Kepler’s laws. KEPLER's LAW:(Johannes Kepler, 1571 - 1630) 1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus. 2. A line joining a planet and the Sun sweeps out equal areas in equal times.
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material bodies have a property called gravitational mass;
due to this property, they can exert a force (gravitational force) on other bodies that also have this property.
the force is attractive and acts along the line connecting the two bodies.
the force acts without physical contact between the bodies (“action at a distance”)
Newton's law of gravitation:
Between any two objects there acts an attractive force that is proportional to the product of the two objects' masses and inversely proportional to the square of the distance between the two objects: Fg = G m1 m2/d2
the proportionality constant G is called “gravitational constant”; G = 6.67x 10 -11 N kg -2 m2
it turns out that gravitational mass is proportional to inertial mass -- set them equal (this fixes value of gravitational constant)
distance d = the distance between the “centers of mass” (centers of gravity) of the two objects
note that gravitational force is a very weak force:
gravitational force between two football players (assume mass = 100kg each) at 1 ft distance is about 7x 10-6 newtons 1.6 x10-6 pounds!
gravitational force is weak, but has infinite range, and is not compensated by any repulsive “antigravity” in spite of its weakness, plays dominant rôle in universe;
governs motion of planets, stars, galaxies,....
instrumental in birth and death of stars
density fluctuation in interstellar gas/dust cloud can lead to run-away accumulation of matter due to gravitational attraction -- “gravitational collapse” = falling together of matter due to gravitational attraction;
formation of “protostar” = huge ball of gas (mainly hydrogen, some helium, traces of heavier stuff);
further contraction of protostar increase of temperature and pressure in its center;
when temperature and pressure high enough, “nuclear fusion” process starts;
“radiation pressure” due to nuclear fusion stops gravitational collapse;
stable midlife star (e.g. Sun): (also called “main sequence star”)
dynamical equilibrium between gravitational attraction and radiation pressure from nuclear fusion of hydrogen into helium;
star generates energy life becomes possible.
death of stars:
when hydrogen is all used up: nothing to balance gravitational attraction collapse;
further fate depends on mass of the star:
“light” star (like our sun): temperature in center not high enough to allow fusion of helium into heavier nuclei end as “white dwarf”
heavy star: fusion of helium into successively heavier elements possible, fusion stops when all is fused into iron; then gravitational collapse, stopped by neutronization: abrupt stop of collapse supernova explosion;