On this page
Orbits make the most sense when you treat them as experiments: predict what a planet will do, run the simulation, then check the result against the physics and against real NASA numbers. Here are four predictions to test in any gravity simulation.
What do you need to set up first?
Use one heavy star, one light planet, a speed control, a velocity arrow and an orbit trail. Launch the planet sideways, at right angles to the line joining it to the star, and write down your prediction before you press play. It is the same method as in our post on learning projectile motion with a simulation. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read, and orbits are one of them.
What speed gives a circular orbit?
For a circle, gravity has to supply exactly the centripetal force. Setting GMm/r² equal to mv²/r gives an orbital speed of v = √(GM/r) (HyperPhysics, orbit velocity). The planet's own mass cancels out, so a light planet and a heavy one need the same speed.
Test: find the speed that keeps the distance constant. Then make the radius four times bigger. Prediction: the speed you need halves.
Check with real numbers: NASA's Earth fact sheet gives Earth's GM as 398,600 km³/s² and its mean radius as 6,371 km. Put those into the formula and you get about 7.9 km/s for an orbit just above the surface, ignoring air resistance.
Why does a planet speed up near the Sun?
According to NASA's page on orbits and Kepler's laws, Kepler's first law says each planet's orbit is an ellipse with the Sun's centre at one focus. His second law says the line joining a planet to the Sun sweeps out equal areas in equal times.
The second law comes from conservation of angular momentum (HyperPhysics, Kepler's laws). At the closest and farthest points the velocity is perpendicular to the radius, so r × v is the same at both points.
Worked example: NASA lists Earth's perihelion as 147.095 million km and its aphelion as 152.100 million km (Earth fact sheet). From that, the speed ratio should be 152.100 ÷ 147.095 ≈ 1.034. The same sheet gives a maximum orbital speed of 30.29 km/s and a minimum of 29.29 km/s, and 30.29 ÷ 29.29 ≈ 1.034.
Test: launch slightly below circular speed and watch the velocity arrow grow on the way in and shrink on the way out. For the history of how Kepler found these laws, read Kepler's three laws in Tycho Brahe's data.
How does the orbital period change with distance?
NASA states Kepler's third law as: the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit (NASA). For a circle, combine T = 2πr/v with v = √(GM/r) to get T² = (4π²/GM) r³.
Worked example: the NASA planetary fact sheet puts Mars 228.0 million km from the Sun and Earth 149.6 million km away. The ratio is 1.524, and 1.524 to the power 1.5 is about 1.88. Multiply 365.2 days by 1.88 and you get roughly 687 days. NASA lists Mars's period as 687.0 days.
Test: double the orbit radius in the simulation. Prediction: the period grows by 2^1.5, about 2.83 times.
What is escape speed, and how is it different from orbital speed?
Escape speed is the launch speed at which an object's kinetic energy equals the size of its gravitational potential energy, so it never falls back: v = √(2GM/r) (HyperPhysics, escape velocity). At any given radius, that is √2 (about 1.41) times the circular orbit speed.
NASA gives Earth's escape velocity as 11.186 km/s (Earth fact sheet). Divide that by the 7.9 km/s circular speed from earlier and you get about 1.41, as predicted.
The prediction ladder. Launch sideways at k times the circular speed and predict before each run:
k = 0.8: an ellipse, and the launch point becomes the farthest point.
k = 1.0: a circle.
k = 1.2: an ellipse, and the launch point becomes the closest point.
k = √2, about 1.414: the planet just escapes and never comes back.
k = 1.6: it escapes faster, on a straighter path.
The rule behind the whole ladder is total energy, ½mv² − GMm/r. If it is negative, the orbit is closed. If it is zero or positive, the planet escapes. Our guide to orbital speed, energy and escape speed problems turns this into exam-style numericals.
What should you do after the simulation?
Write each law in one sentence, with the number that confirmed it. Then try two textbook numericals without notes. If the picture makes sense but your answers still go wrong, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
