Physics · Earth Science · Grades 5–12
Newton’s Mountain
Isaac Newton, in the Principia (A.D. 1687), imagined a cannon on a mountain above the air. A slow shot falls. A faster shot falls farther around the curve of the Earth. Fast enough, and it keeps falling around the Earth: an orbit. Faster still, and it leaves.
Space plays and pauses. R resets. Arrow keys change speed and aim when the picture is focused. Drag the arrow to aim. There is no air in this model, which is why Newton put the cannon above the atmosphere.
Payload 400 kg. Empty stage 1 is 2,500 kg. Empty stage 2 is 800 kg. Fuel is what you set.
What to watch
The shot is always pulled toward the center of the Earth. If it is slow, the pull wins and it lands. If it is fast enough sideways, it falls past the horizon again and again. That closed path is an orbit. Astronauts float because they are falling with their ship, not because gravity has stopped.
A rocket’s job is to reach that sideways speed. Two stages can do it with tanks that one stage cannot, because the empty first tank is dropped.
Acceleration is GM / r² toward the center, with GM = 3.986 × 10¹⁴ m³/s² and Earth’s radius 6,371 km. Circular speed is √(GM / r). Escape speed is √2 times that. Specific energy ½v² − GM / r is negative for a closed orbit and zero or positive for escape.
The path is stepped with velocity Verlet. Equal areas are the sector swept from Earth’s center in equal times: Kepler’s second law, which holds for any central pull.
The rocket equation is Δv = ve ln(mstart / mfinish). After stage 1, its empty mass is dropped before stage 2 fires. The one-stage comparison keeps the same fuel, the same empty mass, and the faster of the two exhaust speeds.
Original School Launch model. No air, no outside data, and nothing you do here is saved or sent. The mountain is a thought experiment, not a place you could stand.