{"id":1814,"date":"2026-08-29T20:25:44","date_gmt":"2026-08-29T20:25:44","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=1814"},"modified":"2026-08-29T20:25:48","modified_gmt":"2026-08-29T20:25:48","slug":"law-of-gravitation","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/law-of-gravitation\/","title":{"rendered":"Newton&#8217;s Law of Gravitation"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nThe law of gravitation states that every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres. Written as an equation, F equals G times m1 times m2 divided by r squared, where G is the gravitational constant.\n<\/p><\/div>\n\n<p>Drop your phone and it falls. Look up, and the Moon does not. For most of human history those looked like two different kinds of event \u2014 earthly things fell, heavenly things circled, and nobody expected one rule to cover both.<\/p>\n\n<p>Newton&#8217;s claim was that they are the same event. The Moon <em>is<\/em> falling; it simply travels sideways fast enough to keep missing the Earth. One equation handles the phone, the Moon and the galaxy.<\/p>\n\n<h2>What Is the Law of Gravitation?<\/h2>\n\n<p>The law of gravitation is Newton&#8217;s statement that any two masses attract each other along the line joining them, with a force that grows in proportion to both masses and shrinks with the square of the distance between them. It applies to every pair of masses in the universe \u2014 hence <em>universal<\/em>.<\/p>\n\n<p>That word carries the whole argument. Newton was not claiming to have found a new force; he was claiming that the force already known to make apples fall was the <em>same<\/em> force keeping planets in their orbits.<\/p>\n\n<h3>What the law actually asserts<\/h3>\n\n<ul>\n<li><strong>It is always attractive.<\/strong> There is no negative mass and no gravitational repulsion \u2014 unlike electric charge, gravity only ever pulls.<\/li>\n<li><strong>It acts along the line of centres.<\/strong> The force on each body points straight at the other.<\/li>\n<li><strong>It is a mutual pair.<\/strong> Both bodies feel the same size of force in opposite directions.<\/li>\n<li><strong>It never reaches zero.<\/strong> The force weakens with distance but has no cut-off range.<\/li>\n<\/ul>\n\n<p>One technical caveat matters for problem-solving. The formula is written for <em>point masses<\/em>, yet Newton proved that a uniform sphere pulls on outside objects exactly as though all its mass sat at its centre.<\/p>\n\n<p>That result is why you can treat the Earth as a 5.97 \u00d7 10<sup>24<\/sup> kg dot 6371 km beneath your feet and still get the right answer.<\/p>\n\n<h2>The Law of Gravitation Formula<\/h2>\n\n<p>The law of gravitation formula gives the attractive force between two masses as the product of the masses divided by the square of their separation, scaled by the gravitational constant G.<\/p>\n\n<div class=\"pf-formula\">F = G m<sub>1<\/sub> m<sub>2<\/sub> \/ r\u00b2<\/div>\n\n<p>Every symbol, with its SI unit:<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Symbol<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Quantity<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">SI unit<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Notes<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\"><strong>F<\/strong><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Gravitational force<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">newton (N)<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Same magnitude on both bodies<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\"><strong>G<\/strong><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Gravitational constant<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">N\u00b7m\u00b2\/kg\u00b2<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">6.674 \u00d7 10<sup>\u221211<\/sup>, the same everywhere<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\"><strong>m<sub>1<\/sub>, m<sub>2<\/sub><\/strong><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">The two masses<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">kilogram (kg)<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Never grams \u2014 convert first<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\"><strong>r<\/strong><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Centre-to-centre distance<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">metre (m)<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Not surface-to-surface<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Two traps live in that table. Masses must be in kilograms, and <strong>r<\/strong> is measured centre to centre \u2014 a satellite 400 km up sits 6771 km from the Earth&#8217;s centre, not 400 km.<\/p>\n\n<p>Once the units are right the arithmetic is routine, and you can check any answer against our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/gravitational-force\">Gravitational Force Calculator<\/a>, which rearranges the same equation to solve for the force, either mass or the separation.<\/p>\n\n<h3>Where G comes from<\/h3>\n\n<p>G is not derived from anything \u2014 it is measured. The instrument that made it possible was a torsion balance designed by John Michell, in which heavy lead spheres twist a delicately suspended dumbbell through a tiny, readable angle.<\/p>\n\n<p>Here is the detail most textbooks get wrong. Michell died before he could use it, and when Henry Cavendish finally ran the experiment in 1798 he was not chasing G at all \u2014 his paper is titled <em>Experiments to determine the Density of the Earth<\/em>, and his answer was that the Earth is 5.48 times as dense as water.<\/p>\n\n<p>A value for G was only extracted from measurements of this kind decades later, once physicists began treating it as a constant worth knowing in its own right. Cavendish supplied the experiment; the constant came afterwards.<\/p>\n\n<p>The currently accepted value is 6.67430 \u00d7 10<sup>\u221211<\/sup> N\u00b7m\u00b2\/kg\u00b2, published in the <a href=\"https:\/\/physics.nist.gov\/cuu\/Constants\/index.html\" target=\"_blank\" rel=\"noopener\">CODATA set maintained by NIST<\/a>. It is the least precisely known of the major constants, which tells you how stubbornly weak gravity is to measure.<\/p>\n\n<svg viewBox=\"0 0 700 460\" role=\"img\" aria-label=\"Diagram of the law of gravitation showing two masses attracting each other and a graph of force falling off as one over r squared\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:28px auto;\">\n  <rect x=\"0\" y=\"0\" width=\"700\" height=\"460\" fill=\"#F5F2EA\" rx=\"4\"><\/rect>\n\n  <text x=\"350\" y=\"34\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#7A1F2B\" text-anchor=\"middle\">Equal pull, opposite directions<\/text>\n\n  <circle cx=\"150\" cy=\"115\" r=\"30\" fill=\"#0A1628\"><\/circle>\n  <circle cx=\"530\" cy=\"115\" r=\"52\" fill=\"#142139\"><\/circle>\n  <text x=\"150\" y=\"176\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"16\" fill=\"#0A1628\" text-anchor=\"middle\">m<tspan font-size=\"11\" dy=\"4\">1<\/tspan><\/text>\n  <text x=\"530\" y=\"192\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"16\" fill=\"#0A1628\" text-anchor=\"middle\">m<tspan font-size=\"11\" dy=\"4\">2<\/tspan><\/text>\n\n  <line x1=\"150\" y1=\"115\" x2=\"530\" y2=\"115\" stroke=\"#C5D0DC\" stroke-width=\"1.5\" stroke-dasharray=\"5 4\"><\/line>\n\n  <line x1=\"188\" y1=\"115\" x2=\"268\" y2=\"115\" stroke=\"#C8932A\" stroke-width=\"5\"><\/line>\n  <polygon points=\"286,115 264,105 264,125\" fill=\"#C8932A\"><\/polygon>\n  <line x1=\"492\" y1=\"115\" x2=\"412\" y2=\"115\" stroke=\"#C8932A\" stroke-width=\"5\"><\/line>\n  <polygon points=\"394,115 416,105 416,125\" fill=\"#C8932A\"><\/polygon>\n\n  <text x=\"232\" y=\"98\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"16\" font-weight=\"700\" fill=\"#7A1F2B\" text-anchor=\"middle\">F<\/text>\n  <text x=\"448\" y=\"98\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"16\" font-weight=\"700\" fill=\"#7A1F2B\" text-anchor=\"middle\">F<\/text>\n\n  <line x1=\"150\" y1=\"210\" x2=\"530\" y2=\"210\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <line x1=\"150\" y1=\"202\" x2=\"150\" y2=\"218\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <line x1=\"530\" y1=\"202\" x2=\"530\" y2=\"218\" stroke=\"#0A1628\" stroke-width=\"1.5\"><\/line>\n  <rect x=\"316\" y=\"196\" width=\"48\" height=\"28\" fill=\"#F5F2EA\"><\/rect>\n  <text x=\"340\" y=\"217\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#0A1628\" text-anchor=\"middle\">r<\/text>\n  <text x=\"340\" y=\"243\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\">centre to centre<\/text>\n\n  <line x1=\"40\" y1=\"262\" x2=\"660\" y2=\"262\" stroke=\"#D9CFB8\" stroke-width=\"1.5\"><\/line>\n  <text x=\"350\" y=\"292\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#7A1F2B\" text-anchor=\"middle\">Double the distance, quarter the force<\/text>\n\n  <line x1=\"150\" y1=\"420\" x2=\"620\" y2=\"420\" stroke=\"#0A1628\" stroke-width=\"2\"><\/line>\n  <line x1=\"150\" y1=\"420\" x2=\"150\" y2=\"310\" stroke=\"#0A1628\" stroke-width=\"2\"><\/line>\n\n  <polyline fill=\"none\" stroke=\"#C8932A\" stroke-width=\"3.5\" stroke-linejoin=\"round\" points=\"180.0,320.0 183.6,323.8 187.1,327.5 190.7,330.9 194.3,334.2 197.8,337.2 201.4,340.1 205.0,342.9 208.5,345.5 212.1,348.0 215.7,350.3 219.2,352.6 222.8,354.7 226.4,356.8 229.9,358.7 233.5,360.6 237.1,362.4 240.6,364.1 244.2,365.7 247.8,367.2 251.4,368.7 254.9,370.1 258.5,371.5 262.1,372.8 265.6,374.1 269.2,375.3 272.8,376.4 276.3,377.6 279.9,378.6 283.5,379.7 287.0,380.7 290.6,381.6 294.2,382.6 297.7,383.4 301.3,384.3 304.9,385.1 308.4,385.9 312.0,386.7 315.6,387.5 319.1,388.2 322.7,388.9 326.3,389.6 329.8,390.2 333.4,390.9 337.0,391.5 340.5,392.1 344.1,392.6 347.7,393.2 351.2,393.7 354.8,394.3 358.4,394.8 361.9,395.3 365.5,395.7 369.1,396.2 372.6,396.7 376.2,397.1 379.8,397.5 383.4,398.0 386.9,398.4 390.5,398.8 394.1,399.1 397.6,399.5 401.2,399.9 404.8,400.2 408.3,400.6 411.9,400.9 415.5,401.2 419.0,401.5 422.6,401.9 426.2,402.2 429.7,402.5 433.3,402.7 436.9,403.0 440.4,403.3 444.0,403.6 447.6,403.8 451.1,404.1 454.7,404.3 458.3,404.6 461.8,404.8 465.4,405.0 469.0,405.3 472.5,405.5 476.1,405.7 479.7,405.9 483.2,406.1 486.8,406.3 490.4,406.5 493.9,406.7 497.5,406.9 501.1,407.1 504.6,407.3 508.2,407.5 511.8,407.6 515.4,407.8 518.9,408.0 522.5,408.1 526.1,408.3 529.6,408.4 533.2,408.6 536.8,408.8 540.3,408.9 543.9,409.0 547.5,409.2 551.0,409.3 554.6,409.5 558.2,409.6 561.7,409.7 565.3,409.9 568.9,410.0 572.4,410.1 576.0,410.2\"><\/polyline>\n\n  <line x1=\"180\" y1=\"320\" x2=\"180\" y2=\"420\" stroke=\"#C5D0DC\" stroke-width=\"1.2\" stroke-dasharray=\"4 4\"><\/line>\n  <line x1=\"360\" y1=\"395\" x2=\"360\" y2=\"420\" stroke=\"#C5D0DC\" stroke-width=\"1.2\" stroke-dasharray=\"4 4\"><\/line>\n  <line x1=\"540\" y1=\"409\" x2=\"540\" y2=\"420\" stroke=\"#C5D0DC\" stroke-width=\"1.2\" stroke-dasharray=\"4 4\"><\/line>\n\n  <circle cx=\"180\" cy=\"320\" r=\"6\" fill=\"#7A1F2B\"><\/circle>\n  <circle cx=\"360\" cy=\"395\" r=\"6\" fill=\"#7A1F2B\"><\/circle>\n  <circle cx=\"540\" cy=\"409\" r=\"6\" fill=\"#7A1F2B\"><\/circle>\n\n  <text x=\"180\" y=\"440\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" fill=\"#0A1628\" text-anchor=\"middle\">r<\/text>\n  <text x=\"360\" y=\"440\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" fill=\"#0A1628\" text-anchor=\"middle\">2r<\/text>\n  <text x=\"540\" y=\"440\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" fill=\"#0A1628\" text-anchor=\"middle\">3r<\/text>\n\n  <text x=\"199\" y=\"314\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">F<\/text>\n  <text x=\"378\" y=\"390\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">F\/4<\/text>\n  <text x=\"558\" y=\"404\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#7A1F2B\">F\/9<\/text>\n\n  <text x=\"104\" y=\"318\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"14\" fill=\"#0A1628\" text-anchor=\"middle\">force<\/text>\n  <text x=\"614\" y=\"442\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"14\" fill=\"#0A1628\" text-anchor=\"middle\">distance<\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">The two forces are always equal in size and opposite in direction, and the strength collapses as 1\/r\u00b2.<\/p>\n\n<h2>How the Inverse-Square Rule Works<\/h2>\n\n<p>Gravity weakens with the square of distance because the influence of a mass spreads out over the surface of an ever-larger sphere. The area of that sphere is 4\u03c0r\u00b2, so at twice the distance the same total influence is thinned across four times the area.<\/p>\n\n<p>This is the same geometry that governs light from a bulb and sound from a speaker. Move twice as far from a lamp and it looks a quarter as bright \u2014 not half.<\/p>\n\n<p>The consequences are dramatic and easy to underestimate:<\/p>\n\n<ul>\n<li>Triple the separation and the force drops to <strong>one ninth<\/strong>.<\/li>\n<li>Halve the separation and the force jumps to <strong>four times<\/strong> its old value.<\/li>\n<li>Ten times further apart means <strong>one hundredth<\/strong> the pull.<\/li>\n<\/ul>\n\n<p>Notice what the rule does <em>not<\/em> say. Mass enters linearly, so doubling one mass simply doubles the force \u2014 only distance gets the squaring.<\/p>\n\n<p>In practice this asymmetry is what makes orbits stable and tides sharp. A body slightly closer to a planet feels a noticeably stronger tug than one slightly further away, and that difference is the entire origin of tidal stretching.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Universal Gravitation Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/universal-gravitation.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>Why Is Gravity So Weak Yet So Dominant?<\/h2>\n\n<p>Gravity is by far the weakest of the four fundamental interactions, but it dominates the universe at large scales because it never cancels out. Electric charge comes in two signs that neutralise each other; mass comes in only one sign, so gravity always accumulates.<\/p>\n\n<p>The size of the gap is hard to overstate. Between two protons, the electrostatic repulsion is roughly 10<sup>36<\/sup> times the gravitational attraction \u2014 a one with thirty-six zeros after it.<\/p>\n\n<p>Put a number on it closer to home. Two 70 kg people standing a metre apart attract each other with about 3.3 \u00d7 10<sup>\u22127<\/sup> N, some two billion times weaker than the pull the Earth exerts on either of them.<\/p>\n\n<p>So why does gravity run the cosmos? Because a star has no negative mass to cancel its positive mass, while a star-sized ball of charge would neutralise itself almost instantly.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Feature<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Law of gravitation<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Coulomb&#8217;s law<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Equation<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">F = G m<sub>1<\/sub>m<sub>2<\/sub> \/ r\u00b2<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">F = k q<sub>1<\/sub>q<sub>2<\/sub> \/ r\u00b2<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Source quantity<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Mass, always positive<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Charge, positive or negative<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Direction<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Attractive only<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Attractive or repulsive<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Constant<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">G = 6.674 \u00d7 10<sup>\u221211<\/sup> N\u00b7m\u00b2\/kg\u00b2<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">k = 8.99 \u00d7 10<sup>9<\/sup> N\u00b7m\u00b2\/C\u00b2<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Can it be shielded?<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">No known shielding<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Yes, by a conducting shell<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Dominates at<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Planetary and cosmic scales<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Atomic and molecular scales<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>The structural similarity is not a coincidence anyone has fully explained, and it is worth studying both together \u2014 the mathematics of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/\">Coulomb&#8217;s law<\/a> transfers to gravitation almost line for line.<\/p>\n\n<h2>Real-World Examples of the Law of Gravitation<\/h2>\n\n<h3>1. Your weight on a bathroom scale<\/h3>\n\n<p>The number under your feet is the Earth pulling on you through this exact equation. Plug in a 70 kg person, the Earth&#8217;s mass and its radius and you get roughly 687 N \u2014 the reading a scale in newtons would show.<\/p>\n\n<h3>2. The Moon&#8217;s orbit<\/h3>\n\n<p>The Earth pulls the Moon with about 1.98 \u00d7 10<sup>20<\/sup> N across 384,400 km. That force does not slow the Moon down; it continuously bends its path sideways, which is precisely what an orbit is.<\/p>\n\n<h3>3. Ocean tides<\/h3>\n\n<p>Tides come from the <em>difference<\/em> in the Moon&#8217;s pull across the width of the Earth. The near side is tugged harder than the far side, and the planet stretches slightly along the Earth\u2013Moon line.<\/p>\n\n<p>This is also why the Sun, despite pulling on Earth about 175 times harder than the Moon does in absolute terms, produces the weaker tides \u2014 it is so far away that its pull barely varies across our diameter.<\/p>\n\n<h3>4. Satellite and GPS orbits<\/h3>\n\n<p>Every satellite altitude is a solved gravitation problem. Setting the gravitational force equal to the required centripetal force fixes the speed at a given radius, which is why geostationary satellites must sit at one particular height.<\/p>\n\n<h3>5. Weighing planets you have never visited<\/h3>\n\n<p>Astronomers rarely measure a planet&#8217;s mass directly. They watch a moon orbit it, measure the period and radius, and invert the law of gravitation to get the mass \u2014 the technique that also revealed Neptune before anyone saw it.<\/p>\n\n<h2>Common Misconceptions About the Law of Gravitation<\/h2>\n\n<h3>Misconception 1: there is no gravity in space<\/h3>\n\n<p>Astronauts on the International Space Station float because they are in continuous free fall, not because gravity has switched off. At the station&#8217;s altitude of roughly 400 km, g is still about 8.7 m\/s\u00b2 \u2014 some 89% of its value at the ground.<\/p>\n\n<p>They fall around the Earth rather than into it, and everything nearby falls with them. That shared fall, covered further in our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/kinematics\/free-fall-physics\/\">free fall<\/a>, is what removes the sensation of weight.<\/p>\n\n<h3>Misconception 2: the Earth pulls you harder than you pull the Earth<\/h3>\n\n<p>The two forces are exactly equal in magnitude. You pull the Earth with the same 687 N that it pulls you \u2014 a textbook <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/newtons-laws-of-motion\/\">Newton&#8217;s third law<\/a> pair.<\/p>\n\n<p>What differs is the <em>acceleration<\/em>, because a = F\/m. The same force applied to 5.97 \u00d7 10<sup>24<\/sup> kg produces an utterly negligible response.<\/p>\n\n<h3>Misconception 3: doubling the distance halves the force<\/h3>\n\n<p>It quarters it. This is the single most common slip in exam scripts, and it comes from reading the formula too fast and missing the square on r.<\/p>\n\n<h3>Misconception 4: mass and weight are the same thing<\/h3>\n\n<p>Mass is the amount of matter, measured in kilograms, and it never changes. Weight is the gravitational force on that mass, measured in newtons, and it changes with location \u2014 a distinction worth nailing down in our explainer on <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/weight-vs-mass\/\">weight versus mass<\/a>.<\/p>\n\n<h2>How the Law of Gravitation Sets g, Weight and Orbits<\/h2>\n\n<p>The law of gravitation is the parent equation from which surface gravity, weight and orbital motion all follow. Each one is the same formula with a different quantity made the subject.<\/p>\n\n<h3>Surface gravity<\/h3>\n\n<p>Set the gravitational force equal to mg and the small mass cancels, leaving a result that depends only on the body you are standing on.<\/p>\n\n<div class=\"pf-formula\">g = G M \/ r\u00b2<\/div>\n\n<p>This is why every object falls at the same rate regardless of its mass \u2014 the falling object&#8217;s own mass drops out of the equation entirely. Feed in the Earth&#8217;s mass and mean radius and you get about 9.8 m\/s\u00b2.<\/p>\n\n<p>The measured value drifts from roughly 9.78 m\/s\u00b2 at the equator to 9.83 m\/s\u00b2 at the poles, because the Earth is not a perfect sphere and its rotation shaves a little off the effective value near the equator.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Body<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Mass (kg)<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Mean radius (km)<\/th>\n<th style=\"text-align:left;padding:10px;border-bottom:2px solid #C8932A;\">Surface g (m\/s\u00b2)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Moon<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">7.35 \u00d7 10<sup>22<\/sup><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">1737<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">1.62<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Mars<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">6.42 \u00d7 10<sup>23<\/sup><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">3390<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">3.73<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Earth<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">5.97 \u00d7 10<sup>24<\/sup><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">6371<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">9.82<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">Jupiter<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">1.898 \u00d7 10<sup>27<\/sup><\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">69,911<\/td>\n<td style=\"padding:10px;border-bottom:1px solid #D9CFB8;\">24.8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Masses and radii above are taken from the <a href=\"https:\/\/ssd.jpl.nasa.gov\/planets\/phys_par.html\" target=\"_blank\" rel=\"noopener\">JPL Solar System Dynamics planetary parameters table<\/a>. If you want to run your own body weight through these numbers, our page on <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/weight-on-other-planets\/\">weight on other planets<\/a> does exactly that.<\/p>\n\n<h3>Orbits<\/h3>\n\n<p>For a circular orbit, gravity supplies the centripetal force and nothing else does. Setting GMm\/r\u00b2 equal to mv\u00b2\/r gives the orbital speed, and the orbiting mass cancels again.<\/p>\n\n<div class=\"pf-formula\">v = sqrt(G M \/ r)<\/div>\n\n<p>Everything about orbital mechanics falls out of this one substitution, which is why <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/centripetal-force\/\">centripetal force<\/a> and gravitation are almost always taught together.<\/p>\n\n<p>Push the algebra one step further and you recover Kepler&#8217;s third law, T\u00b2 = 4\u03c0\u00b2r\u00b3\/(GM). Kepler found that pattern empirically in 1619; Newton explained <em>why<\/em> it had to be true.<\/p>\n\n<svg viewBox=\"0 0 700 500\" role=\"img\" aria-label=\"Newton's cannonball diagram showing trajectories from a mountain top curving further around the Earth until one becomes a circular orbit\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:28px auto;\">\n  <rect x=\"0\" y=\"0\" width=\"700\" height=\"500\" fill=\"#F5F2EA\" rx=\"4\"><\/rect>\n  <text x=\"350\" y=\"34\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"17\" font-weight=\"700\" fill=\"#7A1F2B\" text-anchor=\"middle\">An orbit is a fall that keeps missing<\/text>\n\n  <circle cx=\"350\" cy=\"330\" r=\"150\" fill=\"#0A1628\"><\/circle>\n  <circle cx=\"350\" cy=\"330\" r=\"165\" fill=\"none\" stroke=\"#C8932A\" stroke-width=\"2.5\" stroke-dasharray=\"8 6\"><\/circle>\n  <polygon points=\"350,158 332,182 368,182\" fill=\"#142139\"><\/polygon>\n\n  <path d=\"M350,160 C400,163 428,186 436,207\" fill=\"none\" stroke=\"#C5D0DC\" stroke-width=\"3\"><\/path>\n  <path d=\"M350,160 C432,165 486,218 491,279\" fill=\"none\" stroke=\"#C5D0DC\" stroke-width=\"3\"><\/path>\n  <path d=\"M350,160 C476,168 548,272 486,393\" fill=\"none\" stroke=\"#7A1F2B\" stroke-width=\"3\"><\/path>\n\n  <text x=\"470\" y=\"200\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"14\" fill=\"#0A1628\">too slow<\/text>\n  <text x=\"524\" y=\"272\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"14\" fill=\"#0A1628\">faster<\/text>\n  <text x=\"548\" y=\"360\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"14\" fill=\"#7A1F2B\">faster still<\/text>\n  <text x=\"350\" y=\"128\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" font-weight=\"700\" fill=\"#C8932A\" text-anchor=\"middle\">fast enough: it never lands<\/text>\n\n  <text x=\"350\" y=\"345\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"15\" fill=\"#FAF6EE\" text-anchor=\"middle\">Earth<\/text>\n  <text x=\"350\" y=\"478\" font-family=\"Manrope,Arial,sans-serif\" font-size=\"13\" fill=\"#0A1628\" text-anchor=\"middle\">Schematic, not to scale<\/text>\n<\/svg>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">Fire a projectile fast enough and its curved fall matches the curve of the Earth \u2014 that is orbit.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/medium_1977_0417__0001_.jpg\" alt=\"Cavendish torsion balance apparatus used to test the law of gravitation\" loading=\"lazy\" style=\"width:100%;height:auto;border-radius:4px;\" width=\"768\" height=\"576\">\n\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Cavendish&#8217;s 1798 torsion balance, the experiment that first fixed the value of G.<\/figcaption>\n\n<\/figure>\n\n<h3>Where Newton&#8217;s law stops working<\/h3>\n\n<p>The law of gravitation is an outstanding approximation, not the final word. It breaks down for very strong fields and very high speeds, where general relativity takes over.<\/p>\n\n<p>The classic failure is Mercury&#8217;s orbit, whose perihelion drifts by a small amount that Newton&#8217;s equation cannot account for. For every problem you will meet in school or first-year physics, though, F = Gm<sub>1<\/sub>m<sub>2<\/sub>\/r\u00b2 is entirely sufficient.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">Two lead spheres, each of mass 1000 kg, have their centres 5.0 m apart. What is the gravitational force between them?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Use the law of gravitation, F = G m<sub>1<\/sub>m<sub>2<\/sub> \/ r\u00b2, with G = 6.674 \u00d7 10<sup>\u221211<\/sup> N\u00b7m\u00b2\/kg\u00b2.<\/p>\n<p>Step 2: Substitute. F = (6.674 \u00d7 10<sup>\u221211<\/sup> N\u00b7m\u00b2\/kg\u00b2)(1000 kg)(1000 kg) \/ (5.0 m)\u00b2<\/p>\n<p>Step 3: The numerator is 6.674 \u00d7 10<sup>\u22125<\/sup> N\u00b7m\u00b2, and the denominator is 25 m\u00b2. Dividing gives 2.67 \u00d7 10<sup>\u22126<\/sup> N.<\/p>\n<p><strong>Answer: 2.67 \u00d7 10<sup>\u22126<\/sup> N \u2014 under three micronewtons, which is why you never notice it.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">A student of mass 70 kg stands on the Earth&#039;s surface. Taking the Earth&#039;s mass as 5.972 x 10^24 kg and its mean radius as 6.371 x 10^6 m, find the gravitational force on the student.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: F = G M m \/ r\u00b2, treating the Earth as a point mass at its centre.<\/p>\n<p>Step 2: Substitute. F = (6.674 \u00d7 10<sup>\u221211<\/sup>)(5.972 \u00d7 10<sup>24<\/sup>)(70) \/ (6.371 \u00d7 10<sup>6<\/sup>)\u00b2<\/p>\n<p>Step 3: Numerator = 2.790 \u00d7 10<sup>16<\/sup> N\u00b7m\u00b2; denominator = 4.059 \u00d7 10<sup>13<\/sup> m\u00b2. Dividing gives 687 N.<\/p>\n<p><strong>Answer: 687 N, which agrees with mg = 70 \u00d7 9.81 = 687 N as it must.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A probe sits at a distance of three Earth radii from the centre of the Earth. If g at the surface is 9.82 m\/s2, what is g at the probe?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: g = GM\/r\u00b2, so g is proportional to 1\/r\u00b2. No masses need to be substituted.<\/p>\n<p>Step 2: The distance has tripled, so the field falls by a factor of 3\u00b2 = 9.<\/p>\n<p>Step 3: g = 9.82 m\/s\u00b2 \u00f7 9 = 1.09 m\/s\u00b2.<\/p>\n<p><strong>Answer: 1.09 m\/s\u00b2 \u2014 note it is one ninth, not one third.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Find the gravitational force between the Earth (5.972 x 10^24 kg) and the Moon (7.346 x 10^22 kg), whose centres are 3.844 x 10^8 m apart.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: F = G m<sub>1<\/sub>m<sub>2<\/sub> \/ r\u00b2.<\/p>\n<p>Step 2: Numerator = (6.674 \u00d7 10<sup>\u221211<\/sup>)(5.972 \u00d7 10<sup>24<\/sup>)(7.346 \u00d7 10<sup>22<\/sup>) = 2.928 \u00d7 10<sup>37<\/sup> N\u00b7m\u00b2.<\/p>\n<p>Step 3: Denominator = (3.844 \u00d7 10<sup>8<\/sup> m)\u00b2 = 1.478 \u00d7 10<sup>17<\/sup> m\u00b2. Dividing gives 1.98 \u00d7 10<sup>20<\/sup> N.<\/p>\n<p><strong>Answer: 1.98 \u00d7 10<sup>20<\/sup> N.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">Mars has a mass of 6.417 x 10^23 kg and a mean radius of 3.390 x 10^6 m. Calculate the acceleration due to gravity at its surface.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Start from F = GMm\/r\u00b2 and set it equal to mg. The small mass cancels, leaving g = GM\/r\u00b2.<\/p>\n<p>Step 2: Substitute. g = (6.674 \u00d7 10<sup>\u221211<\/sup>)(6.417 \u00d7 10<sup>23<\/sup>) \/ (3.390 \u00d7 10<sup>6<\/sup>)\u00b2<\/p>\n<p>Step 3: Numerator = 4.283 \u00d7 10<sup>13<\/sup> m\u00b3\/s\u00b2; denominator = 1.149 \u00d7 10<sup>13<\/sup> m\u00b2. Dividing gives 3.73 m\/s\u00b2.<\/p>\n<p><strong>Answer: 3.73 m\/s\u00b2, about 38% of Earth&#8217;s surface gravity.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">At what altitude above the Earth&#039;s surface does g fall to half its surface value? Take the Earth&#039;s radius as 6.371 x 10^6 m.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Since g is proportional to 1\/r\u00b2, halving g means r\u00b2 must double, so r must grow by a factor of sqrt(2).<\/p>\n<p>Step 2: r = 6.371 \u00d7 10<sup>6<\/sup> m \u00d7 1.414 = 9.010 \u00d7 10<sup>6<\/sup> m from the Earth&#8217;s centre.<\/p>\n<p>Step 3: Altitude = r \u2212 R = 9.010 \u00d7 10<sup>6<\/sup> \u2212 6.371 \u00d7 10<sup>6<\/sup> = 2.639 \u00d7 10<sup>6<\/sup> m.<\/p>\n<p><strong>Answer: about 2640 km above the surface \u2014 far higher than most students guess.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">The International Space Station orbits at an altitude of 400 km. Find its orbital speed and the time it takes to complete one orbit.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Work in orbital radius, not altitude. r = 6.371 \u00d7 10<sup>6<\/sup> + 4.00 \u00d7 10<sup>5<\/sup> = 6.771 \u00d7 10<sup>6<\/sup> m.<\/p>\n<p>Step 2: Gravity supplies the centripetal force, so GMm\/r\u00b2 = mv\u00b2\/r, which rearranges to v = sqrt(GM\/r).<\/p>\n<p>Step 3: GM = (6.674 \u00d7 10<sup>\u221211<\/sup>)(5.972 \u00d7 10<sup>24<\/sup>) = 3.986 \u00d7 10<sup>14<\/sup> m\u00b3\/s\u00b2. Then v = sqrt(3.986 \u00d7 10<sup>14<\/sup> \/ 6.771 \u00d7 10<sup>6<\/sup>) = sqrt(5.887 \u00d7 10<sup>7<\/sup>) = 7672 m\/s.<\/p>\n<p>Step 4: Period T = 2\u03c0r \/ v = (2\u03c0)(6.771 \u00d7 10<sup>6<\/sup>) \/ 7672 = 5545 s.<\/p>\n<p><strong>Answer: v = 7.67 km\/s and T = 5545 s, or about 92 minutes per orbit.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is the law of gravitation in simple words?<\/summary><div class=\"pf-faq-item-answer\">\nEvery object with mass pulls on every other object with mass. The pull gets stronger if either object is more massive, and weaker \u2014 very quickly \u2014 as they move apart. Double the distance and the pull drops to a quarter, not a half.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the formula for the law of gravitation?<\/summary><div class=\"pf-faq-item-answer\">\nThe formula is F = G m1 m2 \/ r squared. Here F is the force in newtons, m1 and m2 are the two masses in kilograms, r is the centre-to-centre distance in metres, and G is the gravitational constant, 6.674 x 10^-11 N m squared per kg squared.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why is it called the universal law of gravitation?<\/summary><div class=\"pf-faq-item-answer\">\nBecause Newton claimed it applies to every pair of masses everywhere, with no exceptions. Before him, the physics of falling objects on Earth and the physics of orbiting planets were treated as separate subjects. Showing that one equation covered both was the revolutionary part.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the value of G and how was it measured?<\/summary><div class=\"pf-faq-item-answer\">\nG is 6.674 x 10^-11 N m squared per kg squared. It comes from torsion-balance experiments, in which large lead spheres twist a delicately suspended dumbbell by a tiny, measurable angle. Henry Cavendish ran the first of these in 1798, though his stated aim was the density of the Earth, not G; the constant was derived from such measurements later. G remains the least precisely known of the major constants.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the difference between g and G?<\/summary><div class=\"pf-faq-item-answer\">\nG is the universal gravitational constant, the same value everywhere in the universe. Lower-case g is the gravitational field strength at a particular place, about 9.8 metres per second squared at Earth&#8217;s surface. G is fixed; g depends on which body you stand on and how far you are from its centre.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does the law of gravitation still apply inside a planet?<\/summary><div class=\"pf-faq-item-answer\">\nNo, not in the form F = G m1 m2 \/ r squared. That equation holds only outside a spherical body. Once you are below the surface, the shell of mass above you contributes no net pull, and the field actually decreases as you approach the centre, reaching zero there.\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>The law of gravitation says every mass attracts every other mass, with the pull falling off as the square of the distance. Here is the formula, what each symbol means, seven worked problems and the inverse-square mistake almost everyone makes.<\/p>\n","protected":false},"author":1,"featured_media":1816,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-1814","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanics"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=1814"}],"version-history":[{"count":1,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1814\/revisions"}],"predecessor-version":[{"id":1822,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1814\/revisions\/1822"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/1816"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=1814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=1814"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=1814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}