ABSTRACT
The Study explains how it is possible to calculate and to animate the motion of material points (planets and satellites) under the influence of inertia, gravity and medium resistance forces. Various interesting configurations of planets and their satellites are considered. The motion of a comet is studied on the basis of solving systems of differential and algebraic equations.
Mathematics: Ordinary differential equations (ODEs), system of ordinary differential equations, initial conditions, boundary value problem, integral curves, definite integral, derivative, spherical volume, circle area, second-order curve, hyperbola, ellipse, parabola, Euler’s method for solving systems of differential equations, Runge-Kutta method, Gaussian curve (normal distribution), canonical transformation, attractor, system of linear homogeneous algebraic equations, set of proportional solutions.
Physics: Celestial mechanics, the law of universal gravitation, Newton’s second law, Kepler’s second law, Kepler’s clock, gravitational constant, acceleration of gravity, medium resistance, planets, orbit correction, satellite interception, satellite exchange, parachute jump, rocket motion, barometric formula, satellite of the Earth, meteorite near the Earth, landing of a spacecraft, mathematical and physical pendulum, gravitational train, damped oscillations, profile of tram rails, roller coaster (Russian mountains).
IT: Numerical and symbolic solution of differential equations and their systems, methods for solving differential equations and their systems, computer animation, numerical error.
Art: A.S. Pushkin The Portrait, The Stone Guest, the movie Armageddon.
Study website: https://community.ptc.com/t5/PTC-Mathcad/Celestial-Mechanics/m-p/562213" xmlns:xlink="https://www.w3.org/1999/xlink">https://community.ptc.com/t5/PTC-Mathcad/Celestial-Mechanics/m-p/562213.
Dialogue during a lesson of computer modeling.
Student“Please look, how the two bodies on my screen rotate precisely in orbits!”
The teacher, frowning at the display“Here you do not have two bodies rotating, but three, as Isaac Newton, too, turns over in his coffin…”
