# On the scale of forces

The English language conflates mass and force: its way of stating the mass of a body is to say how much it weighs, i.e. the gravitational force acting on it when at the Earth's surface. Consequently, the pound is used both as a unit of mass and (informally) as a unit of force (a.k.a. thrust); in the latter rôle, formally the pound force, it's implicitly multiplied by the standard gravity, an acceleration of 32.174 foot per second per second. Some maintain that the pound is actually a unit of force; the proper unit of mass is the slug, obtained by dividing it by one of the available units of acceleration, one ft/s/s. One could, of course, use some other unit of acceleration, such as the mile per hour per second and infer a different unit of mass from the pound force.

Fortunately, civilized countries (and even England) now use SI, which takes the trouble to distinguish mass and force ab initio: the unit of force is the Newton = kg.m/s/s.

nN

µN

As a school-boy, I measured Newton's constant, G, by measuring the torque on a beam, which had a heavy object at each end, due to moving two nearby haevy objects, with masses of 7.5 kg, from positions 76 mm (on average) clockwise from the beam's ends to matching positions just anticlockwise of them. If I assume the beam-end masses were also 7.5 kg (they don't affect the result, so weren't recorded as part of the experimental details), the forces my lab partner and I were attempting to measure (via a torque) were about 0.65 micro-Newtons; it is perhaps unsurprising, then, that our results were wrong by a factor of 3.6, despite our best efforts at accuracy.

mN

N

kN

My weight was approximately 1 kN last time I checked.

MN

Each GE90 jet engine on a Boeing 777 delivers 0.41 MN of thrust (two of these suffice to keep the 777 going at 0.27 km/s; and the 777 can fly safely on only one). When empty the Boeing 777's weight is one and a third MN; when fully loaded and fueled, that doubles.

GN

The gravitational force between Pluto and Earth varies between about 90 GN and about 290 GN.

TN

The gravitational force between Pluto and Neptune at their closest approach is of order ten TN.

PN

The gravitational force between Mercury and Venus at closest approach is 42.42 peta-Newtons; that between Earth and Mercury is 15.7 PN, Earth and Mars 41.7 PN, Earth and Uranus 4.631 PN, Earth and Neptune 2.151 PN.

EN

The Sun experiences a force of just over 0.3 exa-Newtons due to the gravitational influence of the α Centauri binary system. The gravitational forces between Saturn and some of its moons are: .19537 EN (Prometheus), .1889 EN (Pandora), .91 EN (Epimetheus), 3.274 EN (Janus), 41.33 EN (Mimas), 48.88 EN (Enceladus), 271.8 EN (Tethys), 280.2 EN (Dione), 315. EN (Rhea), 3419 EN (Titan) and 4.756 (Iapetus). The gravitational force between Venus and Earth at closest approach is 1.13 EN; that between Mars and Jupiter is .2685 EN, Saturn and Uranus 1.562 EN, Uranus and Neptune .2222 EN; between Jupiter and Earth is 1.916 EN, Saturn and Earth .1382 EN.

ZN

The force on The Sun that holds it in its orbit around the centre of the Milky way is a bit over one zetta-Newton. This is dwarfed by the forces on it that hold the planets in their orbits: these are 13.07 ZN (Mercury), 55.19 ZN (Venus), 35.4 ZN (Earth), 1.640 ZN (Mars), 416.2 ZN (Jupiter), 36.89 ZN (Saturn), 1.386 ZN (Uranus) and .669 ZN (Neptune). The gravitational force between Jupiter and Saturn at their closest approach to one another is almost 0.17 ZN; the gravitational forces Jupiter exerts on its four Galilean satelites are 63.56 ZN (Io), 13.50 ZN (Europa), 16.402 ZN (Ganymede) and 3.845 ZN (Callisto); the force between Saturn and Titan (its largest moon) is 3.419 ZN; that between Earth and Moon is just under 0.2 ZN.

YN

harpi (1e27) Newton

The gravitational force between the Milky Way and Andromeda (about 2.5 M ly away and somewhat bigger than the Milky Way) is of order fifty to a hundred harpi Newtons.

Written by Eddy.