Deriving the Relationship Between Intensity and Distance
The Mathematics of the Relationship Between Intensity and Distance
By convention, if the galaxy is moving away from us, V_{r} and therefore Dr, is positive, and the intensity decreases, whereas if the galaxy is moving towards us Dr is negative and the intensity increases. Substituting for D r we get
Expanding this out yields the functional form of the relationship between intensity and time for an object travelling at a speed V_{r} in terms of its velocity and the time elapsed:
Looking at the expression in the denominator of this fraction, you can see that if the initial distance (r) is small compared to the distance the object travels in time Dt, the expression reduces to:
If, on the other hand, the distance travelled in time Dt is small compared to the initial distance of the object, the expression is approximately:
Click here for another example of a 1/R^{2} law. | |
Click here for the lightcurve data from M31 to solve for its velocity. | |
Click here to return to the beginning and try a different approach. |