- Is this a simulation of Einstein's general relativity?
- No. While the 'rubber sheet' analogy is often used to popularize the idea of curved spacetime in GR, this simulator explicitly models Newtonian gravity. The sheet's curvature is a visual representation of gravitational potential energy, not spacetime geometry. The ball's motion is calculated from the slope (the force vector), illustrating F = -∇U, a core Newtonian concept.
- Why does the ball sometimes orbit and sometimes fall in?
- The ball's path depends on its initial speed and direction, analogous to a planet's orbital mechanics. With the right tangential velocity, it can enter a stable orbit where the inward pull (downhill slope) provides the necessary centripetal force. Too little speed, and it falls directly inward; too much, and it may escape the depression on a hyperbolic path. This demonstrates the conservation of energy in a gravitational field.
- What are the main simplifications or limitations of this model?
- The model is confined to two dimensions, whereas real gravity acts in three. The 'mass' creating the depression does not itself move in response to the ball, ignoring Newton's third law. Friction on the sheet is typically neglected, so the ball's mechanical energy is conserved, unlike real satellites that experience atmospheric drag. It is a useful metaphor, not a precise computational tool.
- How is the 'height' of the sheet related to real gravitational energy?
- The height is directly proportional to the negative gravitational potential, U. Lower height means lower (more negative) potential energy. The ball rolls to minimize its potential energy, just as objects in gravity are attracted to regions of lower gravitational potential. The steeper the slope (larger gradient of h), the stronger the gravitational force pulling the ball downhill.