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Slower farther out

Gravity and orbits · level 4, lesson 3 of 6

A question to start

The Earth takes one year to go round the Sun. Mars takes almost two. Is that only because Mars has farther to go, or is it also moving more slowly?

The idea

Farther from the Sun, the Sun's pull is weaker. A weaker pull can only bend a slow path into a circle; a fast planet out there would fly away. So planets farther out move more slowly, and they also have a longer path. Both make their years longer.

Planet Distance from the Sun (Earth = 1) Speed in orbit Length of its year
Mercury 0.39 47 km/s 88 days
Venus 0.72 35 km/s 225 days
Earth 1 30 km/s 365 days
Mars 1.52 24 km/s 687 days
Jupiter 5.2 13 km/s 11.9 years

Mars's path is 1.52 times as long as the Earth's, and it moves at \(24 \div 30 = 0.8\) of the Earth's speed. So its year is about \(1.52 \div 0.8 = 1.9\) times as long, which is 687 days. ✓

The same is true round any planet. Round Mars, its inner moon Phobos is close in and whips round in 7 hours 39 minutes; its outer moon Deimos is farther out and takes 30 hours.

Johannes Kepler found the exact pattern in 1619, long before Newton explained it: square the year, and you get the distance cubed (in the right units). You will use it in level 6.

Worked examples

1. Which planet overtakes? Earth is on the inside track and moves faster, so it keeps catching up with Mars and overtaking it, like a runner on the inside lane. That happens about every 26 months, and it is when Mars looks brightest from Earth.

2. Jupiter. Jupiter is 5.2 times as far out as the Earth and moves at less than half the Earth's speed, so its year is nearly 12 of ours.

Try it

  1. Which moves faster in its orbit, Mars or the Earth?
  2. Give two reasons why the Mars year is longer than ours.
  3. Phobos orbits closer to Mars than Deimos. Which goes round faster?
  4. Mercury is closest to the Sun. Would you expect it to have the shortest or longest year?
Answers
  1. The Earth (30 km/s against Mars's 24 km/s).
  2. Mars has a longer path round the Sun, and it moves more slowly along it.
  3. Phobos.
  4. The shortest: 88 days.

Common mistake

"Outer planets are slower because they are bigger." Size has nothing to do with it. A pebble at Jupiter's distance would go round just as slowly as Jupiter. Only the distance from the Sun matters.

Where it leads