Carbon moves between the atmosphere, oceans, land and rock. Feedbacks decide whether a small push on the climate grows or shrinks.
🏦 Reservoirs and fluxes
A reservoir stores carbon (atmosphere about 850 GtC, ocean about 38 000 GtC, plants and soil, fossil fuels, and carbonate rocks, by far the largest). A flux is the amount moving between reservoirs each year. Residence time = reservoir size ÷ flux out. Fossil-fuel burning moves carbon from a slow reservoir (rock) to a fast one (atmosphere). About half of the added CO₂ is taken up by oceans and land; the rest stays in the air.
atmosphere 800 GtC, flux out 200 GtC/yr
residence time = 800/200 = 4 years
emissions 10 GtC/yr, half stays: 5 GtC/yr
1 ppm ≈ 2 GtC → 5/2 = 2.5 ppm per year
🖼️ See it
Burning fossil fuels moves carbon from slow-cycle storage in rocks into the fast-cycle atmosphere.
🔁 Feedbacks
A positive feedback amplifies change; a negative feedback reduces it. Ice–albedo (positive): warming melts ice, which darkens the surface, which absorbs more heat. Water vapour (positive): a warmer atmosphere holds about 7% more vapour per °C. Permafrost thaw (positive) releases methane and CO₂. Silicate weathering (negative, over geologic time): warmer, wetter climate weathers rock faster and takes up CO₂. Clouds can act either way.
water vapour: +7% per °C
3 °C warmer: ≈ 3 · 7 = 21% more water vapour
feedback loop: warming → ice melts → lower albedo → more absorption → more warming
Tipping points are thresholds beyond which a change becomes self-sustaining or irreversible, such as ice-sheet collapse or dieback of the Amazon.
✏️ Quick check · 1 of 7
Ice–albedo
The ice–albedo feedback is:
It amplifies.
✏️ Quick check · 2 of 7
Largest reservoir
The largest reservoir of carbon on Earth is:
Rock.
✏️ Quick check · 3 of 7
Negative feedback
Silicate weathering is a negative feedback because it:
Takes up CO₂.
✏️ Quick check · 4 of 7
Permafrost
Thawing permafrost is a concern because it:
Stored carbon.
✍️ Type your answer · 5 of 7
The atmosphere holds 800 GtC and 200 GtC leaves it each year.
What is the residence time, in years?
Enter an exact answer, without rounding.
years
reservoir ÷ flux.
✍️ Type your answer · 6 of 7
Emissions are 10 GtC a year and half stays in the air. 1 ppm ≈ 2 GtC.
How many ppm does CO₂ rise per year?
Enter an exact answer, without rounding.
ppm
Half stays: 5 GtC.
✍️ Type your answer · 7 of 7
Warmer air holds 7% more water vapour for each 1 °C.
How many percent more for 3 °C? (approximate, 3 · 7)
Enter an exact answer, without rounding.
%
Multiply.
📝 Lesson quiz · 5 questions
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Question 1 of 5
A positive feedback:
Question 2 of 5
Which is a fast carbon flux?
Question 3 of 5
Oceans take up CO₂ from air by:
Question 4 of 5
Burning fossil fuels transfers carbon from:
Question 5 of 5
A climate tipping point is:
Lesson 2 · Earth history
❄️ Paleoclimate & Orbital Cycles
Earth has swung between ice ages and warm periods. The pacemaker of the recent ice ages is the slow variation of Earth’s orbit.
📜 Reading past climates
Proxies are natural records that stand in for direct measurements: ice cores (trapped air gives CO₂; isotopes give temperature), tree rings, ocean sediments (foraminifera shells record δ¹⁸O and so ice volume), pollen and corals. Ice cores from Antarctica reach back about 800 000 years and show CO₂ always between about 180 ppm (glacials) and 300 ppm (interglacials) before the industrial era.
ice core length 800 000 years, one glacial cycle ≈ 100 000 years
800 000 / 100 000 = 8 cycles
CO₂: 180 → 280 ppm = 100 ppm rise between glacial and interglacial
🖼️ See it
Small, regular changes in Earth’s orbit alter how sunlight is spread over the planet and are the pacemaker of the ice ages.
🔭 Milankovitch cycles
Three orbital changes alter how sunlight is distributed over latitudes and seasons: eccentricity (orbit shape, about 100 000 years), obliquity (axial tilt 22.1°–24.5°, about 41 000 years) and precession (axis wobble, about 23 000 years). Cool northern summers allow snow to survive, and ice–albedo and CO₂ feedbacks then amplify the cooling.
tilt range = 24.5 − 22.1 = 2.4°
410 000 years / 41 000 = 10 tilt cycles
230 000 years / 23 000 = 10 precession cycles
Orbital changes are small; feedbacks (ice, CO₂, albedo) make the climate response large. Today’s CO₂ is far above anything in the last 800 000 years.
✏️ Quick check · 1 of 7
Proxy
A climate proxy is:
Stand-in.
✏️ Quick check · 2 of 7
Ice-core CO₂
Ice cores record past CO₂ because:
Bubbles.
✏️ Quick check · 3 of 7
Obliquity
Obliquity is the:
Tilt.
✏️ Quick check · 4 of 7
Amplification
Why do small orbital changes cause big climate shifts?
Feedbacks.
✍️ Type your answer · 5 of 7
An ice core spans 800 000 years and glacial cycles last about 100 000 years.
How many cycles does it show?
Enter an exact answer, without rounding.
Divide.
✍️ Type your answer · 6 of 7
Earth’s tilt varies from 22.1° to 24.5°.
What is the range, in degrees?
Enter an exact answer, without rounding.
°
Subtract.
✍️ Type your answer · 7 of 7
The obliquity cycle lasts 41 000 years.
How many cycles in 410 000 years?
Enter an exact answer, without rounding.
Divide.
📝 Lesson quiz · 5 questions
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Question 1 of 5
Which orbital cycle is the longest?
Question 2 of 5
Tree rings tell us about:
Question 3 of 5
Glacial periods had CO₂ of about:
Question 4 of 5
δ¹⁸O in foraminifera records mostly:
Question 5 of 5
Which statement about CO₂ today is correct?
Lesson 3 · Geophysics
🧲 Earth’s Magnetism & Sea-Floor Spreading
Earth’s magnetic field comes from moving liquid iron in the core. It protects us, and it leaves a record in rocks that confirmed plate tectonics.
🌀 The geodynamo
Convection of molten iron in the outer core, together with Earth’s rotation, generates the magnetic field (the geodynamo). The field protects the atmosphere from the solar wind and causes auroras. At the surface the field is about 50 μT. The poles wander, and about every few hundred thousand years the field reverses. The last full reversal was about 780 000 years ago.
field at surface ≈ 50 μT = 0.00005 T
last reversal 780 000 years ago
reversal not due on a regular timetable
normal polarity now (called Brunhes) since then
🖼️ See it
Earth’s field has reversed many times, so rock of alternating polarity forms matching stripes on both sides of the ridge, proof of sea-floor spreading.
📏 Magnetic stripes
As lava cools at a mid-ocean ridge, magnetic minerals lock in the field direction at the time (paleomagnetism). Matching stripes of normal and reversed polarity lie symmetrically on both sides of the ridge, which proved sea-floor spreading. The spreading rate is distance ÷ age.
stripe boundary 40 km from the ridge, age 2 million years
rate = 40 km / 2 My = 20 km per My
20 km/My = 2 000 000 cm/1 000 000 yr = 2 cm/yr
full rate = 2 · half rate (both sides)
Compasses point to a magnetic pole, not the geographic one. The gap between them is called magnetic declination.
✏️ Quick check · 1 of 7
Source
Earth’s magnetic field is generated in the:
Liquid metal.
✏️ Quick check · 2 of 7
Auroras
Auroras occur when:
Solar wind.
✏️ Quick check · 3 of 7
Symmetry
Magnetic stripes on both sides of a mid-ocean ridge:
Symmetric.
✏️ Quick check · 4 of 7
Protection
The magnetic field helps protect life by:
Shield.
✍️ Type your answer · 5 of 7
A magnetic stripe boundary is 40 km from a ridge and has an age of 2 million years.
What is the spreading rate, in km per million years?
Enter an exact answer, without rounding.
km/My
distance ÷ age.
✍️ Type your answer · 6 of 7
A rate of 20 km per million years equals how many cm per year? (1 km = 100 000 cm)
Give the number.
Enter an exact answer, without rounding.
cm/yr
Convert units.
✍️ Type your answer · 7 of 7
The half-spreading rate is 2 cm/yr on each side.
What is the full rate of separation, in cm/yr?
Enter an exact answer, without rounding.
cm/yr
Two sides.
📝 Lesson quiz · 5 questions
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Question 1 of 5
Paleomagnetism records:
Question 2 of 5
The magnetic poles:
Question 3 of 5
The field is NOT produced by a:
Question 4 of 5
Sea-floor stripes provided evidence for:
Question 5 of 5
Compasses point to:
Lesson 4 · Planetary science
🪐 Exoplanets & Habitability
Thousands of planets orbit other stars. Scientists find them from tiny dips in starlight and ask which might support life.
🔭 Finding exoplanets
In the transit method, a planet crossing in front of its star blocks a small fraction of the light: depth = (Rplanet / Rstar)². The radial velocity method detects the star’s tiny wobble. The orbital period comes from the time between transits, and from Kepler’s third law the distance follows: T² = a³ for a Sun-like star (years, AU).
Jupiter/Sun radius ratio ≈ 0.1: depth = 0.1² = 0.01 = 1%
Earth/Sun ratio ≈ 0.01: depth = 0.0001 = 0.01%
planet at 0.25 AU: T² = 0.25³ = 1/64
T = 1/8 = 0.125 years ≈ 46 days
🖼️ See it
When an exoplanet passes in front of its star the brightness dips slightly. The depth shows the planet’s size and the spacing of dips its orbital period.The habitable zone is the range of distances where liquid water could exist on a planet’s surface.
🌱 The habitable zone
The habitable zone is the range of orbital distances where a planet could have liquid surface water. The flux a planet receives follows the inverse-square law: flux ∝ 1/d². Atmosphere (greenhouse effect), size, magnetic field and the star’s type and age also matter. Red dwarfs are common and long-lived, but their habitable zones are close in, so planets there are often tidally locked and exposed to flares.
Earth 1 AU: flux 1
Mars 1.5 AU: 1/1.5² = 1/2.25 ≈ 0.44
2 AU: 1/4 = 0.25 of Earth’s flux
brighter star → habitable zone further out
“Habitable” does not mean “inhabited.” It only says surface water is possible. Life itself is searched for by looking at atmospheres for gases like oxygen and methane together.
✏️ Quick check · 1 of 7
Transit
In a transit, the star’s light:
Dimming.
✏️ Quick check · 2 of 7
Habitable zone
The habitable zone is where a planet could have:
Liquid water.
✏️ Quick check · 3 of 7
Brighter stars
The habitable zone of a brighter star is:
Farther.
✏️ Quick check · 4 of 7
Red dwarfs
A planet in a red dwarf’s habitable zone is likely:
One face always toward the star.
✍️ Type your answer · 5 of 7
A planet has a radius one tenth of its star’s radius (ratio 0.1). Depth = ratio squared.
What is the transit depth, in %? (0.1² = 0.01)
Enter an exact answer, without rounding.
%
Square and ×100.
✍️ Type your answer · 6 of 7
A planet orbits a Sun-like star at 4 AU. T² = 4³ = 64.
What is its period, in years?
Enter an exact answer, without rounding.
years
Square root.
✍️ Type your answer · 7 of 7
Flux ∝ 1/d². A planet orbits at 2 AU from a Sun-like star.
What fraction of Earth’s flux does it receive? (1/4)
Enter an exact answer, without rounding.
Inverse square.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The transit method finds planets by:
Question 2 of 5
The inverse-square law says that doubling the distance:
Question 3 of 5
Which factor does NOT directly affect habitability?
Question 4 of 5
The radial velocity method detects:
Question 5 of 5
Biosignature gases could include:
Lesson 5 · Systems
🌍 Earth Systems & Sustainability
The atmosphere, oceans, land, ice and life interact as one system. Sustainability means staying within the limits that system sets.
📦 Stocks, flows and growth
A system has stocks (amounts) and flows (rates). If inflow equals outflow the stock is in steady state. Residence time = stock ÷ flow. A quantity growing at r% a year doubles in about 70 ÷ r years (the Rule of 70). Exponential growth in a finite system cannot last.
lake 600 km³, outflow 30 km³/yr: residence time = 600/30 = 20 years
growth 2% a year: doubling time = 70/2 = 35 years
growth 3.5%: 70/3.5 = 20 years
🖼️ See it
The four spheres exchange matter and energy, so a change in one, such as burning fossil fuels, affects the others.
🌱 Limits and planetary boundaries
Planetary boundaries are limits for key Earth-system processes (climate, biodiversity, nitrogen and phosphorus, land use, freshwater, ozone, ocean acidification) within which humanity can operate safely. The ecological footprint compares demand on nature with what Earth regenerates; humanity currently uses about 1.7 Earths worth each year. Sustainable yield means harvesting no more than the resource regrows.
stock 1000 units, regrows 5% a year: max sustainable harvest = 0.05 · 1000 = 50 units/yr
harvest 80 → stock falls by 30 units a year
footprint 1.7 Earths: overshoot = 1.7 − 1 = 0.7 Earth
Circular economy: design out waste, keep materials in use and regenerate natural systems.
✏️ Quick check · 1 of 7
Steady state
A system is in steady state when:
Balanced.
✏️ Quick check · 2 of 7
Sustainable harvest
A sustainable harvest is:
Keep the stock.
✏️ Quick check · 3 of 7
Boundaries
Planetary boundaries describe:
Limits.
✏️ Quick check · 4 of 7
Exponential growth
Exponential growth in a finite system:
Limits exist.
✍️ Type your answer · 5 of 7
A lake holds 600 km³ and loses 30 km³ each year.
What is the residence time, in years?
Enter an exact answer, without rounding.
years
stock ÷ flow.
✍️ Type your answer · 6 of 7
A population grows at 2% a year. Use the Rule of 70.
How many years to double?
Enter an exact answer, without rounding.
years
Divide 70 by the rate.
✍️ Type your answer · 7 of 7
A fishery stock of 1000 units regrows 5% a year.
What is the maximum sustainable harvest, in units a year?
Enter an exact answer, without rounding.
units
Multiply.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The Rule of 70 gives approximate:
Question 2 of 5
An ecological footprint of 1.7 Earths means humanity is:
Question 3 of 5
Which is an example of a stock?
Question 4 of 5
A circular economy aims to:
Question 5 of 5
Eutrophication from fertiliser is linked to the boundary for:
Lesson 6 · Technology
🛰️ Remote Sensing & Earth Observation
Satellites watch the planet continuously. Their images and measurements track forests, ice, oceans, cities and weather.
📡 How satellites see
Satellites detect electromagnetic radiation reflected or emitted by the surface. Passive sensors use sunlight or thermal emission; active sensors (radar, lidar) send their own pulse and time the echo. Resolution is the size of the smallest feature, the pixel. Geostationary satellites (about 36 000 km) hover over one place; polar orbiters (about 800 km) scan the whole globe. GPS finds position from signal travel times.
radar echo distance = (c · t)/2
GPS signal time 0.07 s: d = 300 000 · 0.07 = 21 000 km
10 m pixels, 1 km² square (1000 m side): 100 · 100 = 10 000 pixels
🖼️ See it
Different surfaces reflect different wavelengths, so healthy vegetation, water and bare soil can be told apart from space.
🌿 Reading the images
Healthy plants reflect much near-infrared and absorb red light. The NDVI (vegetation index) = (NIR − Red) ÷ (NIR + Red) ranges from −1 to +1; dense healthy vegetation is near 0.6–0.9, bare soil near 0.1 and water is negative. False-colour images assign visible colours to invisible bands. Time series show deforestation, ice melt, urban growth and crop health.
NIR = 0.6, Red = 0.2:
NDVI = (0.6 − 0.2)/(0.6 + 0.2) = 0.4/0.8 = 0.5
glacier retreat: 1.2 km in 24 years = 1.2/24 = 0.05 km/yr = 50 m/yr
Ground truth matters: scientists check satellite results against measurements on the ground.
✏️ Quick check · 1 of 7
Active sensor
Which sensor is active?
Sends a signal.
✏️ Quick check · 2 of 7
NDVI
A high NDVI value indicates:
Green plants.
✏️ Quick check · 3 of 7
Geostationary
A geostationary satellite:
Hovers.
✏️ Quick check · 4 of 7
Resolution
A 10 m resolution image can show features:
Pixel size.
✍️ Type your answer · 5 of 7
A GPS signal takes 0.07 s to reach a receiver. Light travels 300 000 km/s.
How far has it travelled, in km?
Enter an exact answer, without rounding.
km
distance = speed · time.
✍️ Type your answer · 6 of 7
NIR reflectance is 0.6 and Red reflectance is 0.2. NDVI = (NIR − Red)/(NIR + Red).
What is the NDVI?
Enter an exact answer, without rounding.
Compute carefully.
✍️ Type your answer · 7 of 7
An image has 10 m pixels. A square 1 km (1000 m) on a side.
How many pixels cover it?
Enter an exact answer, without rounding.
pixels
100 pixels each way.
📝 Lesson quiz · 5 questions
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Question 1 of 5
Lidar measures:
Question 2 of 5
Polar-orbiting satellites are useful because they:
Question 3 of 5
Satellites track deforestation by:
Question 4 of 5
Ground truth is:
Question 5 of 5
Which is NOT a type of remote sensing?
Final Challenge
🏆 12-Question Challenge Quiz
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
0 / 12
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · The Carbon Cycle & Feedbacks
Residence time of a reservoir is:
Q2 · The Carbon Cycle & Feedbacks
A climate tipping point is:
Q3 · Paleoclimate & Orbital Cycles
The main driver that starts glacial–interglacial cycles is:
Q4 · Paleoclimate & Orbital Cycles
Which statement about CO₂ today is correct?
Q5 · Earth’s Magnetism & Sea-Floor Spreading
The geodynamo needs:
Q6 · Earth’s Magnetism & Sea-Floor Spreading
Compasses point to:
Q7 · Exoplanets & Habitability
The first step to calculating a planet’s distance from the transit method is finding its:
Q8 · Exoplanets & Habitability
Biosignature gases could include:
Q9 · Earth Systems & Sustainability
Harvesting more than the regrowth each year will:
Q10 · Earth Systems & Sustainability
Eutrophication from fertiliser is linked to the boundary for: