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That is, the individual gravitational forces exerted on a point at radius r 0 by the elements of the mass outside the radius r 0 cancel each other. As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.
Vesta (radius 262.7 ± 0.1 km), the second-largest asteroid, appears to have a differentiated interior and therefore likely was once a dwarf planet, but it is no longer very round today. [74] Pallas (radius 255.5 ± 2 km ), the third-largest asteroid, appears never to have completed differentiation and likewise has an irregular shape.
The second major reason for the difference in gravity at different latitudes is that the Earth's equatorial bulge (itself also caused by centrifugal force from rotation) causes objects at the Equator to be further from the planet's center than objects at the poles. The force due to gravitational attraction between two masses (a piece of the ...
Animations of the Solar System's inner planets orbiting. Each frame represents 2 days of motion. Animations of the Solar System's outer planets orbiting. This animation is 100 times faster than the inner planet animation. The planets and other large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic ...
The gravitational field equation is [7] = = = | | =, where F is the gravitational force, m is the mass of the test particle, R is the radial vector of the test particle relative to the mass (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a particular point in space ...
In tightly packed planetary systems, the gravitational pull of the planets among themselves causes one planet to accelerate and another planet to decelerate along its orbit. The acceleration causes the orbital period of each planet to change. Detecting this effect by measuring the change is known as transit-timing variations.
The blue planet feels only an inverse-square force and moves on an ellipse (k = 1). The green planet moves angularly three times as fast as the blue planet (k = 3); it completes three orbits for every orbit of the blue planet. The red planet illustrates purely radial motion with no angular motion (k = 0).
[4] [verification needed] A more complex example is the one at right, the Earth's Hill sphere, which extends between the Lagrange points L 1 and L 2, [clarification needed] which lie along the line of centers of the Earth and the more massive Sun. [not verified in body] The gravitational influence of the less massive body is least in that ...