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The green path in this image is an example of a parabolic trajectory. A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
If is zero or a negative real number, the orbit is a parabola or a hyperbola, respectively. In these latter two cases, u 2 {\textstyle u_{2}} represents the distance of closest approach; since the orbit goes to infinity ( u = 0 {\textstyle u=0} ), there is no distance of furthest approach.
The trajectory then generalizes (without air resistance) from a parabola to a Kepler-ellipse with one focus at the center of the Earth (shown in fig. 3). The projectile motion then follows Kepler's laws of planetary motion. The trajectory's parameters have to be adapted from the values of a uniform gravity field stated above.
If one of the principal curvatures is zero: κ 1 κ 2 = 0, the Gaussian curvature is zero and the surface is said to have a parabolic point. Most surfaces will contain regions of positive Gaussian curvature (elliptical points) and regions of negative Gaussian curvature separated by a curve of points with zero Gaussian curvature called a ...
Weightlessness is the complete or near-complete absence of the sensation of weight, i.e., zero apparent weight. It is also termed zero g-force, or zero-g (named after the g-force) [1] or, incorrectly, zero gravity. Microgravity environment is more or less synonymous in its effects, with the recognition that g-forces are never exactly zero.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
It may be more predictable assuming a flat Earth with a uniform gravity field, and no air resistance. The horizontal ranges of a projectile are equal for two complementary angles of projection with the same velocity. The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight.