Download The Inverse Square Law and Surface Area

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
L
I
2
4r
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.
P
A
4
T
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