# Moving Diagrams > Interactive explainers on science, maths and how things work: simulations you can play with, short videos, and every number sourced. Each explainer is an interactive simulation with short chapters, a narrated "watch" mode, and a list of sources. Every number traces to a cited source; where a visual is simplified or exaggerated, the page says so. Videos: https://www.youtube.com/@movingdiagrams ## Explainers - [How GPS Needs Einstein's Relativity](https://movingdiagrams.com/topics/gps-relativity/): GPS satellite clocks gain about 38 microseconds a day because of relativity. Without correcting it, your position would drift by around 10 km a day. See why, step by step. - [How the Heart Pumps: the Cardiac Cycle, Explained](https://movingdiagrams.com/topics/heart/): An interactive explainer of the cardiac cycle: how the SA node times each beat, what the ECG's P, QRS and T waves mean, and how about 70 mL leaves the heart with every beat. - [How Black Holes Bend Light (and Why the First Image Is a Ring)](https://movingdiagrams.com/topics/black-holes/): Why the first picture of a black hole shows a glowing ring, not a black dot: light bending, the photon sphere and the shadow, with a live ray-traced black hole you can explore. - [Why Is the Sky Blue? An Interactive Explainer](https://movingdiagrams.com/topics/sky/): Why the sky is blue and sunsets are red, with a live, physically based sky you can control: Rayleigh scattering, air mass at sunset, altitude and haze. - [Compound Interest, Explained Interactively](https://movingdiagrams.com/topics/compound-interest/): See compound interest work: $100 at 10% for 30 years becomes $1,745, the rule of 72, where the number e came from, and Benjamin Franklin's 200-year bet. Example rates, not advice. - [Solar Eclipses, and the Total Eclipse of 2 August 2027](https://movingdiagrams.com/topics/solar-eclipse/): Drag the Moon over the Sun, see why it fits so exactly, follow the 2 August 2027 total eclipse across Spain and Egypt (6 min 23 s of totality), and find the next eclipse near you. ## How GPS Needs Einstein's Relativity URL: https://movingdiagrams.com/topics/gps-relativity/ ### Why does GPS need relativity? GPS satellites orbit about 20,200 km up at about 3.9 km/s. Their speed makes their clocks run slow by about 7 microseconds a day (special relativity), and the weaker gravity up there makes them run fast by about 45 (general relativity). The net effect is about +38 microseconds a day. ### How big would the error be without the correction? Light travels about 30 cm per nanosecond, so 38 microseconds a day is roughly 11 km of ranging error a day. Neil Ashby's analysis puts the gravitational term alone at about 13.7 km a day. ### How is it corrected? Before launch, each satellite clock is set slightly slow, to 10.22999999543 MHz, so that from the ground it ticks at exactly 10.23 MHz. Receivers also correct a small extra term from the orbit's eccentricity. Sources: - [GPS.gov: Space Segment](https://www.gps.gov/systems/gps/space) - [Penn State GEOG 862: The Satellite Clock](https://www.e-education.psu.edu/geog862/node/1714) - [N. Ashby: Relativistic Effects in the Global Positioning System (AAPT)](https://www.aapt.org/doorway/tgru/articles/ashbyarticle.pdf) - [N. Ashby (2003): Relativity in the Global Positioning System, Living Reviews in Relativity 6](https://link.springer.com/article/10.12942/lrr-2003-1) - [National Academies (1995): GPS technical overview](https://www.nationalacademies.org/read/4920/chapter/89) ## How the Heart Pumps: the Cardiac Cycle, Explained URL: https://movingdiagrams.com/topics/heart/ ### What sets the heartbeat? The sinoatrial (SA) node in the right atrium fires first. The signal spreads across the atria, pauses at the atrioventricular (AV) node so the ventricles can finish filling, then races down the bundle of His and Purkinje fibres. ### How long is one heartbeat? At about 75 beats a minute a cycle lasts 0.8 s: roughly 0.1 s of atrial contraction, 0.3 s of ventricular contraction and 0.4 s of relaxation. ### How much blood does each beat pump? At rest, about 70 mL per beat (stroke volume), which at 70–75 beats a minute is about 5 litres a minute. ### What makes the lub-dub sound? “Lub” is the AV valves (tricuspid and mitral) closing as the ventricles start to contract; “dub” is the aortic and pulmonary valves closing as they relax. Sources: - [OpenStax Anatomy & Physiology 2e, 19.3 Cardiac Cycle](https://openstax.org/books/anatomy-and-physiology-2e/pages/19-3-cardiac-cycle) - [NHLBI: How the Heart Works](https://www.nhlbi.nih.gov/health/heart) - [Cardiac cycle lecture (University of Al-Mustaqbal)](https://www.uomus.edu.iq/img/lectures21/MUCLecture_2024_102449662.pdf) - [A&P lecture: Heart, cardiac cycle (mc3cb)](https://mc3cb.com/pdf_ap_lectures/C19_3_heart_cardiac_cycle_2025_10_30.pdf) ## How Black Holes Bend Light (and Why the First Image Is a Ring) URL: https://movingdiagrams.com/topics/black-holes/ ### Why does a black hole image look like a ring? Gravity bends light around the black hole. Light that passes close to the photon sphere (1.5 times the event-horizon radius) is bent towards us from every side, outlining a dark “shadow” about 2.6 times wider than the horizon itself. ### How big is the M87* ring? The Event Horizon Telescope measured a ring about 42 microarcseconds across in 2017 data, around a black hole of about 6.5 billion solar masses, 55 million light-years away. ### Why is one side of the ring brighter? Gas moving towards us is brightened by relativistic Doppler beaming, so the side rotating towards Earth looks brighter. ### How was the image taken? The EHT linked radio dishes across the planet into an Earth-sized virtual telescope observing at 1.3 mm, giving a resolution of about 20 microarcseconds. Sources: - [Event Horizon Telescope Collaboration (2019): First M87 EHT Results. I. The Shadow of the Supermassive Black Hole](https://iopscience.iop.org/article/10.3847/2041-8213/ab0ec7) - [AAS Nova: First images of a black hole from the Event Horizon Telescope](https://aasnova.org/2019/04/10/first-images-of-a-black-hole-from-the-event-horizon-telescope/) - [Narayan, Johnson & Gammie (2019): The Shadow of a Spherically Accreting Black Hole](https://arxiv.org/abs/1910.02957) - [UNLV: Black hole shadow notes](https://www.physics.unlv.edu/~jeffery/astro/black_hole/black_hole_shadow.html) ## Why Is the Sky Blue? An Interactive Explainer URL: https://movingdiagrams.com/topics/sky/ ### Why is the sky blue? Air molecules scatter short wavelengths far more than long ones (Rayleigh scattering, proportional to 1/λ⁴). Blue light at 450 nm is scattered about 5.9 times more than red at 700 nm, so blue reaches you from every direction. ### Why isn't the sky violet? The Sun emits less violet than blue, and our eyes are less sensitive to violet, so the scattered mix looks blue. ### Why are sunsets red? Near the horizon, sunlight crosses about 38 times as much air as at noon. Most blue is scattered out along the way, leaving reds and oranges. ### Why are clouds white? Cloud droplets (around 10 µm) are much larger than light waves, so they scatter all colours about equally (Mie scattering). Sources: - [Wikipedia: Rayleigh scattering](https://en.wikipedia.org/wiki/Rayleigh_scattering) - [NASA SpacePlace: Why is the sky blue?](https://spaceplace.nasa.gov/blue-sky/en/) - [Live Science: Why is the sky blue?](https://www.livescience.com/planet-earth/why-is-the-sky-blue) - [Wikipedia: Air mass (astronomy), Kasten & Young formula](https://en.wikipedia.org/wiki/Air_mass_(astronomy)) - [NOAA: Why are clouds white?](https://noaa.gov/node/10326) - [E. Bruneton: Precomputed Atmospheric Scattering (model parameters)](https://ebruneton.github.io/precomputed_atmospheric_scattering/atmosphere/demo/demo.cc.html) ## Compound Interest, Explained Interactively URL: https://movingdiagrams.com/topics/compound-interest/ ### What is compound interest? Interest that is added to the balance and then earns interest itself. $100 at 10% a year for 30 years grows to about $1,745 compounded, against $400 with simple interest (example rate). ### What is the rule of 72? Divide 72 by the yearly rate in percent to estimate the years to double: at 6% about 12 years (exact: 11.9). Its earliest known written use is Luca Pacioli's Summa de arithmetica (1494). ### Where does the number e come from? In 1683 Jacob Bernoulli asked how $1 at 100% grows if interest is paid in ever smaller slices: $2 yearly, $2.25 twice a year, $2.61 monthly, $2.71 daily, approaching e = 2.71828… ### Did Einstein call compound interest the eighth wonder of the world? There's no evidence he did. The line first appears in an unsigned 1925 bank advert; the first known Einstein attribution is from 1988. Sources: - [Quote Investigator: The Eighth Wonder of the World Is Compound Interest](https://quoteinvestigator.com/2019/09/09/interest/) - [Wikipedia: e (mathematical constant)](https://en.wikipedia.org/wiki/E_(mathematical_constant)) - [Britannica: e](https://www.britannica.com/topic/e-mathematics) - [Wikipedia: Rule of 72 (Pacioli, Summa de arithmetica, 1494)](https://en.wikipedia.org/wiki/Rule_of_72) - [City of Boston Archives: Guide to the Franklin Fund records](https://www.cityofboston.gov/images_documents/Guide%20to%20the%20Franklin%20Fund%20records_tcm3-20691.pdf) - [Franklin's codicil (text), ExplorePAhistory](https://explorepahistory.com/odocument.php?docId=1-4-2DE) - [Snopes: Ben Franklin's bequest (citing the New York Times, 1990)](https://www.snopes.com/fact-check/ben-franklin-2000-dollars/) - [Federal Reserve G.19: Consumer Credit (credit-card interest rates)](https://www.federalreserve.gov/releases/g19/current/) ## Solar Eclipses, and the Total Eclipse of 2 August 2027 URL: https://movingdiagrams.com/topics/solar-eclipse/ ### When is the next total solar eclipse? On 2 August 2027 the Moon's shadow crosses Morocco, southern Spain, Algeria, Libya, Egypt, Saudi Arabia, Yemen and Somalia. Totality lasts up to 6 minutes 23 seconds, near Luxor, Egypt (NASA). ### How long is totality on 2 August 2027? Computed from NASA's eclipse elements: about 6 min 20 s in Luxor, 6 min 09 s in Benghazi, 4 min 50 s in Tangier and 2 min 52 s in Cádiz. The path of totality is about 258 km wide. ### Why isn't there an eclipse every month? The Moon's orbit is tilted about 5.1° to Earth's, so most new moons pass above or below the Sun. Eclipses happen only when a new moon falls near a node, in eclipse seasons about every six months: 2 to 5 solar eclipses a year. ### Why does the Moon fit the Sun so exactly? The Sun is about 400 times wider than the Moon and about 390 times farther away. The Moon is moving away by 3.8 cm a year, so in roughly 600 million years total eclipses will start to run out. ### When is it safe to look at an eclipse? Only during totality, when the Moon completely covers the Sun (NASA). Before and after, use eclipse glasses that meet ISO 12312-2. Sources: - [NASA/GSFC (F. Espenak): Besselian elements, total solar eclipse of 2027 Aug 02](https://eclipse.gsfc.nasa.gov/SEsearch/SEdata.php?Ecl=+20270802) - [EclipseWise: Total solar eclipse of 2027 Aug 02](https://eclipsewise.com/solar/SEprime/2001-2100/SE2027Aug02Tprime.html) - [NASA: Moon fact sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html) - [NASA: Sun fact sheet](https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html) - [NASA: Eclipse safety](https://science.nasa.gov/eclipses/safety/) - [NASA SVS: Lunar eclipses and the Moon’s orbit](https://svs.gsfc.nasa.gov/4158/) - [NASA SVS: Discovering the Sun’s mysteriously hot atmosphere](https://svs.gsfc.nasa.gov/12903) - [Sky & Telescope: When will the last total solar eclipse occur?](https://skyandtelescope.org/astronomy-resources/astronomy-questions-answers/when-will-the-last-total-solar-eclipse-occur/) - [Astronomy.com: How often do solar eclipses occur?](https://www.astronomy.com/observing/how-often-do-solar-eclipses-occur/) - [Wikipedia: Baily's beads](https://en.wikipedia.org/wiki/Baily%27s_beads) - [NASA Eclipse 2017: Lunar shadow speed](https://eclipse2017.nasa.gov/lunar-shadow-speed) - [astronomy-engine (D. Cross): eclipse search used for “When’s yours?”](https://github.com/cosinekitty/astronomy) - [NASA: ΔT and the uncertainty of future eclipse paths](https://eclipse.gsfc.nasa.gov/SEhelp/deltaT.html) - [Natural Earth (via world-atlas): coastlines and borders](https://www.naturalearthdata.com/)