Solar system

Model the four terrestrial planets (Mercury, Venus, Earth, Mars) orbiting the Sun with their real distances and speeds in the FizziQ Web Orbits and Gravitation simulation.

Learning objectives:

The student configures a five-body system in the Orbits and Gravitation simulation: the Sun and the four terrestrial planets (Mercury, Venus, Earth, Mars) with their real masses, distances and orbital speeds. The student runs the simulation and observes the four nested coloured orbits around the Sun. The student measures each planet's orbital period and compares it to astronomical values (88, 225, 365 and 687 days). The student discovers that a more distant planet orbits more slowly and computes T²/r³ ratios to highlight a pattern common to all four orbits.

Level:

Author:

Middle school

FizziQ

Duration (minutes) :

40-60

What students will do :

'- Configure a five-body system in the FizziQ Web Orbits and Gravitation simulation
- Enter the real masses, distances and orbital speeds of the four terrestrial planets
- Measure each planet's orbital period and compare to known astronomical values
- Identify the qualitative relationship between distance to the Sun and the duration of one revolution
- Discover a numerical regularity common to all four orbits (T² ÷ r³ ≈ 1 in years and AU)

Scientific concepts:

'- Solar system
- Terrestrial planets
- Universal gravitation
- Heliocentric orbit
- Orbital period
- Orbital speed
- Astronomical unit
- Kepler's regularity

Sensors:

'- FizziQ Web Orbits and Gravitation simulation

What is required:

'- Computer, tablet or smartphone with FizziQ Web
- FizziQ experiment notebook

Experimental procedure:

Open the Orbits and Gravitation simulation in FizziQ Web (Experiment → Simulations → Orbits and gravitation).
Set the distance scale to 1,500,000 km/pixel (ruler icon) to see orbits up to Mars, and the time scale to 6 hours per frame (speed icon) to observe several revolutions.
Select body 1 and configure it as the Sun: mass 333,000 M⊕ (slider on "Sun"), speed 0 km/s, angle 0°. Leave it at the centre of the screen.
Select body 2 and configure it as Mercury: custom mass 0.055 M⊕, speed 47.4 km/s, angle -90°. Drag it to the right of the Sun until the "distances" panel reads about 58 million km.
Add a new body via the "+" tab and configure it as Venus: mass 0.815 M⊕, speed 35.0 km/s, angle -90°, distance to Sun 108 million km.
Add the Earth body: mass 1 M⊕, speed 29.8 km/s, angle -90°, distance to Sun 150 million km.
Add the Mars body: mass 0.107 M⊕, speed 24.1 km/s, angle -90°, distance to Sun 228 million km.
Assign a different colour to each planet via the palette button to distinguish them easily.
Click the body 1 (Sun) centering button in the Centering area to lock the view on the Sun throughout the simulation.
Click the red REC button to start recording. The simulation launches automatically and traces the four nested coloured orbits around the Sun.
Let the simulation run until Mars completes at least one full revolution (~687 days, about 30 seconds on screen). During this time, Mercury will have orbited about 8 times.
Click REC again to stop recording. The x_i and y_i positions of each planet are automatically exported to the experiment notebook.
In the experiment notebook, plot for each planet the x coordinate versus time. The curve is sinusoidal: the duration between two successive maxima gives the period T.
Fill in a 5-column table: Planet, Distance r (million km), T measured (days), T real (days), Deviation (%). Expected real values: Mercury 88 d, Venus 225 d, Earth 365 d, Mars 687 d.
Convert T to years (T_days ÷ 365.25) and r to astronomical units (r_M_km ÷ 150). Compute T² ÷ r³ for each planet and verify that this ratio is almost 1 for all four planets: this is Kepler's regularity.

Expected results:

The four planets appear in nearly circular nested orbits around the Sun, all rotating in the same direction. Mercury, the closest, completes one revolution in about 88 days; Venus in 225 days; Earth in 365 days; and Mars, the farthest, in about 687 days. Measured periods match astronomical values within a few percent due to the symplectic Euler numerical integration and limited simulation duration. When converting T to years and r to astronomical units (Earth = 1 year, 1 AU), the T²/r³ ratio is almost exactly 1 for all four planets: this is the regularity Kepler discovered in 1619. This result illustrates that the same law of gravitation governs all the planets in the solar system.

Scientific questions:

'- Why do planets closer to the Sun orbit faster than more distant ones?
- What would happen if the Sun were removed from the simulation? How would the planets' trajectories evolve?
- Why is the T²/r³ ratio nearly identical for Mercury, Venus, Earth and Mars?
- Why aren't the orbits perfectly circular even with a fixed initial speed?
- How could Kepler's regularity be used to predict the period of a planet whose distance to the Sun is the only known value?

Scientific explanations:

The solar system is composed of the Sun and eight planets. The four closest to the Sun — Mercury, Venus, Earth and Mars — are called terrestrial planets because they have rocky surfaces. The four farther out (Jupiter, Saturn, Uranus, Neptune) are gas giants, much more massive.

All planets orbit the Sun thanks to universal gravitation described by Isaac Newton. The Sun, with its enormous mass (333,000 times that of Earth), attracts each planet and keeps it in a nearly circular orbit.

The closer a planet is to the Sun, the stronger the gravitational attraction it experiences, and the faster it must move to avoid falling into the Sun. Mercury races at 47 km/s, while Mars, farther away, moves at only 24 km/s.

The farther a planet is, the longer the path to travel and the slower it moves: its orbital period is therefore much longer. The period goes from 88 days for Mercury to 687 days for Mars, almost 8 times longer.

The astronomical unit (AU) equals 150 million km, the mean Earth-Sun distance. Mercury is at 0.39 AU, Venus at 0.72 AU, Earth at 1 AU and Mars at 1.52 AU.

In 1619, Johannes Kepler discovered an astonishing regularity: for all planets, the ratio T² / r³ is constant. If T is expressed in years and r in astronomical units, this ratio equals 1 for the four terrestrial planets as for the others.

The simulation reproduces this regularity because it applies the same law of gravitation to all planets: this result illustrates that the same Newtonian physics governs all bodies in the solar system.

Extension activities:

Frequently asked questions:

Q: Why can't I include all eight planets of the solar system?
A: The simulation accepts at most 5 simultaneous bodies. So we can model the Sun and 4 planets only, which is enough to study the fundamental principles and Kepler's regularity.

Q: How can I place a planet precisely at the right distance from the Sun?
A: Drag the body with the mouse and watch the "distances" panel in the upper right, which displays in real time the distance between all bodies. The scale indicator at the bottom left also helps to estimate.

Q: Why are all initial angles set to -90°?
A: So that all planets orbit in the same direction around the Sun and their initial velocity is perpendicular to the Sun-planet direction — the condition for a circular orbit.

Q: Why do my orbits cross or become unstable?
A: The initial speeds must match the real circular orbital speeds (47.4 / 35.0 / 29.8 / 24.1 km/s). An error of a few km/s makes the orbit elliptical; too large an error can make the planet escape or fall into the Sun.

Q: How do I express T² ÷ r³ in years² per AU³?
A: Convert T to years (T_days ÷ 365.25) and r to astronomical units (r_km ÷ 150,000,000). With these units, the ratio equals 1 for Earth and stays very close to 1 for all other planets in the solar system.