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The gravitational force that a celestial body exerts on a space vehicle is modeled with the body and vehicle taken as point masses; the bodies (Earth, Moon, etc.) are simplified as spheres; and the mass of the vehicle is much smaller than the mass of the body so that its effect on the gravitational acceleration can be neglected.
In the absence of other forces, gravity results in a constant downward acceleration of every freely moving object. Near Earth's surface the acceleration due to gravity is g = 9.8 m⋅s −2 and the gravitational force on an object of mass m is F g = mg. It is convenient to imagine this gravitational force concentrated at the center of mass of ...
The period of the resultant orbit will be longer than that of the original circular orbit. The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecrafts are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster.
where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry ...
The speed (or the magnitude of velocity) relative to the centre of mass is constant: [1]: 30 = = where: , is the gravitational constant, is the mass of both orbiting bodies (+), although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths.
The gravitational constant is a physical constant that is difficult to measure with high accuracy. [7] This is because the gravitational force is an extremely weak force as compared to other fundamental forces at the laboratory scale. [d] In SI units, the CODATA-recommended value of the gravitational constant is: [1]
In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime ...