Why apples fall and planets orbit: gravity, satellites, the Solar System, the Moon, the seasons, stars and galaxies, explained with diagrams, animations and worked examples.
According to a famous story, Isaac Newton was prompted to think about gravity when he saw an apple fall from a tree. The story is probably embellished, but the question he asked was real and enormous: if gravity pulls an apple to the ground, could the same force also hold the Moon in its orbit? His answer, published in 1687, was yes, and it unified the physics of falling objects on Earth with the motion of the Moon, the planets and the tides. Gravity is the force that shapes the universe: it pulled the Sun together from a cloud of gas, keeps the planets in orbit, and holds galaxies together. This article explains how gravity works, how orbits and satellites work, and what we know about the Solar System, the stars and the universe.
Gravity is the force of attraction between any two objects that have mass. It is always attractive, it acts over any distance (becoming weaker as the distance grows), and it is by far the weakest of the fundamental forces. We notice it only when one of the masses is enormous, such as a planet. Newton's law of universal gravitation gives the force between two masses:
F = G × m₁ × m₂ ÷ r²
m₁ and m₂ are the masses (kg), r is the distance between their centres (m), and G is the gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg². Two things follow: the force is proportional to each mass, and it follows an inverse-square law: double the distance and the force becomes one quarter; triple the distance and it becomes one ninth.
The Earth's mass is 5.97 × 10²⁴ kg, the Moon's mass is 7.35 × 10²² kg, and the distance between their centres is 3.84 × 10⁸ m. Find the gravitational force.
Step 1. F = G m₁ m₂ ÷ r² = (6.674 × 10⁻¹¹ × 5.97 × 10²⁴ × 7.35 × 10²²) ÷ (3.84 × 10⁸)².
Step 2. Numerator ≈ 2.93 × 10³⁷; denominator ≈ 1.47 × 10¹⁷.
Step 3. F ≈ 2.0 × 10²⁰ N. By Newton's third law, the Moon pulls on the Earth with the same size of force.
Around any mass there is a gravitational field. The gravitational field strength g at a point is the force on each kilogram placed there (N/kg), which is also the free-fall acceleration (m/s²). For a planet of mass M and radius R, at its surface:
g = G M ÷ R² (and at a distance r from the centre, g = G M ÷ r²)
Weight W = m g
The Moon has M = 7.35 × 10²² kg and R = 1.74 × 10⁶ m. Find g at its surface.
g = GM ÷ R² = (6.674 × 10⁻¹¹ × 7.35 × 10²²) ÷ (1.74 × 10⁶)² = 4.91 × 10¹² ÷ 3.03 × 10¹² ≈ 1.6 N/kg, about one-sixth of the value on Earth.
| Body | Surface g (N/kg), approximate |
|---|---|
| Moon | 1.6 |
| Mercury | 3.7 |
| Mars | 3.7 |
| Uranus | 8.9 |
| Venus | 8.9 |
| Earth | 9.8 |
| Saturn | 10.4 |
| Neptune | 11.2 |
| Jupiter | 24.8 |
Even on Earth, g is not exactly the same everywhere: it is slightly smaller at the equator (about 9.78) than at the poles (about 9.83), because of the Earth's rotation and slightly flattened shape, and it decreases with altitude. The standard value used for reference is 9.80665 N/kg.
The International Space Station (ISS) orbits about 400 km above the surface. The Earth's radius is 6371 km and GM for the Earth is 3.986 × 10¹⁴ m³/s². Find g at that height.
r = 6371 + 400 = 6771 km = 6.771 × 10⁶ m. g = GM ÷ r² = 3.986 × 10¹⁴ ÷ (6.771 × 10⁶)² = 8.7 N/kg.
That is about 89% of the surface value. Astronauts on the ISS feel "weightless" not because gravity has disappeared but because they and the station are in continuous free fall together around the Earth.
Newton imagined a cannon on a very high mountain. A ball fired slowly lands nearby. A ball fired faster lands farther away. Since the Earth's surface curves away, there is a speed at which the ball falls towards the Earth but keeps missing it; it is then in orbit. An orbit is a continuous free fall around a body. The only force is gravity, and it supplies the centripetal force that bends the path into a circle or ellipse.
For a circular orbit of radius r around a mass M, setting gravity equal to the centripetal requirement gives:
v = √(G M ÷ r) and T = 2πr ÷ v
A satellite closer to the Earth must travel faster. The orbital speed does not depend on the satellite's own mass.
Find the orbital speed and period of the ISS at r = 6.771 × 10⁶ m. (GM = 3.986 × 10¹⁴ m³/s²)
Step 1. v = √(GM ÷ r) = √(3.986 × 10¹⁴ ÷ 6.771 × 10⁶) = √(5.89 × 10⁷) ≈ 7670 m/s ≈ 7.7 km/s (over 27 000 km/h).
Step 2. T = 2πr ÷ v = 2π × 6.771 × 10⁶ ÷ 7670 ≈ 5550 s ≈ 92 minutes.
So the ISS circles the Earth about 15–16 times a day, and its crew see a sunrise roughly every 90 minutes.
Before Newton, the German astronomer Johannes Kepler (1571–1630) analysed careful observations of the planets and found three patterns, published between 1609 and 1619:
Mars orbits at about 1.52 AU from the Sun. Using Earth's values (T = 1 year at 1 AU), find the length of the Martian year. (1 AU is the average Earth–Sun distance, about 1.50 × 10¹¹ m.)
T² = r³ → T = r^1.5 = 1.52^1.5 = 1.52 × √1.52 = 1.52 × 1.233 ≈ 1.87 years (about 685 Earth days; the measured value is 687 days).
The Solar System is the Sun and everything bound to it by gravity. The Sun contains about 99.86% of the total mass. It is a star: a huge ball of hot gas, mainly hydrogen and helium, in which nuclear fusion releases energy. About 4.6 billion years ago it formed, with the planets, from a collapsing cloud of gas and dust.
| Planet | Type | Distance from Sun (AU) | Orbital period |
|---|---|---|---|
| Mercury | Rocky | 0.39 | 88 days |
| Venus | Rocky | 0.72 | 225 days |
| Earth | Rocky | 1.00 | 365.25 days |
| Mars | Rocky | 1.52 | 687 days |
| Jupiter | Gas giant | 5.20 | 11.9 years |
| Saturn | Gas giant | 9.58 | 29.4 years |
| Uranus | Ice giant | 19.2 | 84 years |
| Neptune | Ice giant | 30.1 | 165 years |
One astronomical unit (AU) is the average Earth–Sun distance: 149 597 870 700 m, about 150 million km. Light from the Sun takes about 8.3 minutes to reach us.
The Moon orbits the Earth once every 27.3 days, and takes about 29.5 days to go through its cycle of phases (the phases take longer because the Earth also moves round the Sun). Half of the Moon is always lit by the Sun. What changes is how much of the lit half we can see from Earth. The Moon always shows nearly the same face to us because it rotates once for each orbit.
The Earth spins on its axis once in about 24 hours (precisely, 23 hours 56 minutes relative to the stars), which gives day and night. It orbits the Sun once in about 365.25 days. The Earth's axis is tilted by about 23.4° to the plane of its orbit, and it points in nearly the same direction in space all year. This tilt, not the distance from the Sun, causes the seasons. (In fact the Earth is nearest to the Sun in early January, during the northern winter.)
When a hemisphere is tilted towards the Sun, the Sun climbs higher in the sky, sunlight strikes the ground more directly (so the same energy is spread over a smaller area), and the days are longer. Near the poles there are weeks of continuous daylight in summer and continuous darkness in winter.
Stars form inside giant clouds of gas and dust called nebulae. Gravity pulls a clump together; as it shrinks it heats up until the core is hot and dense enough for hydrogen to fuse into helium. At that point the star begins its long main sequence life, in which the outward pressure of the hot gas balances the inward pull of gravity. Our Sun is about halfway through this stage, with roughly five billion years to go.
What happens next depends on the star's mass:
Stars are very far away. The nearest star after the Sun, Proxima Centauri, is about 4.2 light-years away: its light takes about 4.2 years to reach us, even though light covers 300 000 km every second. When we look at stars, we see them as they were in the past.
One light-year is the distance light travels in one year. Find it in kilometres, using c = 3.00 × 10⁸ m/s.
1 year ≈ 365.25 × 24 × 3600 = 3.156 × 10⁷ s. Distance = ct = 3.00 × 10⁸ × 3.156 × 10⁷ = 9.47 × 10¹⁵ m = 9.47 × 10¹² km (the accepted value is 9.46 × 10¹² km).
Proxima Centauri at 4.2 light-years is about 4.2 × 9.46 × 10¹² ≈ 4.0 × 10¹³ km away.
Stars are grouped into huge systems called galaxies, held together by gravity. Our Sun is one of hundreds of billions of stars in the Milky Way, a spiral galaxy about 100 000 light-years across. The Sun orbits the Milky Way's centre once every 220–250 million years. There are billions of other galaxies; the nearest large one, Andromeda, is about 2.5 million light-years away.
In the 1920s Edwin Hubble showed that distant galaxies are moving away from us, and the farther away a galaxy is, the faster it recedes. The light from distant galaxies is stretched to longer wavelengths, an effect called redshift. This tells us that the universe is expanding. Running the expansion backwards leads to the Big Bang theory: the universe began in an extremely hot, dense state about 13.8 billion years ago. A major piece of evidence is the cosmic microwave background, faint microwave radiation filling the whole sky, discovered in 1965 by Arno Penzias and Robert Wilson. Astronomers also find that visible matter is only a small part of the universe: most of it appears to be dark matter and dark energy, whose nature is still unknown.
| Year | Milestone |
|---|---|
| 1957 | Sputnik 1, the first artificial satellite, is launched by the Soviet Union (4 October). |
| 1961 | Yuri Gagarin becomes the first human in space (12 April). |
| 1969 | Apollo 11: Neil Armstrong and Buzz Aldrin land on the Moon (20 July). |
| 1977 | Voyager 1 and 2 are launched; Voyager 1 later entered interstellar space (2012). |
| 1990 | The Hubble Space Telescope is launched. Pakistan launches its first satellite, Badr-1, the same year. |
| 1998–2000 | Assembly of the International Space Station begins; it has been continuously occupied since November 2000. |
| 2021 | The James Webb Space Telescope is launched to observe the universe in infrared light. |
Space missions are used for telecommunications, weather forecasting, navigation, mapping resources and monitoring climate, as well as for science. Rockets work by Newton's third law, as described in the article on force and motion. NASA, ESA, SUPARCO and other agencies publish current mission schedules, including plans to return people to the Moon, so check their websites for the latest news.
Try each question before opening the answer.
It becomes one ninth (1 ÷ 3²).
W = mg = 50 × 3.7 = 185 N. Its mass is still 50 kg.
They and their spacecraft are in free fall around the Earth, accelerating at the same rate, so nothing pushes on them to give the sensation of weight.
Slower, because v = √(GM ÷ r) decreases as r increases.
T = 4.0^1.5 = 4.0 × 2.0 = 8.0 years.
At new Moon, when the Moon is between the Sun and the Earth.
When the north is tilted away from the Sun, the south is tilted towards it, so it receives more direct sunlight and longer days.
It will explode as a supernova and leave behind a neutron star or a black hole.
Activities that need little equipment: use a torch and two balls to model the Moon's phases; stretch a rubber sheet and roll marbles to show orbits; place a globe near a lamp, tilted, to demonstrate seasons; build a scale model of the Solar System along a corridor or playground (for example, Neptune about 30 times as far from the Sun as the Earth); use a free stargazing app to find planets and the Moon, and observe the Moon's phase for a month. Never look directly at the Sun, and use certified solar viewers for eclipses. Numerical values are rounded; please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions, constants and facts were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: planetary data are rounded; cosmological values such as the age of the universe are current best estimates and may be refined. Please check numerical values against your own syllabus or exam board specification before relying on them.
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