Earth & Space Science · Unit 1 · Lesson 3 · Explore 1

What are orbits like in our solar system?

The phenomenon

Comet Borrelly has water that is frozen most of the time, but every several years it shoots out a jet of vaporized water and dust.

Your job: examine and graph the Solar System Orbital Data below, looking for evidence of patterns that might help you form a claim about why water exists in different phases on different objects in the solar system — and why the water on Comet Borrelly keeps changing phase.

1 · Solar System Orbital Data

Click any column heading to sort. Sorting is itself a way to hunt for patterns. One AU is Earth's average distance from the Sun.

Celestial Object Average Distance
from Sun (AU) 		Period of Revolution
(Earth years) 		Minimum Distance
from Sun (AU) 		Maximum Distance
from Sun (AU) 		Max − Min
(AU) 		Phase of majority
of water
Note on the table: the Max − Min column is not on your paper handout. It is included here because it is one of the things worth calculating when you go looking for patterns: it tells you how much an object's distance from the Sun changes over one trip around.

2 · Build a graph

Pick what goes on each axis, the same choice you would make in Sheets or Excel. Try several combinations. You are looking for relationships that hold for every object — and for objects that break the pattern.

A curved graph is hard to turn into an equation, but a straight one is easy. So the axis menus also offer the squares and cubes of distance and period. One pairing out of all of them turns the curve into a straight line. Hunt for it.

vapor liquid ice changes during the orbit

How to hunt for a straight line

  • Start with a on the bottom and T on the side. The points make a curve, not a line.
  • Now try raising one or both to a power. Keep a on the bottom and put T² on the side, then try a³ on the bottom instead. Only one pairing lines the points up.
  • Turn on line of best fit to judge it honestly. R² tells you how close the points are to that line: R² = 1.0000 means they sit on it exactly. That is the same trendline tool you would use in Sheets or Excel.
  • When you find the straight line, write down its equation. You have just built a mathematical model of the solar system from nothing but a table of numbers.
Why the log option is there: some of these numbers are tiny (Mercury, 0.39 AU) and some are huge (Pluto, 39 AU), so the inner planets pile up in one corner. Stretching the axes spreads them out. It does not change the data — only how much of the pattern you can see at once. With both axes stretched, the fit reports the power that links the two variables instead of a slope.

3 · How far does each object actually get?

The average distance is only one number. Each bar below runs from an object's minimum distance to its maximum distance from the Sun, with a tick at the average. The shaded bands mark the only distances where this data set actually reports each phase of water.

50 AU

Read this chart carefully

  • For most planets the bar is so short it is almost a dot — their distance from the Sun barely changes.
  • Two bars are long. Find them, and check what the table says about the water on each one.
  • The bands come straight from your data, not from a textbook: vapor is only reported inward of Venus's farthest point, liquid only at Earth's orbit, ice only from Mars's closest point outward. The gaps between bands are distances where this data set simply does not tell you.

4 · Watch the orbits

Press play. Every orbit is drawn to the same scale from the minimum and maximum distances in the table, and each object moves at its own real speed relative to the others. Keep your eye on Comet Borrelly.

1.2 yr/s
7 AU
Elapsed
0.00 yr
Borrelly distance
—
Borrelly orbits done
0
Earth distance
—
One honesty note: the data table does not say which direction each orbit's long axis points, so the orbits here are turned to arbitrary angles to keep them readable. The sizes, shapes, and speeds are all from the data.

5 · See — Think — Wonder

Fill this in on your own after you have graphed the data and talked with your group. What you type is saved in this browser, and the Print button gives you a clean copy to hand in.

SeeThinkWonder

Before you move on

  • What pattern do you see between an object's average distance from the Sun and the phase of its water?
  • What pattern do you see between average distance from the Sun and period of revolution? Does every object fit it?
  • Which pair of quantities had to be graphed to get a straight line? What is its equation?
  • What is different about the minimum and maximum distances for Comet Borrelly and for Pluto?
  • Which of these patterns helps explain why Comet Borrelly's water vaporizes every several years?