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The following box is a condensation of my pages Gravity 1+, not necessarily updated.
In Newtonian gravity, every element of mass attracts every other element with a force proportional to the product of their masses divided by the square of the distance between them.
G is about 6.675×10-11 m3 kg-1 s-2. The local field, g, is about 9.81 m s-2 at Earth's surface.
A uniform spherical shell causes no field inside itself. Outside a symmetrical sphere, its field is as if all its mass were at the centre.
Circular orbital speed balances "centrifugal force" and gravity, v = √gr. Escape speed is the speed needed to reach infinity, √2gr. Surface escape speed is what would be needed to attain a height of one radius against the surface field.
The period of a circular orbit about a spherically symmetric mass distribution depends only and inversely on the square root of the average density D within the circumscribing sphere; it is √ ( 3π / (G D) ). That relates immediately to Kepler's Third Law.
Kepler's Laws, derived from observation :-
Newton showed? that they apply in the case of two bodies interacting by any attracting force along the line of their centres, proportional to the product of their masses and inversely proportional to the square of their separation. The Third Law applies among the secondaries of a given primary.
The path of the Moon is everywhere curved towards the Sun, because the Sun's pull exceeds the Earth's.
Seen from a celestial pole, the paths of Europa and Dione cross themselves, because they orbit at higher speeds than their planets.
The paths of Uranian satellites look peculiar, as the system is tilted so.
The true paths of our other major natural satellites are wavy lines, like the path of Earth around the Galactic centre and the paths of artificial satellites.
If a lesser mass is in a circular orbit around a much greater, there are co-rotating locations (the Lagrange Points, L1..L5) where a particle may reside, stably or unstably.
For the Earth-Moon system, points L3, Earth, L1, Moon, L2 are in that order in a straight line. Points L4 & L5 are 60° away, approximately in the Moon's orbit; L4 leads, L5 trails.
(However, Henry Spencer has said that astronomers prefer the order L1, Earth, L2, Moon, L3; again L4 leads, L5 trails.) - IS HE RIGHT?
Points L1, L2 and L3 are not stable. Halo orbits exist around them and are used. The SOHO solar observatory orbits the Sun-Earth L1 point. Herschel and Planck are goung to orbit Sun-Earth L2. The future James Webb Space Telescope may go to Sun-Earth L2.
If the primary:secondary mass ratio exceeds almost 25:1 (total/secondary almost 26), there are stable regions around the "Trojan Points" L4 & L5. The original Trojan asteroids, named after heroes in Homer's Iliad, are in the L4 & L5 regions of the Sun-Jupiter system.
I don't know much about this - please advise. It concerns the greatest radius from a planet at which a satellite will be bound and not escape onto Solar orbit.
Sea-tides are mainly caused by the lunar gravity gradient (with a component from the solar).
"Spring" tides occur when Earth, Sun, and Moon are in line, and the gradients reinforce; "Neap" tides occur when Sun, Earth, and Moon form a right angle. Eclipses only occur at Spring Tides.
Tides tend to cause the orbits of planets and moons to circularise and synchronise. The tidal effect of a body is proportional to its density & the cube of its apparent angular diameter, only.
Roche's Limit for a non-cohesive non-rotating satellite of a primary body is that the satellite will be broken up tidally if the centre-centre distance is less than about 2.423 primary radii times the cube root of the density ratio.
The outer limits of the icy particulate ring systems of the four major planets of the Solar System are near, but within, the Roche limit.