Question

Our current best estimate of the distance to the Andromeda galaxy (M31) is 2.54 +- 0.11 Mly (millions of light years). Our current best estimate of the diameter of M31 is 141 +- 3 kly (thousands of light years). Thinking of the galaxy as being basically flat and covering a certain area of space, what is the approximate area of M31, and what is the uncertainty in the area? Express your answer in the form nominal +- error, as an interval, and as a single number with the correct number of significant digits.

Answer 1

The value of area is given by

Area (A) =

Where r is the radius and d is the diameter

Uncertainty in Area can be obtained by the uncertainty propagation formula which gives,

Now, d = 141 kly

And, = 3 kly

A = =   = 15615 kly²

So,

= 15615(2x3/141) kly² = 664 kly²

So, the uncertainty in Area is 664 kly²

The area is 15615 +- 664 kly²