Newton's Universe --------------- In Newton's day and for a century after there was no application for gravity in the world except within the solar system. It had everything known to move around. The stars beyond were a sort of background against which the planets &c were gaged for position and motion. The real character of the stars was indeterminate, altho there were many philosophical and theological ideas. Newton could believe that the world beyond the solar system was populated with luminous bodies, each having a definite mass, ranging on and on into infinite depths. Already the new telescope was unveiling stars far fainter than could be discerned by eye and these were plausibly far more renote than the naked-eye stars. With each increase in telescope strength more and fainter stars were seen, giving a vivid impression that the universe is indefinitely deep and thick with stars. If these stars had gravity toward each other, why did they not collapse together or exhibit orbital motion? Newton felt that they wre arrayed uniformily thruout space such that in opposite directions around any one there were equal numbers of stars pulling at it. Thus for every star the gravity toward one direction balanced that in the opposite direction and the whole enchillada remained stationary. (Orbital motion in binary stars and proper motion in individual stars was still far in the future.) Early Problems ------------ A moment's consideration reveals that there is a very serious difficulty with Newton's world. Not only does the gravity cancel out in opposite direction around a star but the separate strength of the two gravity forces is infinite! Stars range outward for infinite distances thereby putting an infinite number of stars on the two opposite sides. The gravity of the two sets of stars is infinite. There is a tug-of-war of incredibly massive scale in all directions around every point in the universe! Should there be even the merest imbalance in the summed up masses of stars the forces become unbalanced and the central star runs off in chaotic motion. This upsets the mass for other points and soon the whole world is in utter upheavel as stars spiral and career all over the place. The balance of mass must be absolutely exact or else. In Newton's time there was no solution. He lived when Euclid was simply the geometry and space was an externality and gravity was an instantaneous action-at-a-distance. Newton seems to have been troubled by this situation as evidenced by correspondence he carried on with Bentley. But in the main astronomers sort of ignored it and simply accepted that the universe is infinite in extent yet remained stable and flat. Even the discovery of proper motion and binary stars and even open clusters didn't disturb astronomers greatly. These effects were very localized and for stars far apart the forces still netted out. Impossible World -------------- In the climate of Einstein physics we can see that the world of Newton is actually impossible. We can not have a world populated by gravitational bodies in a Euclid space with constant scalefactor. 2*k*c^2 / R^2 = 4 * pi * gamma * rho0 / R^3 - (q + 1) * H^2 4 * pi * gamma * rho0 / R^3 = (q + 1) * H^2+2 * k * c^2 / R^2 = 0 for a constant scalefactor and k = 0 for a Euclid geometry. So 4 * pi * gamma * rho0 / R^3 = (q + 1) * 0^2 + 2* 0 * c^2 / R^2 = 0 + 0 = 0 which is false. The leftside term has all nonzero factors. The universe can not be both Euclid and static under self-gravitation. Either k or H may be zero, but not both together. Zollner in 1872 is probably the first to offer a fix. He used the newly emerging nonEuclid geometries. In Riemann geometry space is spherical. So the farther away one goes from a given point the incremental mass engulfed around that point tends to a finite limit. Ergo, the stars deploy a finite mass around any point and the gravity of these stars is finite. Zollner had no way to appreciate that a curved space is itself, as Einstein much later demonstrated, the equivalent of gravity. One could not have both curved space and Newton gravity at the same time. Gravitation under Newton ---------------------- We review the concept of gravitation in Newton physics. Newton declared that gravitation was an innate property of matter. Matter in turn lives in an external and absolute reference frame in space and time. Gravitation percolates, as it were, from the matter into the surrounding space and time. This gravity acts on other bodies. Orbits, trajectories, collisions, and so forth are described against the external reference frame in which the bodies sit or move. A very popular and easy means to visualize gravitation in Newton physics is thru the notion of fields. We think of body #1 as establishing in space and time a field of gravity around it. At some point #2 remote from the body the field attains a certain strength to act on other bodies placed at that point. The gravity field strength produced at point #2 by the body #1 is G{1/2} = -gamma * m1 / r{1 / 2}^2 gamma is the Newton constant that doctors up the sense, units, and values so they balance. Its value is 6.672E-11n.m^2/Kg^2. The French brackets tell the sense of the calculation: from point #1 to point #2. In English we can read them as 'G of 1 on 2' and 'r from 1 to 2'. The negative signum reminds that the action of the field is TOWARD point #1 while the distance is measured FROM #1. When an other body is placed in the field, it is acted on by a force from, or is accelerated by, the field in proportion to its own mass m2 F{1/2} = (-gamma * m1 / r{1/2}^2) * m2 -gamma*m1*m2/r{1/2}^2 This is Newton's law of universal gravitation. The 'universal' he asserted comes from the premise that each and every bit of matter in the whole universe has the property of gravitation. In his day the only things beyond the Earth he could test his theory on were the the Moon, planets, and the comet of 1680. Not until the discovery of binary stars a century later did Newton physics extend to deep space. Newton's signal achievement was the clear distinction between force and mass. These quantities were totally fuzzy before his day. In fact in his own Principia Newton never actually uses terms comparable to today's 'mass' or 'force'. Not even in the original Latin. Definition of Force ----------------- Newton and physicists today treat mass as the fundamental property of matter and force as an incidental feature depending on the peculiar situation that mass finds itself. We define separately the unit of force and Newton did so by his second law of motion F = m * 2der(r,t) The unit of force is that force which on one unit of mass produces one unit of acceleration. [unit of force] = [kg]*([m]/[s^2]} = [kg] * [m]/[s^2] = [kg.m/s^2] [newton] = [kg.m/s^2] This is named in honor of Newton. One newton is the force producing one meter/second^2 of acceleration on a one kilogram mass. In the oldstyle system of measures the force is the prime entity, as the force of gravity on a unit of matter and the mass within that matter is the derived unit. The old 'pound' was the unit for the force of gravity and we used to deal with 'pounds' of matter. But soonest it was discovered that the gravity field strength varies over the Earth, even if only slightly, and it is altogether different in outer space, this system of measures was junked. Two Interpretations of Field Strength ----------------------------------- The field of gravity pulls on an other body with a certain force. It also accelerates that body. That is, the measure of the field strength at point #2 may be either the acceleration or the force of attraction caused at that point. Consider the law of gravitation. F{1/2} = -gamma * m1 * m2 / r{1/2}^2 = [n] = [Kg.m/s^2] = [kg]*[m]/[s^2] [n]/[kg] = [m]/[s^2] = -gamma * m1 / r{1/2}^2 = G{1/2} In other words, the gravity field strength is either expressed in meter/second^2 of acceleration or newton/kilogram of force on a unit mass. Astronomers exploit this equivalence routinely in their work in celestial dynamics.