# Using the force constant in equations

by marcus
Tags: constant, equations, force
 Astronomy Sci Advisor PF Gold P: 23,235 Back in post #71 I listed some rough sizes, including these force and power benchmarks. weight of 50 kg sack of cement E-40 power of a 160 watt lightbulb E-49 I am thinking of the force E-40 as a "sack" force benchmark and imagine a 50 kg weight on a pulley descending at speed E-9 (which is 2/3 mph, or a billonth of the speed of light) and as it descends it does work, like turning a spindle, maybe even generating electricity. The power output of that descending weight is E-49. To see that, you just have to multiply the force E-40 by the speed E-9 and you get the power. of course if you are generating electricity there will be some loss because of inefficiencies. but basically this force exerted at that speed delivers that much power. and I'm going to call that level of power a BULB of power. this is a drastic solution to the problem of remembering the brightness of sunlight. the solar constant at this distance from the sun---the power per unit area delivered by direct unattenuated sunlight----is 5.7 BULBS PER SQUARE PACE. In natural unit terms, a pace (81 cm) is E34 and a square pace is E68 and a bulb of power is E-49. So a bulb of power spread over a square pace is E-49/E68 = E-117 I am saying that the brightness of sunlight is 5.7 times that. It is like about SIX of those 160 watt litebulbs set in a pace-wide square. In natural units, 5.7E-117 is what the handbook value of the solar constant actually turns out to be. but I dont find that so easy to remember. So I visualize it as 5.7 bulbs per sq. pace. A pace is just one of my steps----around 32 inches----so I can easily pace out a square that size on the flagstones in the garden. It is an easy area for me to visualize. and the litebulbs are easy to visualize. so I have a visual handle on this 5.7E-117 =================== In the "Force" system of natural units, the unit of power is of course E49 bulbs (because bulb was defined as E-49) and it is the power delivered by the unit Force pushing at the speed of light. this is a lot of power and if you count as fast as you probably can outloud, say 222 counts a minute, then WITH EVERY COUNT UNIT POWER DELIVERS ENOUGH ENERGY TO CREATE 2000 SUNS. We discussed this, it is enough power to create a galaxy in something on the order of 100 days. or if you wanted to produce such a power by annihilating stars and converting their whole mass into energy then you would have to annihilate about 2000 stars like the sun with every count. As with conventional Planck units, these natural units are fundamentally Big Bang-scale. the temperature, the density, the pressure, ...and so on...are mostly at the level of big bang conditions. I guess that could be seen as reassuring. You can be sure ahead of time that you are not going to encounter any temperature less than zero or greater than one. the physical scales tend to be bounded between zero and one----like with speed too.
 Astronomy Sci Advisor PF Gold P: 23,235 An explorer once visited three planets and went into low orbit around each in order to take pictures with his digital camera to put on his website. He finds each planet more delightful than the one before it and, while skimming around the third, he breaks down and calls you on the cellphone. Hello, says the explorer, on each planet it took a different length of time to travel one radian of the low orbit. In natural time units it took 7E45 4E45 and 3E45 on planets A, B, and C respectively. what are the densities of the three planets? the formula for the density is D = 6/T2 you just divide 6 by the square of the radian time, so the three densities are 6/(49E90) = 1.224E-91 6/(16E90) = 3.75E-91 and 6/(9E90) = 6.66E-91 the first, you tell the explorer, is virtually the same the density of water. planet B, on the other hand, is slightly over 3 times the density of water and is therefore comparable to many of the solar system's satellites including the earth's moon planet C, however, is 5.4 times the density of water, quite close to earth itself, which is 5.5! Indeed, says the explorer, that is within experimental error. I believe I am just passing over Sausalito. BTW E45 natural time units was listed a couple of posts back as lasting 4.5 minutes, so the radiantime for low orbit in the earth-like case, namely 3E45, becomes 3 x 4.5 = 13.5 minutes. that is for a hedgetop skimming orbit neglecting air--- not practical, of course, but raising it above the atmosphere does not make the orbit all that much slower. so it is a pretty good estimate. (multiply 13.5 minutes by 2pi to get the period)
 Astronomy Sci Advisor PF Gold P: 23,235 Another time the explorer cruises by the nightsides of each of 3 planets in order to gauge the infrared heat brightness from each. He wants to know how warm or cold they are. He finds that the heatglow brightness of the three is as follows: 1.4E-117 1.9E-117 and 2.5E-117 the question is, what is the night-time surface temperature on each planet? Simply put, you just multiply each number by 6 and take the fourth root (press square root twice) although officially what you multiply each number by is 60/pi2. However, pi-square is almost the same as ten, and 60/10 is six, so it's almost the same either way. So let's multiply each planet's heatglow by 60/pi2 8.511 E-117 11.55 E-117 15.20 E-117 and press the squareroot button twice to get the temps 0.960 E-29 1.037 E-29 1.110 E-29 The first is below freezing, the second is room temperature, and the third is the perfect temperature for a hot tub! To help with interpreting these temperatures, remember all those we usually experience are close to E-29 and 1.000E-29 is our basic reference 49 Fahrenheit. Going up from 1.000 to 1.110 is equivalent to going up 110 halfFahrenheit steps, that is 55 F-degrees, which if you add it to 49 gets you 104 Fahrenheit. On the other hand, going from 1.000 up to 1.037 is equivalent to 37 of those steps which is 18-some Fahrenheit-degrees. Adding that which to 49 gets you 67 Fahrenheit, and what could be a more comfortable than that? So the moral is: go for the planet that glows 1.9 E-117 in the infrared.
 Astronomy Sci Advisor PF Gold P: 23,235 two more benchmarks the temperature in the energyproducing core of the sun is 5E-25 (remember that solar surface temp is 2E-28 and avg earth surface temp is E-29 the way to remember solar surface is that E-28 is an eQ and green photons have energy 10eQ, so solar surface is going to be around E-28, and the temp there happens to be 2E-28. so from core out to surface, temp goes down by factor of 2500) and middle D on piano is (1/2)E-39, have to go, back later that means the D in the soprano/alto range, on the fourth line of the treble clef, is E-39 the natural unit frequency is E39 times higher than that note the sopranos in our chorus sing---maybe I could get it in falsetto. THE CAT ENGINES OF ORNISH I suspect Kea of liking cats, so I have devised a story about the wicked space pirates of Planet Ornish and how they propel their giant Bagel-shaped troopships. I hope this will scandalize Kea.
 Astronomy Sci Advisor PF Gold P: 23,235 ------THE CAT ENGINE OF THE SHIPS OF ORNISH---- The ships of Ornish are driven by Cat Motors which consume cats as fuel by converting each cat entirely into energy. The captain of a ten-million-pound troopship wishes to achieve a speed of E-3 (one thousandth of the speed of light, about 300 km/second) in order to depart a plundered system. Once in the clear he will enter warp and rendezvous with the rest of the pirate band. The initial change of velocity is accomplished by the ship's efficient photon drive. How many standard 10 pound cats must be converted? ---answer--- "pound" is just a handle on E8 mass units so clearly the mass of each cat is one billion mass units (10 pounds is 10 E8 units). so since c = 1 each cat yields one billion natural energy units. (the mass is the same number as the energy in natural units) The ship mass is 10 million pounds (E15), so the desired momentum change is E15 x E-3 = E12 momentum units. This requires discharging a photon pulse with E12 energy units, which consumes 1000 cats.
 Astronomy Sci Advisor PF Gold P: 23,235 ---------FAST FOOD EXERCISE------ According to Defense Analyst Daniel Pinkwater, the earth is in danger of invasion by the Fat Men: a space-faring race which plunders other planets for their fast food. Their planet, planet Ornish, is deficient in basic resources like french fries, mayonaise, potato pancakes, Colonel Sanders fried chicken, and sour cream, which has forced them into a life of nomadic piracy. The Fat Men spacewar uniforms consist of loud plaid sports-jackets, green dacron slacks, loafers, and eyeglasses with heavy black plastic frames. They travel by the millions in a fleet of troopships shaped like enormous bagels. Professor Pinkwater fears that, before long, hordes of Fat Men will descend on earth and ravage our fast food outlets. The defense analyst has calculated that one raid by the Fat Men could deplete the earth of a million pounds of its mayonaise. How much energy does this represent? ---answer--- If you just go into the kitchen and look on a jar of Best Foods Real Mayonaise it will say that a 13 gram serving has 90 food Calories. One of our (E8 natural mass unit) pounds is 434 grams so it contains almost exactly 3000 Calories. Also to a reasonably close approximation, the natural unit of energy is 100 thousand food Calories. So a million pounds of mayonaise, with its 3 billion Calories, represents 30 thousand natural energy units.
 Astronomy Sci Advisor PF Gold P: 23,235 I think Quantum Gravity research is probably going to succeed and get a quantum theory of spacetime (and of its shape, which we call gravity) and I expect physics will be rebuilt on this new spacetime (just like since 1680 it has been built mostly on newton's absolute flat spacetime and the 1905 minor variation of that) and today as usual I looked at a QG paper and as usual it was using nonmetric QG units where c and hbar are set equal one (or something else convenient) and G likewise---so it is some variant of the planck units (which we've had around since 1899 or so). As physics gets rebuilt on a quantum spacetime basis, I expect people will gradually get used to gauging things in natural units: scales intrinsic to quantum spacetime. So after reading I went out in the garden, bright with insects flying around and some stuff opening, a few leaves coming out to get the sun, and I thought: 5.7E-117 spells life and it is a longterm number. It's the brightness of sunlight expressed in natural units----as long as sunlight is this level, as long as there is a rich chemistry, as long as the rivers run... some crows were talking, a redtail hawk cried, some other birds were calling too well I am going for a walk up the hill with my wife, for exercise etc. be back later these longlasting numbers that spell earth, spell home, most are not too interesting E-29 is global avg. surface temp E-50 is a "gee" E-91 is the density of water E-106 is a "bar"----standard air pressure but 5.7E-117 is the brightness of sunlight, not too strong or too weak, that is driving all this life, the crows cawing, trees budding, wind stirring the branches, and all that, so if I happened to be riding around with some aliens in their saucer I think I would would ask to be put off at a planet with steady 5.7E-117 sunlight. it is the number that more than any other characterizes home btw in natural units what I gave for gee and bar etc were only approximate the official gee is more like 0.9E-50 and the normal density of water is more like 1.2E-91 and the usual sealevel pressure norm is 1.4E-106 but I dont care too much about a few percent. I think I could be adapt (as long as the chemistry was good) somewhere with gravity E-50 and pressure E-106. But I think I might get depressed, or sick of the place, if illumination wasnt right.
 Astronomy Sci Advisor PF Gold P: 23,235 Freshman physics on the round number planet. I'm thinking of a planet with the same general chemistry as on earth, air has the same composition, soil and vegetation similar etc. but where some basic features like the surface gravity are round numbers. E-29 is global avg. surface temp E-50 is a "gee" E-106 is a "bar"----standard air pressure E33 is the planet's mass E50 is the year (Note that on earth the official gee is not exactly E-50 but more like 0.9E-50, the usual sealevel pressure norm more like 1.4E-106, the planet mass 1.4E33, although estimates vary the average temperature is close to E-29, and the year is 1.167E50 instead of exactly E50. So this round number planet is not an exact match to Terra but akin to it.) One thing we will not compromise about is the brightness of sunlight. It is 5.7E-117 expressed in natural units. And as to some things like the proton mass and the density of water we have no choice: 1.2E-91 is the density of water at standard temperature and pressure (E-29 and E-106). 2.6E18 protons make one mass unit, so if we need a figure for the mass of a water or air molecule we can say 18/(2.6E18) and (29/2.6E18). I'm thinking of a series of exercises---a kind of natural units Yoga---which is finding out about this round number planet: the speed of sound, the threshhold of convection in the air, the minimal orbit time, the planet's radius and density, the escape velocity, the rate pressure falls with altitude, the equilibrium temperature in direct sunlight. these might be good exercises to do for several reasons.
 Astronomy Sci Advisor PF Gold P: 23,235 summary of inputs easy numbers: E-29 is global avg. surface temp E-50 is a "gee" E-106 is a "bar"----standard air pressure E33 is the planet's mass E50 is the year hard numbers: 5.7E-117 is the brightness of sunlight. 1.2E-91 is the density of water. 2.6E18 protons make one mass unit. ------------------- so to begin, let's calculate the planet radius. surface gravity = E-50 = GM/R2 = (1/8pi)E33/R2 R2 = (1/8pi)E83 R = 6.308E40 = 6.3E40 rounded. to humanize this recall E37 is half a mile. the radius is 6308 halfmiles.
 Astronomy Sci Advisor PF Gold P: 23,235 summary of inputs easy numbers: E-29 is global avg. surface temp E-50 is a "gee" E-106 is a "bar"----standard air pressure E33 is the planet's mass E50 is the year E-4 is the planet's orbit speed around its sun hard numbers: 5.7E-117 is the brightness of sunlight. 1.2E-91 is the density of water. 2.6E18 protons make one mass unit. ------------------- Let's calculate the speed of sound at the planet's surface. the speed of sound formula for biatomic gas at temp T speed2 = (7/5) kT/(mass of molecule) In our case the average mass of the air molecule is 29/(2.6E18) and temp is E-29 speed2 = (7/5) E-29 (2.6E18)/29 = 1.255E-12 speed = 1.12E-6 just over a millionth of the speed of light BTW I added the planet's orbit speed to the list of easy numbers. It matches the earth's orbit speed almost exactly and will allow us to calculate the mass of the planet's sun.
 Astronomy Sci Advisor PF Gold P: 23,235 summary of inputs easy numbers: E-29 is global avg. surface temp E-50 is a "gee" E-106 is a "bar"----standard air pressure E33 is the planet's mass E50 is the year E-4 is the planet's orbit speed around its sun hard numbers: 5.7E-117 is the brightness of sunlight. 1.2E-91 is the density of water. 2.6E18 protons make one mass unit. ------------------- I want to use just these inputs and demonstrate how various things follow from them. mass of the sun, in natural units the mass M is related to the year period P and the orbit speed v by M/4 = P v3 = E50 (E-4)v3 = E50 E-12 = E38 M = 4E38 remember the planet mass is E33, so this is 400,000 times that. (rather like how earth and sun masses are related, you can always try comparing between what we get for the round number planet and the handbook data for Earth and it usually wont be far off. in this case jupiter is a bit less than 1/1000 of sun and earth is roughly 1/300 of jupiter and 400,000 wouldnt be a bad guess)