Kepler's third law

🌞 Imagine the Sun is in the center of a playground.

Two planets – Earth and Jupiter – are running in circles around it, like two kids on a race track.

Let’s see how far they are and how long they take to go around the Sun once.

🌍 EARTH

Distance from Sun: About 150 million km

Time to go around the Sun (1 revolution): 1 year

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🪐 JUPITER

Distance from Sun: About 778 million km

Time to go around the Sun (1 revolution): 11.86 years (almost 12 years)

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🧮 Now let’s do Kepler’s Third Law Step-by-Step:

Step 1: Take the time and square it (Time × Time)

Earth:

Time = 1 year

1 × 1 = 1

Jupiter:

Time = 11.86 years

11.86 × 11.86 = about 140.7

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Step 2: Take the distance and cube it (Distance × Distance × Distance)

Let’s use Astronomical Units (AU) instead of kilometers to make it easier.

1 AU = distance from Earth to the Sun = 150 million km

Earth:

Distance = 1 AU

1 × 1 × 1 = 1

Jupiter:

Distance = 5.2 AU

5.2 × 5.2 × 5.2 = about 140.6

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🧩 Now compare:

Planet Square of Time (Years²) Cube of Distance (AU³)

Earth 1 1

Jupiter 140.7 140.6

✅ The two numbers for Jupiter are almost equal!

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🎉 What does this tell us?

Kepler’s Third Law works perfectly!

The time it takes a planet to go around the Sun, when squared, matches the distance to the Sun, when cubed!

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👦 In simple kid language:

Jupiter is much farther from the Sun, so it takes much longer to go around it.

The special rule says:

If we square the time and cube the distance, we get matching numbers!

So farther planets take more time, and they follow a magic math pattern!