EricF wrote:Aero wrote:G is a fundamental physical constant, the Newtonian constant of gravitation.
It is experimentally determined to equal 6.674 28(67) x 10-11 m3 kg-1 s-2
See
http://physics.nist.gov/cgi-bin/cuu/Val ... l+constant
I hope this link works. For some reason the standard method of entering a URL is not working for me today. You may need to copy and paste ...
I copied and pasted it, thanks
The statement they give looks like jibberish, there are expressions they could simply solve and simplify and I don't understand why it hasnt lol
Why is there a space between 6.674 and 28(67) with no operator, and why does it say
28(67) instead of just multiplying it out to 1876?
then for X 10^-11 m^3 kg^-1 s^-2 I suppose you multiply all those together? I'm guessing m is meters, kg is kilograms obviously, I have no idea what s is though.
Y'see, this is why you need to read the math portions of Feynman's lectures in addition to just trying to get the gist of things. He explains things like units, dimensional analysis, etc.
Basically, everything done in science or engineering is based on measurements. Measurements have "units" -- we say things are 2 meters long, or took 5 minutes, or consumed 5kiloWatt-hours of electricity, etc. In reporting a measurement the units are just as important as the number. Saying that my mass is 127 is meaningless unless you know if I am talking about pounds or kilograms or stones. My actual mass has different numbers attached to it when measured in those three units.
It's also important, when comparing things, to make sure that the units are similar on both sides of the equation. It means something to say that 5'7" = 170.18cm, but it doesn't mean anything useful to say that 170cm = 34kg. In the first case, 5'7" is a measurement of length, as is 170.18cm. In the second case 170cm measures length while 34kg measures mass. The units aren't compatible. The study of what units are compatible is called "dimensional analysis". In general, you can't compare, add, or subtract quantities which are have incompatible units, but you can create new units by multiplying and dividing existing units.
In the case of gravitation, Newton's law of gravitation says (in English, not formula) that "The Gravitational Force between two bodies is proportional to each of their masses and inversely proportional to the square of the distance between them."
To say that x is "proportional to" y, mathematically, means that there is a number k such that x = ky. To say that x is "inversely proportional to" y means that there is a number k such that x = k/y (think "proportional to the inverse of y"). So that means that, using f for force, m and M for the two masses, and r for the distance, the law of gravity is f = km, f=lM, f=n/r^2, or all put together, f = -GMm/r^2, where G is the appropriate proportionality constant. The proportion constant is written -G because people like the value of G to be positive, and the negation implies that the force is attractive.
But what of the units of G?
Force on a body is defined by Newton as F=ma, where m is the mass of the body and a is the acceleration, or 2nd time rate of change of position. m has units of mass (kilograms, or kg, in the International System of Units (SI)), while acceleration has units of distance (meters, m, in SI) divided by time (seconds, s, in SI) squared. So force is measured in units of mass times distance divided by time squared, or m kg/s^2 in SI units.
So looking just at units, in gravitation you have:
m kg/s^2 = -G(kg)(kg)/(m^2) = -G kg^2/m^2
Multiplying the mess my square meters and dividing by square kilograms, you get
-G = m^3/(kg s^2)
Since you can write division as negative exponents, this becomes G = m^3 kg^-1 s^-2, or (assuming the exponentiation can be inferred) G = m3 kg-1 s-2.
You also asked about the spaces and the parenthetical numbers.
The spaces are easy. Americans would normally write Mpi as 3,141,159.2623589793 using a comma for grouping and a period for a radix point. Europeans would nromally write Mpi as 3.141.159,2623589793 using a period for grouping and a comma for a radix point. If you saw a figure reported as 1,900 m without fulling knowing the context, is that about as tall as a tall man, or halfway across town? The agreed convention is to used a space for grouping (on both sides of the radix point) and either a point or comma for the decimal marker. Using that convention, 1 900 m is halfway across town while 1.900 m is a tall man.
So the figure of 6.674 28 x 10-11 m3 kg-1 s-2 is specified with 5 digits after the decimal point.
The number in the parenthesis indicate possible error. Every measurement made by any researcher anywhere has some error. With care, proper technique, and oftentimes a lot of work, this error can be minimized, but it's still there, based on limitations of the measuring equipment, calibration issues, etc. The number in the parentheses is how much off, plus or minus, the last few reported digits could be. In this case it indicates that the actual figure could be as much as 0.000 67 x 10-11 m3 kg-1 s-2 above or below the figure I gave in the last paragraph. In other words, it's somewhere between 6.673 61 x 10-11 m3 kg-1 s-2 and 6.674 95 x 10-11 m3 kg-1 s-2.
With any luck it will give me an idea of what to pay special attention to when I finally get to calculus and physics.