units to the power of -1?

Kareir

Hey all,

Given the equation

4(pi)/6.24x10^15 m^3 km^-1 sec^-2

What do the -2 and -1 powers mean? I know that the ^3 on Meters is a cubic metre, but the other two?

_Kar

(Unit)^-1 just means 1/(that unit). For example, m/s is the same as ms^-1 (i.e. metres per second). It's just a way of writing it without using /'s that makes it possible to use the laws of indices on units.

Another example:

2^-2 = 1/(2^2)
kg.m.s^-1 = (kg.m)/s

Tails142

Kareir wrote: »

Hey all,

Given the equation

4(pi)/6.24x10^15 m^3 km^-1 sec^-2

What do the -2 and -1 powers mean? I know that the ^3 on Meters is a cubic metre, but the other two?

_Kar

It means they're in the denominator as a fraction i.e. below the line - m^3/(km^1 x sec^2)

Fremen

The interpretation is "per kilogram" and "per second, per second". The second quantity here measures an event which changes over time, where the change itself is changing. Acceleration is an example of this (change in speed which itself is change in distance)

It's sometimes a good idea not to worry too much about interpretations and just trust that the maths works out.