help here ASAP!!!?
R= event horizon radius
G=newtonian gravatational constatnt
C=speed of light in a vacuum
Heres what I understand
R is the final result
I know the equation
What I do not understand is
Does M have to be in pounds, kilograms or does it matter
What is newtonian gravatational constant
What is the speed of light in a vacuum
Now can you show me STEP BY STEP how to do this
- oldprofLv 75 years agoBest Answer
You don't need step by step, you need to learn units analysis. The fundamental tenet of which is that the units on the LHS of the = will equal the same units on the RHS of the = when the equation is correctly balanced. So whatever units you have in G, M, and c^2 you must have the same units in R.
And that's why we have standard units, the so-called SI units. One standard set is the mks SI units...meter, kilogram, and second. If you use that, then R must...must...be in meters because R is a length. So that means GM/c^2 ~ meters ~ R as well.
Mass is in kg and speed is in m/s; so GM/c^2 ~ G kg/(m/s)^2 ~ meters ~ R and that makes G ~ Rc^2/M ~ m.(m/s)^2/kg ~ m^3/kg.s^2
NOTE we can convert the G units as (kg/kg)m.(m/s)^2/kg ~ m^2kg.m/s^2//kg^2 ~ Nt.m^2/kg^2 but why would you?
- nyphdinmdLv 75 years ago
It doesn't matter what units you select as long as you use the same system of units for all the quantities. In physics we tend to work in System International - the mertic system - so lenghts are in meters, mass in kilograms, time in seconds. So
R = 2GM/c^2 will have dimensions of
meters = Nt-m^2/kg^2 kg/(m/s)^2 = kg m/s^2 m^2 /kg^2 kg/(m/s)^2 = m
Now G = 6.67x10^-11 Nt-m^2/kg^2, c = 3x10^8 m/s --> these are both physical constants.
So for any mass M you can use these values to find the Schwarzschild radius. Not sure what help, step-by-step, you need.