Math practice · Unit #09 · 7th grade · The solar system & light

Marble Math

The solar system is too big to imagine — so we don't imagine it, we scale it. Earth becomes a marble, the numbers come down to Earth, and space finally fits in your head. Every sunset is still 8 minutes old.

skills: scale models scientific notation unit rates ≈ 35 min
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Name Period Date
PART A

The marble model

Our scale: 1 cm = 10,000 km. Earth's diameter is 12,742 km, the Sun's is 1,392,700 km, and the Earth–Sun distance is 149,600,000 km. Convert each to model size — then we'll go walk it.

Scale: divide the real km by 10,000 → model cm
ObjectReal size (km)Model size
Earth (diameter)12,742
Sun (diameter)1,392,700
Earth → Sun distance149,600,000

  1. Convert your model sizes to everyday units: Earth ≈ ___ cm (a marble), Sun ≈ ___ m (a giant beach ball), distance ≈ ___ m (how many football fields, at 100 m each?).

  2. In this model, could the Sun fit in our classroom? Could the Earth–Sun distance fit on campus? One sentence each.

PART B

Scientific notation, in the wild

Astronomers don't write zeros — they write powers of ten. Practice on real numbers.

  1. Write in scientific notation: 149,600,000 km (Earth–Sun distance).

  2. Write in scientific notation: 5,900,000,000 km (Sun–Pluto distance, rounded).

  3. The Sun's mass is 1.989 × 10³⁰ kg and Earth's is 5.97 × 10²⁴ kg. About how many "Earths" of mass is the Sun? (Divide — then round to a friendly number.)

PART C

How old is the light?

time = distance ÷ speed light speed ≈ 300,000 km/s
Light is fast, but space is faster. Everything you see is old news — compute how old.

Light travel times (show seconds, then convert)
FromDistance (km)Time (s)…in friendly units
The Sun149,600,000
The Moon384,400
Pluto (rounded)5,900,000,000

  1. Fill the table. Convert the Sun's seconds to minutes, and Pluto's seconds to hours.

  2. If the Sun vanished at this exact moment, how long would we keep happily tanning before anyone knew? Use your table.

PART D

How many Earths fit in Jupiter?

Jupiter's diameter is 139,820 km; Earth's is 12,742 km. Careful — this question has a trap in it, and the trap is the whole point.

  1. Diameter ratio: 139,820 ÷ 12,742 ≈ ___. So across the middle, about how many Earth-marbles wide is Jupiter?

  2. But volume grows with the cube of the diameter: 11³ = 11 × 11 × 11 = ___. THAT's roughly how many Earths of stuff fit inside Jupiter. Why is the volume answer so much bigger than the diameter answer?

  3. Road trip: you drive to the Moon (384,400 km) at a steady 100 km/h, no stops. How many hours is that? How many days? Will you make it by Friday?

Answer key — teachers

Part A

Earth ≈ 1.27 cm · Sun ≈ 139.27 cm (≈1.4 m) · distance ≈ 14,960 cm.

  1. Earth ≈ 1.3 cm (marble ✓); Sun ≈ 1.4 m; distance ≈ 149.6 m ≈ 1.5 football fields.
  2. The 1.4 m Sun fits in a classroom corner; the 150 m Earth–Sun distance will not fit on most campuses — the model's point: space is mostly space.

Part B

  1. 1.496 × 10⁸ km
  2. 5.9 × 10⁹ km
  3. 1.989 × 10³⁰ ÷ 5.97 × 10²⁴ ≈ 3.3 × 10⁵ ≈ 330,000 Earths.

Part C

Sun: ≈499 s ≈ 8.3 min · Moon: ≈1.28 s · Pluto: ≈19,667 s ≈ 5.5 h.

  1. (conversions above)
  2. ≈ 8.3 minutes of blissful ignorance.

Part D

  1. ≈ 11 Earths wide.
  2. 11³ = 1,331. Volume counts three directions at once — doubling size grows volume 8×, not 2×.
  3. 384,400 ÷ 100 = 3,844 h ≈ 160 days. Not by Friday.