Every path in this app comes from one gravity rule: Earth pulls things toward its centre, weaker with distance. The thrown-ball scenes integrate that rule directly. The satellite scenes use perfect circles worked out from the same rule, with Earth's real size and real spin.
Left out on purpose: air, mountains, the Moon and Sun, and Earth's slight flattening. The mightiest throw pretends there is no air to slow the ball. Drawings are not to scale; the speeds and times are real. A one-day orbit means one Earth spin (about 23 hours 56 minutes), not exactly the clock day.
Sources: ESA's orbit guides for kids and for spacecraft, NASA's space flight basics, and the IERS standards for Earth's numbers. Links are in the project readme.