1.3. Dominant Error

In your lab more often than not, you will combine measurements of different quantities to obtain the final quantity you want. Let's assume we know the error associated with each individual quantity. The question is how to find the error of the combined quantity.

We will deal with this question in detail in a later section. However, it is very helpful to understand the concept of dominant error before doing any calculations. The idea of dominant error is very simple. Consider the two supermassive black holes first spotted in the NGC 6240 galaxy by NASA's Chandra X-ray observatory on July 29, 2001.

Two black holes in the NGC 6240 galaxy. Image credit: NASA/CXC/MPE

How far from Earth (in the Milky Way galaxy) is this pair of black holes (in the NGC 6240 galaxy)? The usual way of calculating large cosmic distances is to apply Hubble's Law, which states that the velocity with which two galaxies move away from each other is proportional to the distance between the galaxies. Algebraically we express Hubble's Law as

V = H × D

Thus, if we know the velocity V of NGC 6240 relative to the earth and the so-called Hubble constant H, we can calculate the distance D between the Earth and the pair of black holes. On Earth, we can measure the velocity V quite precisely. However, we know the Hubble constant H only with a precision of about 10%. Therefore, the error estimate on the distance D is almost entirely determined by the large error of the Hubble constant, and we can safely ignore the small error of the velocity V.