Question

Using only the constants G = 6.67 x 10^-11 m^3/kg/s^2 and c = 3.00 x 10^8 m/s and dimensional analysis, estimate the peak power that was emitted in gravitational waves recently detected by LIGO from two merging black holes. (Hint: the SI unit of power is a watt, 1 W = 1 kg m^2 s^-3.) [3 marks]

Answer 1

$$P=G^xc^y$$

$$kg\cdot m^2\cdot s^{-3}=(kg^{-1}\cdot m^3\cdot s^{-2})^x(m\cdot s^{-1})^y$$

Thus,

$$1=-x\to x=-1$$

$$2=3(-1)+y\to y=5$$

Thus,

$$P=G^{-1}c^5=(6.67\cdot 10^{-11})^{-1}(3\cdot 10^8)^5=3.64\cdot 10^{52}W$$