Using Slooh’s Online Telescope and integrated NGSS aligned Quest learning activities, you can create your own posters about Kepler’s laws while learning more about planetary motion. In the Footsteps of Kepler - Planetary Motions is one of 60+ curriculum-aligned STEM Quest learning activities on Slooh for students 4th grade to college.

Slooh’s Online Telescope:

## Kepler's Laws of Planetary Motion

### Ellipses

To be able to understand Kepler’s laws, let’s first quickly look at the geometry of ellipses. Ellipses are curves that can be described by two focus points, or focal points. A circle is a particular case of an ellipse with only one focus point at its center, where the distance between it and every point on the circle’s perimeter is the same. Ellipses look like a squashed circle. The way that ellipses are described is by the quantity called eccentricity (E). A shape's eccentricity defines the kind of conic section it is: zero for a circle, zero to one for an ellipse, one for a parabola, and greater than one for a hyperbola.

Take a look at the diagram below with ellipses with an eccentricity of 0.6. The leftmost ellipse in the diagram has the locations of its center and two focal points marked. The foci are at unique locations inside an ellipse. The sum of the distances from each focus to any other point on the ellipse is the same for a given ellipse. The semi-major (SMJA) and semi-minor axes (SMNA) are the longest and shortest distances from the ellipse’s center to the perimeter. The apoapsis (A) and periapsis (P) are the longest and shortest distances from one focal point to the perimeter along the semi-major axis.

There are many geometrical relationships between the eccentricity, semi-major axis, semi-minor axis, periapsis, and apoapsis; the diagram above contains a few equations of these relationships. The two foci points converge to the center when an ellipse loses ellipticity and becomes a circle. Not only that, notice how the semi-major axis, semi-minor axis, periapsis, and apoapsis all become the same length for circles.

Now let’s look at Kepler’s laws of planetary motion!

### Kepler's First Law

Kepler’s first law states that the orbital path of a planet around the Sun is an ellipse with the Sun at one of the focal points. The early geocentric and heliocentric models of the Solar System break this law because they assumed the planets had circular orbits.

This law tells us that the distance between the planet and the Sun is not constant. A planet is at its closest approach at perihelion and its furthest point at aphelion. Note that these terms are similar to periapsis and apoapsis except with different suffixes. The suffix of peri-/apo- changes depending on the focal point (see table below), but the geometric meaning remains the same. Also note that, although the diagram shows a dramatic eccentricity of 0.4, most planets in the solar system have very low eccentricities. In other words, their orbital paths are nearly, but not precisely, circular.

You can observe Kepler’s first law in action when looking at the Earth-Moon system. The Moon orbits the Earth in an ellipse, with the Earth at a focal point. That means that the distance between the Earth and Moon is continuously changing. A supermoon occurs when a Full Moon is near perigee, and a micromoon happens when the Full Moon is near apogee.

Celestial Object | Suffix | Celestial Object | Suffix |

Generic Object | -apsis | Jupiter | -jove |

Mercury | -hermion | Saturn | -chron |

Venus | -cythe | Sun | -helion |

Earth | -gee | Star | -astron |

Moon | -lune | Black Hole | -bothron |

Mars | -areion | Galaxy | -galacticon |

Suffixes for the periapsis and apoapsis depending on the kind of object the body is orbiting

### Kepler's Second Law

Kepler’s second law states that a line from a planet to the Sun sweeps out equal areas during equal time intervals. See the diagram below for an illustration of this law.

The amount of time it takes for the planet to travel the perimeter of each shaded region is the same, and the area that those journeys carve out is also the same. This law means that the planet must be moving slower when traveling along the perimeter of the shaded region on the left than along the right region. In general, a planet slows down when it nears apoapsis, and it speeds up as it nears periapsis.

### Kepler's Third Law

Kepler’s third law states that the square of the orbital period is directly proportional to the cube of the semi-major axis of its orbit. Writing this in equation form gives the following:

In the equation, “p” is the orbital period (the time it takes the object to complete a full orbit), “a” is the semi-major axis, and “C” is the constant of proportionality. The constant is the same for every planet in the solar system. Graphically, this means that, when the square of the orbital period and the cube of the semi-major axis are plotted, they should form a linear graph, as shown below.

In general, the further a planet is from the Sun, the longer it takes to complete its orbit.

Planet | Semi-Major Axis (AU) | Orbital Period (years) | Eccentricity (-) |

Mercury | 0.3871 | 0.2409 | 0.205 |

Venus | 0.7233 | 0.6152 | 0.007 |

Earth | 1.000 | 1.000 | 0.017 |

Mars | 1.524 | 1.881 | 0.094 |

Jupiter | 5.204 | 11.86 | 0.049 |

Saturn | 9.582 | 29.42 | 0.057 |

Uranus | 19.20 | 83.75 | 0.046 |

Neptune | 30.05 | 163.7 | 0.011 |

Table showing the orbital properties of our Solar System's planets

## More About Slooh's In the Footsteps of Kepler - Planetary Motions Quest

The wandering planets follow the same physical laws as all matter in the universe. In this quest, you will discover how humanity unveiled the extraordinary physical laws of orbital motion. You'll learn about Johannes Kepler and his three laws of planetary motion. You'll also learn about Sir Isaac Newton and his theory of gravitation. By the end of the quest, you will discover the similarities between Kepler's laws and Newton's gravity, and how these laws apply to our tiny corner of the galaxy—the Solar System.

### Related Slooh Quests

Solar System Explorer

Stars Like Ours

The Mystery of the Changing Moon

## More About Slooh's Astronomy NGSS Aligned Learning Activities

Slooh’s Online Telescope is a learning platform designed to support any educator in teaching astronomy to meet NGSS requirements by collecting and analyzing real-world phenomena. No previous experience with telescopes is necessary to quickly learn how to use Slooh to explore space with your students.

You can join today to access Slooh's Online Telescope and all 60+ Quest learning activities if you are able to make astronomy a core subject of study for the semester or year. If you only have a few weeks to study astronomy, we also have a curriculum designed to fit your busy academic schedule and budgetary limitations. To learn more about our offers, click here.