Gravity and Orbital Motion
2. Planetary Motion
Learning outcomes
- I can describe Kepler's Laws of Planetary Motion.
- I can explain elliptical orbits.
- I can relate orbital speed to orbital distance.
- I can explain why planets remain in orbit.
- I can apply Kepler's Laws qualitatively.
Planetary Orbits
Planets travel around the Sun along paths called orbits. Early astronomers often assumed that these orbits were perfect circles. However, observations showed that planetary motion could not be fully explained using circular orbits.
In the early 1600s, astronomer Johannes Kepler used detailed observations of planetary positions to develop three laws describing how planets move around the Sun. These are known as Kepler's Laws of Planetary Motion.
Kepler's First Law: The Law of Ellipses
Planets orbit the Sun in elliptical paths, with the Sun located at one focus of the ellipse.
An ellipse is an oval-shaped path. It has two special points called foci.
The Sun is located at one focus rather than at the exact centre of the orbit.
This means that the distance between a planet and the Sun changes as the planet moves through its orbit.
Two important positions are:
- Perihelion – the point where a planet is closest to the Sun.
- Aphelion – the point where a planet is farthest from the Sun.
Most planetary orbits in our Solar System are only slightly elliptical, so they can appear almost circular.
Important Idea
The Sun is not normally at the centre of a planet's elliptical orbit. It is located at one focus.
Kepler's Second Law: The Law of Equal Areas
A line connecting a planet to the Sun sweeps out equal areas during equal intervals of time.
This law tells us something very important about orbital speed.
A planet does not travel at exactly the same speed throughout its orbit.
- When the planet is closer to the Sun, it travels faster.
- When the planet is farther from the Sun, it travels slower.
For example, imagine a planet travelling for 30 days near perihelion and another 30 days near aphelion. The areas swept out by the line connecting the planet to the Sun will be equal, but the planet must travel a greater distance during the 30 days near perihelion.
Therefore, it must be moving faster.
Orbital Distance and Speed
Closer to Sun → faster orbital speed
Farther from Sun → slower orbital speed
Kepler's Third Law: The Law of Periods
Kepler's Third Law connects the size of a planet's orbit with the time required to complete the orbit.
Planets farther from the Sun take longer to complete one orbit.
The time required for one complete orbit is called the orbital period.
For example:
| Planet | Average Distance from Sun. | Orbital Period |
|---|---|---|
| Mercury | 58 million km | 88 days |
| Earth | 150 million km | 365 days |
| Mars | 228 million km | 687 days |
| Jupiter | 778 million km | 11.9 years |
| Neptune. | 4.5 billion km | 164.8 years |
The pattern is clear:
Greater orbital distance → longer orbital period
The mathematical form of Kepler's Third Law is:
where:
- T = orbital period
- a = semi-major axis, representing the size of the orbit
At this level, the important idea is the relationship rather than calculations: planets with larger orbits take longer to travel around the Sun.
Why Do Planets Remain in Orbit?
Kepler described how planets move, but Newton later helped explain why they move this way.
The Sun's gravitational force pulls each planet toward the Sun.
At the same time, the planet has a forward velocity.
The combination of these two effects produces an orbit.
Think of a planet as continually falling toward the Sun but missing it.
Without gravity, the planet would continue moving approximately in a straight line.
Without sufficient sideways motion, the planet would fall toward the Sun.
Together, gravity and the planet's motion produce its curved orbital path.
Applying Kepler's Laws
Kepler's Laws allow us to make predictions without performing complicated calculations.
Example 1
Planet A is much farther from the Sun than Planet B. Which planet probably has the longer year?
Planet A.
Kepler's Third Law tells us that planets farther from the Sun have longer orbital periods.
Example 2
A comet approaches the Sun. What happens to its orbital speed?
It increases.
Kepler's Second Law tells us that an orbiting object moves faster when it is closer to the Sun.
Example 3
A planet moves from perihelion toward aphelion. What happens to its speed?
Its speed gradually decreases because it is moving farther from the Sun.
Kepler's Laws at a Glance
| Law | Main Idea |
|---|---|
| First Law | Planetary orbits are ellipses with the Sun at one focus. |
| Second Law. | Planets move faster near the Sun and slower farther away. |
| Third Law | Planets farther from the Sun have longer orbital periods. |
Did You Know?
Kepler developed his laws before Newton developed his theory of universal gravitation. Kepler could accurately describe the patterns of planetary motion, but Newton later showed that these patterns could be explained by gravity.
This was an important step in connecting observations of the Solar System with the laws of physics.
Key Terms
- Orbit – the path followed by an object around another object.
- Ellipse – an oval-shaped closed curve with two foci.
- Focus – one of two special points used to define an ellipse.
- Perihelion – the point in an orbit closest to the Sun.
- Aphelion – the point in an orbit farthest from the Sun.
- Orbital speed – the speed of an object as it travels through its orbit.
- Orbital period – the time required to complete one orbit.
- Semi-major axis – half the longest diameter of an elliptical orbit.
- Gravity – the attractive force between objects with mass.
Key Takeaways
- Planets move around the Sun in elliptical orbits.
- The Sun is located at one focus of a planetary orbit.
- Planets move faster when closer to the Sun and slower when farther away.
- Planets farther from the Sun generally have longer orbital periods.
- Gravity provides the inward force that keeps planets in orbit.
- Kepler's three laws describe important patterns in planetary motion.