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Shrink the universe

If the Sun were a 1 m ball, Earth would be a 9 mm bead 107 m away. Scale the solar system, the Moon and the nearest star, and feel the sizes.

  • Number sense
  • Untimed
  • Endless levels

How it plays

Pick a size for the model Sun; every other length is divided by the same factor. With the Sun 1 m across, the Earth is a 9 mm bead about 107 m away, Jupiter a 10 cm ball over half a kilometre off.

Levels go from the Earth, to the other planets and how many of each fit across the Sun, to the Earth and Moon on their own scale, to the nearest star — thousands of kilometres away on a model whose planets fit in a town. Past the last kind the clock tightens.

Only bodies with a sourced value are used, and the working names the source and whether it is exact (the astronomical unit, the light-year) or a quoted measurement. Answers are to three figures; a typed answer within 5% counts. The wrong options are the slips of scale: a power of ten out, radius for diameter.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This builds a feel for the relative sizes and distances in the solar system and quicker, surer scaling by one factor. It claims nothing wider.

Learn

How to get better at shrink the universe: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Find the scale: what real length became what model length. The Sun’s 1,392,700 km became the ball you were given; the Earth’s 12,742 km, in the Moon questions.
  2. Turn the thing you are asked about into a multiple of that reference body: Earth is 1/109 of the Sun’s width; Earth’s distance is 107 Sun-widths; the Moon is 30 Earth-widths away.
  3. Multiply that multiple by the model’s size. Keep the unit in view the whole time: centimetres in, metres or millimetres out.
  4. Put the answer into the unit the options use — mm under a centimetre, cm under a metre, m under a kilometre, km beyond — and check it is the right power of ten.

Techniques and tricks

  • Start from a 1 m Sun

    Learn the model at a Sun 1 m across, then scale it. Every other model Sun is a simple fraction or multiple of a metre.

    e.g. Sun 1 m: Earth is a 9.15 mm bead 107 m away. Sun 20 cm: × 0.2, so Earth is 1.83 mm across and 21.5 m away.

  • Distances in Sun-widths

    One astronomical unit is about 107 Sun-widths. Multiply a planet’s distance in AU by 107 to get its distance in model Suns.

    e.g. Jupiter is 5.2 AU out: 5.2 × 107 ≈ 559 Sun-widths, so 559 m from a 1 m Sun

  • Sizes in Earths

    Carry each planet’s width as a multiple of Earth’s: Jupiter 11.2, Saturn 9.5, Uranus 4.0, Neptune 3.9, Venus 0.95, Mars 0.53, Mercury 0.38. Then scale the Earth and multiply.

    e.g. Sun 1 m: Earth is 9.15 mm, so Jupiter is about 9.15 × 11.2 ≈ 103 mm, about 10 cm

  • How many fit across

    Divide the Sun’s width by the planet’s. From the Earth multiples: 109 Earths across, so 109 ÷ 11.2 ≈ 9.7 Jupiters.

    e.g. 1,392,700 ÷ 4,879 ≈ 285 Mercurys side by side

  • The Moon in Earth-widths

    The Moon is about 30 Earth-widths away and a little over a quarter of Earth’s width (0.27).

    e.g. Earth a 2 cm ball: the Moon is 2 × 0.27 ≈ 5.5 mm across and 2 × 30.2 ≈ 60 cm away

  • The nearest star in Sun-widths

    Proxima Centauri, 4.25 light-years off, is about 29 million Sun-widths away — about 269,000 times the Earth–Sun distance.

    e.g. Sun 1 m: about 28,900 km away. Sun 10 cm: about 2,890 km.

As the levels climb

  • You start with the Earth alone: how big and how far, for a model Sun from 10 cm to 2 m. Learn the 1 m model — 9.15 mm at 107 m — and the rest is multiplying by the Sun’s size in metres.
  • Next come the other planets and how many fit across the Sun. The sizes in Earths and the distances in AU do the work; Saturn at 9.57 AU and Neptune at 30.2 AU are worth remembering.
  • Then the Earth and the Moon on their own scale, with a model Earth from 1 cm to 30 cm; the reference body changes from the Sun to the Earth, so re-read which ball you were given.
  • Last, the nearest star — thousands of kilometres away on a model whose planets fit in a town. Expect kilometres in the answer, and check the power of ten twice.
  • Between the new kinds and after the last one, the questions stay the same size and the clock tightens instead, down to half the starting time. The anchors above are what make that time enough.

Traps to avoid

  • A power of ten out. Ten times too big and ten times too small are the first slips the wrong options are built from. Say the answer with its unit aloud: “about 2 metres”, not “2”.
  • Radius for diameter. The model size is the ball’s width; halving or doubling it gives an option exactly 2 times off.
  • Kilometres read as metres, or centimetres as metres. A factor of 1,000 or 100 slips in when the model is given in cm and the answer comes out in m or km.
  • For “how many fit across”, the count squared or cubed. Side by side across the Sun is a ratio of widths; area or volume would give a far bigger number.

How to practise

  • Use “Kinds of question” to practise “The Earth” alone until the 1 m model is automatic, then add “The other planets”.
  • Switch “Answer by” to “Typing the answer” when choosing is easy: within 5% counts, and the unit is stated in the question, so you must get the power of ten yourself.
  • Raise “Options shown” to 6 or 8 to see the ×10, ×2 and ×1,000 slips side by side; naming which slip made each wrong option is good practice in itself.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More number sense

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