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Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
In this example, a speed of 50 % of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90 %, 15 seconds to reach 99 % and so on. Higher speeds can be attained if the skydiver pulls in his or her limbs (see also freeflying). [3]
In the simplest case the speed, mass, and radius are constant. Consider a body of one kilogram, moving in a circle of radius one metre, with an angular velocity of one radian per second. The speed is 1 metre per second. The inward acceleration is 1 metre per square second, v 2 /r.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
If angle is measured in radians, the linear velocity is the radius times the angular velocity, =. With orbital radius 42,000 km from the Earth's center, the satellite's tangential speed through space is thus v = 42,000 km × 0.26/h ≈ 11,000 km/h
In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...
At a higher speed, the centrifugal force is higher. On the contrary, higher cant creates the higher centripetal force. The calculation for this assumes a constant train speed on a constant radius curve. When the speed of the train and the amount of cant are in balance (centrifugal matches centripetal), it is called equilibrium. This would make ...