h/c.
- (a) t = 2(3.58 × 10⁷)/(3.00 × 10⁸) = 0.239 s.
- (b) t = 2(5.5 × 10⁵)/(3.00 × 10⁸) = 3.7 × 10⁻³ s.
(a) About 0.24 s; (b) about 0.004 s. That is why video calls and online games work better through low-orbit constellations. The trade-off: a low satellite sees only a small patch of Earth, so thousands are needed, which adds to crowding and debris.
Accelerators, medicine and the environment
The expectation for this strand gives a second example: particle accelerators used for medical imaging.
- PET scans use positron-emitting isotopes such as fluorine-18 (half-life about 110 minutes), made in hospital or regional cyclotrons. Because the isotope decays so quickly, it must be made close to where it is used.
- Technetium-99m, the most widely used medical isotope, was long made mainly in nuclear reactors, including Canada's NRU reactor at Chalk River, which supplied a large share of the world's needs for decades until it stopped routine isotope production in 2016 (it closed in 2018). Canadian teams, including researchers at TRIUMF, developed ways to make it with medical cyclotrons instead, with no nuclear reactor or uranium targets needed and far less long-lived radioactive waste.
- Linear accelerators in cancer centres treat many thousands of Canadians every year.
Costs and concerns: large research accelerators use a lot of electricity (CERN's yearly use is comparable to that of a mid-sized city); building them takes concrete, steel and large budgets; superconducting magnets (in accelerators and MRI) need helium, which is non-renewable and escapes to space once released; and accelerators produce some radioactive materials that must be handled and stored safely. Supporters point to medical benefits, spin-offs (the World Wide Web was invented at CERN in 1989) and training for scientists and engineers.
| Technology | Main benefits | Main costs or concerns |
|---|
| GPS | navigation, emergency response, precision farming, timing for networks | dependence, jamming and spoofing, location privacy |
| weather and Earth-observation satellites | storm warnings, sea-ice maps, flood and fire mapping, ship tracking | surveillance and privacy, cost, launch emissions |
| large internet constellations | fast, low-latency internet in remote areas | debris, crowded orbits, telescope streaks, re-entry pollution |
| medical cyclotrons and linacs | PET imaging, isotope supply, cancer treatment | cost, electricity, radioactive waste (small amounts) |
| MRI | detailed images without ionizing radiation | cost, wait times, helium use, strong-magnet hazards |
A summary of benefits and costs. Each row is a starting point for an argument, not a final answer.A decision-making process for technology issues
- Define the issue in one sentence.
- Identify stakeholders: who benefits, who bears the costs (including people in other countries and future generations)?
- Gather evidence from reliable sources, and separate facts from opinions.
- List benefits and costs: social, economic, health, environmental.
- Compare alternatives, including "do nothing".
- Decide and justify: state your position, the strongest evidence for it, and what would change your mind.
Just for funIf you ignore relativity, GPS gets you lost by kilometres in a day. Einstein never used a phone app, but every phone that finds its location relies on his theories.
Hands-on activityPosition paper: a field technology in your community
Choose one issue:
- Should Canada launch more radar satellites for Arctic surveillance and sea-ice monitoring?
- Should large internet constellations face stricter rules on debris and brightness?
- Should your region fund a new medical cyclotron for PET scans?
- Should phone apps be allowed to sell location data from GPS?
Use the six-step decision-making process in the tip above to write a one-page position paper (or record a 3-minute talk). Include at least one calculation from this unit (for example a latency, a debris kinetic energy or a GPS timing error) and at least two reliable sources (for example the Canadian Space Agency, Natural Resources Canada, Environment and Climate Change Canada, CERN or TRIUMF). Then interview a family member about whether they use GPS or satellite internet daily and whether they would accept the trade-offs you found.
What to look for: a clear position; stakeholders on more than one side; evidence that is cited and accurate; at least one alternative considered; a correct calculation used to support a point.
Grown-up note: help your teen check that sources are reliable (government, university, agency or established news sites), and talk honestly about your own views while letting them form theirs.
Your turn
1A GPS satellite is directly overhead, 2.02 × 10⁷ m away. How long does its signal take to reach you?
t = d/c = 2.02 × 10⁷ / 3.00 × 10⁸ = 6.73 × 10⁻² s (about 67 ms).
2A receiver's clock is off by 10 ns. What distance error does that cause?
Δd = cΔt = (3.00 × 10⁸)(10 × 10⁻⁹) = 3.0 m.
3Why does a GPS receiver need signals from at least four satellites?
It has four unknowns: three position coordinates and its own clock error. Each satellite gives one equation, so it needs four.
4GPS satellite clocks run fast because of general relativity but slow because of special relativity. Explain the cause of each.
Fast: they are higher up, where Earth's gravitational field is weaker, and general relativity says clocks run faster in a weaker field. Slow: they move at about 3.9 km/s, and special relativity says moving clocks run slow. The gravity effect is bigger, so the net effect is fast.
5Give one benefit and one concern of using radar satellites such as RCM to track ships.
Benefit (any): catching illegal fishing or pollution, search and rescue, safer shipping in ice. Concern (any): surveillance and privacy, cost, the data being misused or shared without consent.
6Fluorine-18 has a half-life of about 110 minutes. Explain why PET centres need a cyclotron nearby.
After a few hours most of the F-18 has decayed (after 220 minutes only a quarter is left), so it cannot be stored or shipped far. It must be made close to the hospital and used the same day.
More practice: warm-up
1About how high do GPS satellites orbit?
2What does the RADARSAT Constellation Mission use to see Earth's surface through cloud and at night?
Radar (synthetic aperture radar, using microwaves).
Human-made objects in orbit that no longer work: dead satellites, rocket stages and fragments.
4Name a medical isotope made in cyclotrons for PET scans.
5Why can a geostationary weather satellite watch one region continuously?
It orbits above the equator with a period of one day, in the same direction Earth spins, so it stays above the same spot.
More practice: on your own
1A video call goes from you, up to a geostationary satellite (3.58 × 10⁷ m up), down to your friend, and the reply comes back the same way. Estimate the delay before you hear the reply, ignoring processing time.
Four trips of 3.58 × 10⁷ m: d = 1.432 × 10⁸ m. t = d/c = 1.432 × 10⁸ / 3.00 × 10⁸ = 0.48 s, about half a second, which is noticeable in conversation.
2A 5.0 g bolt hits a satellite at a relative speed of 10 km/s. Find its kinetic energy and the speed of a 1500 kg car with the same energy.
Ek = ½(5.0 × 10⁻³)(1.0 × 10⁴)² = 2.5 × 10⁵ J. Car: v = √(2(2.5 × 10⁵)/1500) = √333 = 18.3 m/s ≈ 66 km/h.
3Give two arguments for and two against allowing many thousands more internet satellites in low orbit.
For (any two): fast internet for remote and northern communities; lower latency than geostationary satellites; backup communications in disasters; economic opportunities. Against (any two): more debris and collision risk; streaks that interfere with astronomy; pollution from launches and re-entries; a few companies controlling key infrastructure.
4Explain why a GPS outage could affect banks, power grids and cellphone networks, even though none of them is "navigating".
They use GPS time signals to synchronize their equipment. Transactions need accurate time stamps, cell towers need to stay in step, and power grids use precise timing to match the phases of their generators and monitor the grid. Without GPS time (and without backups) their clocks would slowly drift apart.
5Superconducting MRI magnets are cooled with liquid helium. Use what you know about escape speed and molecular speeds to explain why released helium is lost from Earth.
Helium atoms are very light, so at a given temperature they move faster than heavier molecules. In the hot, thin upper atmosphere a small fraction of helium atoms reach speeds above Earth's escape speed (about 11 km/s near the surface; see Gravitational Potential Energy, Escape Speed and Black Holes) and leave for good. So helium used and released on Earth is not recovered, which is why recycling it and using less matters.
Challenge
1Two pieces of debris in circular orbits 800 km up cross paths head-on. (a) Find each one's orbital speed. (b) Find the kinetic energy of a 1.0 kg fragment at the closing speed, and compare it with the energy in TNT (about 4.2 × 10⁶ J/kg).
(a) r = 6.37 × 10⁶ + 8.0 × 10⁵ = 7.17 × 10⁶ m. v = √(GM/r) = √(3.982 × 10¹⁴ / 7.17 × 10⁶) = 7.45 × 10³ m/s. (b) Closing speed ≈ 2(7.45 × 10³) = 1.49 × 10⁴ m/s. Ek = ½(1.0)(1.49 × 10⁴)² = 1.1 × 10⁸ J, the energy of roughly 26 kg of TNT.
2The net relativistic gain of a GPS clock is 38 μs per day. (a) What fraction of a day is that? (b) GPS clocks are based on a 10.23 MHz signal. By about how many hertz must that frequency be lowered before launch so that, once in orbit, it appears to be exactly 10.23 MHz from the ground?
(a) 38 × 10⁻⁶ s / 86 400 s = 4.4 × 10⁻¹⁰. (b) Lower it by the same fraction: (10.23 × 10⁶ Hz)(4.4 × 10⁻¹⁰) = 4.5 × 10⁻³ Hz, so the clock is set to about 10.229 999 995 5 MHz. A tiny change, but essential.
3Your regional health authority must choose between (1) buying a medical cyclotron to make PET isotopes locally and (2) continuing to ship isotopes from a city 400 km away. Use the six-step decision process to outline a recommendation.
Sample outline: Issue: how should the region supply PET isotopes? Stakeholders: patients and families, hospital staff, taxpayers, the supplier, nearby residents. Evidence: F-18's half-life is about 110 minutes, so after a 4 to 5 hour trip only roughly a sixth to a quarter is left, cancelled scans when deliveries are late; the cost of a cyclotron, shielding and staff; patient numbers. Benefits and costs: local supply means more scans, shorter waits and new isotopes for research, but high upfront cost, electricity use and a small amount of radioactive waste to manage. Alternatives: share a cyclotron with a neighbouring region; air transport. Decision: for example, "Buy the cyclotron if the region does more than a set number of scans a year, because shipping wastes most of the isotope and delays care; I would change my mind if a shared facility closer than 100 km became available." Any well-supported decision earns full marks.
Check your understandingQuiz
1. Why does a GPS receiver need signals from at least four satellites?
2. Which is the main advantage of radar satellites such as RCM over ordinary cameras?
3. Scientists worry most about space debris because
4. PET isotopes such as fluorine-18 are usually made in cyclotrons close to hospitals because
5. If engineers ignored relativity, GPS positions would drift by roughly
6. Which is an environmental concern linked to large constellations of internet satellites?
For parents and teachersBig idea (D1.2, D1.1): field technologies such as GPS, Earth-observation satellites, internet constellations, accelerators and MRI bring large benefits, but also costs: privacy, dependence, space debris, energy use and waste. Good decisions weigh evidence for everyone affected and compare alternatives.
How to help: The position-paper activity works well as a dinner-table debate. Ask your teen how GPS knows where your phone is, then ask who else might know. Share your own experiences (for example, with satellite internet, weather warnings or medical imaging) without telling them what to conclude.
Common difficulties:
- Giving only benefits or only costs. Ask, "Who would disagree with you, and why?"
- Using opinions without evidence, or unreliable sources.
- Forgetting that the speed of light makes tiny timing errors into large distance errors.
Safety: none for this lesson; encourage careful checking of online sources.