1. The problem statement, all variables and given/known data Is there any standard method known to work with units in which speed of light (c), planck's constant (h), boltzmann constant (kb) are given by: c=1 h=2*pi (i.e. h_cross=1) kb=1 For example, how can we calculate Newton's Gravitational Constant (G) in these units. If there's any systematic method for this please help. 2. Relevant equations n/a 3. The attempt at a solution Basically, I tried to calculate the G by expressing G in terms of c, h and kb, but I have not been able to do so.
Those units alone will not be enough to completely define the units of the gravitational constant though they can go some way toward it. It can be shown that you need 7 base units in order to have a complete system i.e. one in which any quantity can be expressed as a combination of base units. (in SI these are m, s, kg, A, mol, K, candela) the three units you propose could be expressed in SI as m.s^-1, kg.m^3.s^-2 and kg.m^3.s^-2.K^-1 These on their own do not form a complete set, however they can easily be used to express measurements of energy and some other measures. These three units alone would not be suitable for measuring, for instance length, as there is no combination of these units that leaves only metres in the answer. In terms of the constant G with units m^3.kg^-1.s^-2 you could get close by expressing it in terms of: c^6.hbar^-1.s^2 or c^4.hbar^-1.m^-2 but that is the simplest you could achieve as m and s cannot be expressed separately by these units alone. Introucing an additional unit of planck length L would allow you to express G in terms of these units as G = 123456789x c^4.hbar^-1.l^-2 (123456789 is an example number, you'd have to work it out yourself) EDIT: the system of planck units is well established and does for a complete set: http://en.wikipedia.org/wiki/Planck_units note there is no 7th planck unit since it takes mols as being a single atom and in SI and other system mols is just a defined multiplier