Solar System Simulator — Planetary Orbits & Kepler's Laws
Explore eight elliptical planetary orbits with the Sun at a focus. Compare orbital periods and semi-major axes, and try enlarged moon orbits and examples. This educational model does not predict configurations for real dates.
Simulation Settings
Model elapsed time: 0.000 years
Focus (center and scale)
Display Options
Controls
Planet Info
Aerospace CAE Connection
Orbital mechanics forms the basis of satellite trajectory design (Hohmann transfers, gravity assists). CAE tools handle spacecraft structural loads during launch, thermal cycling in orbit, and aerodynamic heating during atmospheric re-entry.
Results
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Selected
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Period (yr)
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Semi-major axis (AU)
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Mass (Earth=1)
Solar System — Top View (Ecliptic Plane)Click a planet for details
Planetary orbits
This educational planar two-body model places the Sun at an ellipse's focus and solves M = E − e sin E for orbital position. All planets start at perihelion; inclinations, orbital orientations and perturbations are omitted. It does not predict actual planetary configurations for calendar dates or observing locations. Planet and moon sizes are exaggerated. The Moon and four Jovian moons use circular approximations with aligned initial phases, not actual satellite configurations. Orbital formula reference: NASA/JPL
Try perihelion and aphelion
Each example pauses and focuses the chosen planet. Compare r = a(1 − e) with a(1 + e), then play to observe the changing distance. These distances are calculated from this educational model, not for a real calendar date.
Explore enlarged satellite orbits
Enlarged circular orbits centered on the parent planet. Orbital distance ratios are preserved; body sizes alone are exaggerated for visibility. This is not a configuration for a real date.
Note: Planet sizes are exaggerated for visibility. On true scale, even Jupiter is tiny compared to its orbital radius. Scroll or use the slider to zoom.
Theory & Key Formulas
Orbital period $T$ and semi-major axis $a$:
$$T^2 \propto a^3$$
In AU/year units: $T^2 \approx a^3$. Neptune's period ≈ $30.07^{3/2}$ ≈ 164.8 years.
What is Orbital Mechanics & Kepler's Laws?
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What exactly are Kepler's Laws? I see planets moving in the simulator, but what's the rule behind their paths?
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They describe ideal two-body orbits. Real planetary motion also includes perturbations. The first law places the Sun at a focus of an ellipse. This educational view omits orbital inclinations and orientations; it is not a map of the planets on a real calendar date.
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Wait, really? So a planet doesn't move at a constant speed? That seems weird.
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That is Kepler's Second Law: equal areas are swept out in equal times, so speed increases near perihelion and decreases near aphelion. Pause or reduce the playback speed to inspect Mercury's motion. Orbit lines do not change color to mark these points.
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Okay, I see the speed change. But what connects a planet's "year" to its distance from the Sun? Is there a formula?
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Great question! That's Kepler's Third Law. It gives us a precise mathematical relationship: the square of a planet's orbital period is proportional to the cube of its average distance from the Sun. A common case is comparing Earth and Mars. Try changing the "Focus On" parameter to Mars. You'll see its year is much longer, and that's because its orbit is so much larger—and the law tells us exactly how much longer.
Physical Model & Key Equations
The most famous and practical of Kepler's Laws is the Third Law, which relates a planet's orbital period (its "year") to the semi-major axis of its elliptical orbit (essentially its average distance from the Sun).
Where $T$ is the orbital period (e.g., in Earth years), and $a$ is the semi-major axis (often in Astronomical Units, AU, where 1 AU is the Earth-Sun distance). The constant is the same for all objects orbiting the same central body (like our Sun).
When we include Newton's Law of Universal Gravitation, we can derive the exact constant, leading to a more powerful form of the law.
$$T^2 = \frac{4\pi^2}{G(M_{\odot} + m)}a^3$$
Here, $G$ is the gravitational constant, and $M_{\odot}$ and $m$ are the masses of the Sun and the planet. Since the Sun's mass is enormous, $M_{\odot}+ m \approx M_{\odot}$. This equation is the foundation for calculating orbits of planets, asteroids, and human-made satellites.
Real-World Applications
Satellite Trajectory Design: Kepler's Laws are the ABCs of placing satellites in correct orbits. Engineers use them to calculate the precise speed and altitude needed for a communications satellite to remain in geostationary orbit, appearing fixed over one point on Earth.
Space Mission Planning: Every interplanetary mission, like the Mars rovers, relies on these laws. Mission planners calculate efficient transfer orbits (called Hohmann transfers) based on Kepler's Third Law to determine launch windows and flight duration with minimal fuel.
Exoplanet Discovery: Astronomers apply these laws in reverse to discover planets around other stars. By measuring the periodic wobble or dimming of a star (caused by an orbiting planet), they can use Kepler's Third Law to estimate the planet's orbital distance and mass.
Aerospace CAE & Simulation: Before launch, CAE software uses orbital mechanics to simulate structural loads on a spacecraft during launch, predict thermal cycles it will experience in orbit, and model the extreme aerodynamic heating it must withstand during atmospheric re-entry.
Common Misconceptions and Points to Note
This page draws elliptical orbits with the Sun at a focus. Low-eccentricity orbits may look nearly circular. With the model’s Mars values a=1.524 AU and e=0.093, perihelion distance is a(1−e)=1.382268 AU and aphelion distance is a(1+e)=1.665732 AU. This distance variation alone does not determine a spacecraft launch window. Actual planetary configurations and transfer-orbit calculations are outside this page’s scope.
Second, understand that the simulation ignores the gravitational influence of other planets. This simulation is fundamentally based on the two-body problem of "the Sun and one planet." However, in reality, the gravity of massive planets like Jupiter perturbs the orbits of others. Practical trajectory calculations must handle this "n-body problem," making the computations significantly more complex.
Third, distinguish playback speed from the orbital method. This tool solves Kepler's equation from elapsed time; it does not advance positions by Euler integration of gravitational acceleration. Faster playback causes larger jumps between frames, making fine motion harder to inspect. Slow down or pause. Matching a real calendar date would also require initial phases and orbital orientations that this educational model omits.
Yes. Values 1–7 are seven speed levels, not real-time multipliers. The default level 3 advances approximately 30 model days per real second; level 7 advances one model year per real second. Pause the animation to inspect the view.
Pause, adjust the zoom, and click or tap the planet circle. Information appears within this page, not in a separate pop-up window. Choosing a planet in the focus dropdown centers and enlarges the view to its orbital scale. This is separate from selecting a planet for information.
No. This is an educational planar two-body model using rounded planetary data. It places the Sun at a focus and solves Kepler’s equation. All planets start at perihelion; orbital orientations, inclinations and perturbations are omitted. The clock shows model elapsed time, not actual planetary configurations on calendar dates.
Yes. Open Parameters to use the speed and zoom sliders or number fields, and tap a planet. There is no drag-to-rotate feature or dedicated pinch-to-zoom control.
How to use
Choose speed level 1–7 and use Pause or Play to inspect the motion. These values are level numbers, not multipliers.
Adjust zoom from −12 to 12. Sun focus shows the whole system; planet focus centers and enlarges the view to that planet’s orbital scale.
Click or tap a planet circle to read its period, semi-major axis and mass on the page. If planets overlap, pause, focus on the target planet, then adjust zoom.
Worked example
The page uses Mercury’s a=0.387 AU, e=0.206 and T=0.2408 years. Its perihelion distance is a(1−e)=0.307278 AU, and its aphelion distance is a(1+e)=0.466722 AU. For Earth, a=1 AU and e=0.017 give 0.983 AU and 1.017 AU. The semi-major axis stays constant, but instantaneous distance from the Sun changes. T²/a³ is approximately 1 in Earth-based AU/year units; rounded tabulated values are not exactly identical.
Model limitations
Planet sizes are exaggerated for visibility. Do not infer actual planet-to-planet distances from the sizes of their drawn circles.
The model does not time-integrate gravitational acceleration. Faster playback increases frame-to-frame movement; it does not demonstrate accumulating Euler-integration errors.
Actual observing positions, launch windows and navigation require suitable orbital elements or ephemerides and separate calculations.