How to play Satellite Launch
- Choose a launch and read the satellite's mass, its height, or the period on the card. G, M, and R are under the list.
- Use F = G·M·m ÷ r² or g = G·M ÷ r², always with r = R + h measured from Earth's centre, in metres.
- Type your answer and press Launch. A force or gravity answer is checked against the measurement; a speed launches the satellite; a radius places the geostationary orbit.
- After each launch, read the graph: at twice the distance from the centre, the pull is a quarter as strong.
What is the law of universal gravitation?
Newton's law of universal gravitation says that any two masses attract each other with a force F = G·M·m ÷ r², where r is the distance between their centres and G = 6.674 × 10⁻¹¹ N·m²/kg². The force grows with each mass and falls with the square of the distance: twice as far, a quarter of the force. Dividing by m gives the acceleration due to gravity, g = G·M ÷ r², which is the same for every object at that distance. A satellite in orbit is falling all the time, but it moves sideways fast enough that the ground curves away beneath it. For a circular orbit, gravity supplies exactly the centripetal force: G·M·m ÷ r² = m·v² ÷ r, so v = √(G·M ÷ r).
A focused learning model
Earth and the satellite are point masses, Earth stays fixed at the centre, and there is no air drag or pull from the Moon or the Sun. The path is the exact ellipse, circle, or hyperbola of the launch, timed with Kepler's equation. Hitting the ground, leaving the view, and completing an orbit are found exactly. Earth's rotation is shown only in the geostationary mission. Orbits are drawn to scale and played faster, by the factor shown on the canvas.