Part V.   Center of Mass and Relative Gravitational Acceleration
BB.   The Surface Gravity of Any Celestial Body Also Exemplifies the Concept of Relative Gravitational Acceleration

The surface gravity of any celestial body is the gravitational acceleration of any other gravitating material body which is being pulled from the center of such celestial body.[1] It is measured at the point where this surface begins, and with a solid celestial body this is the point where its solid surface terminates such gravitational acceleration.

This was the gravitational acceleration of any relatively small object (i.e. a cannonball) which Galileo measured during the early 17th century near the solid surface of the Earth to be 9.8 m/s/s (Figure 4). The surface gravity of the mass of any small object is often described as its weight in kilograms.

Surface gravity is normally expressed as a constant number (although it actually varies slightly depending upon the opposing masses involved) and such surface gravities of the major gravitating bodies in our solar system (i.e. the Sun, planets, moons, asteroids and comets) also vary widely (Figure 16E). However, these somewhat misleading relative surface gravities only assume that a relatively small object like a cannonball is accelerating towards the surface of these much larger gravitating masses[2] (Figure 27). The illusion created is that only the much larger body is not relatively accelerating toward the smaller object.

For example, if the planet Jupiter is gravitationally accelerating toward the center of the Sun (as is shown on Figure 16), then the surface gravity of Jupiter should be described as the ratio 318:330,000 (expressed in Earth masses). On the other hand, the surface gravity of the Sun which is reciprocally slightly gravitationally accelerating toward Jupiter should be described by the ratio 330,000:318 (also expressed in Earth masses). In other words, the concept of surface gravity (like most other concepts of gravitational interaction) is completely relative to the masses involved, and the distance of the surface from the center of each mass.

As a final example of relative gravitational acceleration of unequal masses, let us describe the known surface gravity of any celestial body. The magnitude of the surface gravity of any body in the solar system, as compared to the relative surface gravity of 1 for the Earth, ranges from 1/6th for the Moon, to 2.5 for Jupiter, to 230 for the Sun (Figure 16 again). It is an undisputed fact that surface gravity for any body depends upon its mass and the distance from its surface to its center: in other words, its centripetal force diminished by the inverse square of such radial distance.

The relative weight (heaviness) of an astronaut on each different surface is a result of such relative magnitude of surface gravity. As we shall discover in another treatise to follow this one, the phenomenon of weight or heaviness (sometimes called “gravitational mass”) is actually the same phenomenon as gravitational acceleration, except that (with weight or heaviness) such acceleration (free-fall) has been totally restrained by a solid surface. For example, a parachutist who does not sense his own weight when he is free-falling toward Earth regains his sense of heaviness when he lands on the surface of the Earth. In this scenario, the parachutist’s gravitational acceleration and sensation of heaviness is primarily produced by the quantity of relative intensity of centripetal force of each gravitating body in all directions, which is received by and acting upon both the parachutist and the Earth, and the relative inertial resistances of the two opposing bodies (Figure 28).

This means that the same mass of a parachutist will fall (gravitationally accelerate) differently on or near the surface of each different celestial body or mass. Also, the magnitude of each such different acceleration will be proportional to each different surface gravity, and therefore to the mass of each different opposing celestial body. We empirically know this, because we have experienced and measured such different accelerations of the same mass on the Earth, on the Moon, and more recently on the planet Mars, the moons of Saturn, and other planetary bodies.