The Inverse Square Law and Surface Area Calculating Distances to Stars

Measuring Distances There are several techniques used to measure distances to stars. The distance to the very closest stars can be measured by trigonometric parallax

The diagram shows Earth Orbit around the Sun. The position of a nearby star changes by a tiny amount over a six month period. This allows us to use trigonometry to find its distance. The angles are extremely small. This direct method is the most accurate way of determining distance

Using The Inverse Square Law. Every instant a star radiates its energy into space The energy which was at the surface is distributed at the surface of an expanding sphere

r The amount of energy on every square metre at the surface of the expanding sphere obeys an inverse square law.

The Inverse Square Law The power received from a star per metre squared at the Earth is called the intensity (I) of the star’s radiation This is related to the power output per metre squared L of the star’s surface in this way Where r is the radius of the sphere i.e. the distance from Earth to the star

Stars of Known Power Output There are several classes of stars with known power output. Stars which have the same surface temperature ( and spectral characteristics) as the sun all have the same power output We can readily calculate the power output of nearby stars and classify their power output and compare them with more distant stars The following very bright objects of known luminosity can be identified in distant galaxies Cepheid Variable Stars Suopernovae

The Sun has a power output of 3.91 x 1026W. Knowing this and knowing its surface temperature allows us to calculate its surface area using P=σ.AT4 This Now allows us to calculate the radius of the Sun