Physics · Gravitation and the universe · Grade 7

The Solar System

If the Sun were a ball 1 m across, where would the Earth be?

The situation

At night in the Tashkent sky Jupiter and Saturn are bright, but they look like tiny points. In textbook pictures, though, the planets are drawn as big balls lined up beside the Sun. How big, and how empty, is the Solar System really? If the Sun were a ball one metre across, where would the Earth be, and how many minutes would sunlight take to reach us?

Topic

The Solar System. Size and distance of the planets — to true scale

Key ideas

Scale
Speed of light
Planetary years

Formulas

t = \frac{d}{c}, c \approx 3 \cdot 10^{5} km/s

Light travel time: distance divided by the speed of light.

1 AU = 149.6 million km \Rightarrow t_{\oplus︎} = \frac{1.496 \cdot 10^{8} km}{3 \cdot 10^{5} km/s} \approx 499 s

The astronomical unit (AU) is the average distance from the Earth to the Sun. Sunlight reaches it in ≈ 8 min 20 s.

k = \frac{D_{m o d e l}}{D_{⊙}}, d_{m o d e l} = k d

Scale: all lengths are reduced by the same factor $k$ ( $D_{⊙} = 1 391 400$ km).

\frac{T^{2}}{a^{3}} = const (T — in years, a — in AU: T^{2} = a^{3})

Kepler's third law: the year of a distant planet is longer.

v \approx \frac{2 π a}{T}

Average speed along the orbit: Earth ≈ 29.8 km/s, Neptune ≈ 5.4 km/s.

Theory

Why do pictures “lie”?

The distances between planets are thousands of times greater than their sizes. The diameter of the Earth is 12 742 km, while the distance to the Sun is 149.6 million km — 11 700 Earth diameters. To fit everything on one page, pictures shorten the distances and enlarge the planets. Press “True scale”: the planets turn into invisible dots and the Solar System is almost completely empty.

Planetary years

Each planet moves round the Sun along its own orbit. A distant planet both moves more slowly and travels a longer path, so its year is long: 88 days on Mercury, ≈ 12 Earth years on Jupiter, ≈ 165 years on Neptune. This relationship is Kepler's third law: $T^{2} = a^{3}$ (in years and AU). Speed up time and watch the inner planets “overtake” the outer ones. Model: the planets move along Kepler ellipses with their true periods and eccentricities; the starting positions are calculated for today's date from mean orbital elements (accurate to a degree or two); the orbits are taken in one plane and the mutual attraction of the planets is ignored. In Illustrative mode the distances are compressed as $\sqrt{r}$ and the sizes enlarged; time is sped up (1× = 10 days/s), while rotation about their own axes is slowed down.

Light also takes time on the way

Light travels ≈ 300 000 km every second. Even at that speed sunlight takes ≈ 8 min 20 s to reach the Earth and ≈ 4.2 hours to reach Neptune. So we see the Sun as it was 8 minutes ago. The “Light pulse” button sends a wave of light out from the Sun — next to each planet its arrival time is shown.

Terrestrial planets and giant planets

The inner four planets form the terrestrial group: small, dense (≈ 3.9–5.5 g/cm³), made of an iron core and a silicate mantle, with solid surfaces. Their atmospheres are very different: almost none on Mercury, a very dense CO₂ “greenhouse” on Venus, nitrogen and oxygen on Earth, thin CO₂ on Mars. A magnetosphere arises from currents in a liquid conducting layer inside the planet (the dynamo): Earth's liquid outer core gives a strong field, while Venus and Mars have no global field. The outer four planets are the giants: Jupiter and Saturn are gas giants, made mostly of hydrogen and helium (inside, hydrogen under pressure is metallic — the source of a strong magnetic field), and Uranus and Neptune are ice giants, rich in water, ammonia and methane “ices”. All the giants have rings (the brightest, on Saturn, are pieces of ice) and many moons. Choose a planet: its internal structure, atmosphere and magnetic field appear in the information window.

Small bodies and the origin of the Solar System

The asteroid belt (2.1–3.3 AU) between Mars and Jupiter consists of pieces of rock and metal: Jupiter's gravity prevented them from combining into one planet. Beyond Neptune, at ≈ 30–50 AU, lies a ring of icy bodies — the Kuiper belt; among its trans-Neptunian objects is the dwarf planet Pluto. It is the source of short-period comets, while long-period comets come from the spherical Oort cloud at ≈ 2 000–100 000 AU (it has not been observed directly, but is inferred from comet orbits). A comet is a mixture of ice and dust: as it approaches the Sun, the ice evaporates and forms a tail pointing away from the Sun. Origin: ≈ 4.6 billion years ago a rotating cloud of gas and dust contracted, forming the Sun at the centre and a flat disc around it. In the hot inner part of the disc only rock and metal stayed solid — the terrestrial planets were assembled from these; farther out ice also froze, and large ice-and-rock cores pulled in gas and became the giants. That is why all the planets orbit in almost the same plane and in the same direction.

Exoplanets and the habitable zone

Planets around other stars are exoplanets. The first around a Sun-like star, 51 Pegasi b, was discovered in 1995 (M. Mayor and D. Queloz, Nobel Prize 2019); in September 2025 the number of confirmed ones passed 6 000. The main methods: transit — when a planet passes in front of the star's disc, the light dims by the fraction ${(R / R_{*})}^{2}$ (Earth dims the Sun by ≈ 0.008 %, Jupiter by ≈ 1 %); radial velocity — the star and planet orbit their common centre of mass, and the star's spectrum shifts periodically through the Doppler effect (Jupiter “wobbles” the Sun at ≈ 12.5 m/s, Earth only at ≈ 0.09 m/s); there are also direct imaging and gravitational microlensing (see the “Black holes” experiment). Choose a planet — these quantities are calculated for it. The habitable zone is the range of distances at which liquid water can exist on a planet's surface; for the Sun a conservative estimate is ≈ 0.99–1.70 AU (R. Kopparapu et al., 2013). Being in the zone is not enough: Mars lies in it, but it is small, its atmosphere is thin and its water is frozen.

Did you know?

About 99.86 % of the mass of the Solar System is in the Sun itself. The mass of Jupiter is about 2.5 times the total mass of all the other planets.
If the Sun were a ball 1 m across, the nearest star, Proxima Centauri (4.2 light-years), would be about 29 000 km away. That is almost three quarters of the length of the Earth's equator.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Scales of the universe — Grade 9
Newton's cannon: an artificial satellite — Grade 10
Special relativity — Grade 10
Law of universal gravitation — Grade 10
Relativistic dynamics — Grade 10
Kepler's laws — Grade 10
Physics of stars — Year 1
The expanding universe — Year 1
Black holes — Year 4