Download 2.5.4 astronomical distances Parallax and Distances to Stars





Parallax, p, is defined as half
the angle through which a
star’s direction changes as
the Earth moves from one
extremity of its orbit to the
other.
This change in angle is
measured against the
relatively stationary
background stars.
An important concept here
the distance of the AU.
The AU, or astronomical unit,
is defined as the average
distance from the Earth to
the Sun (~1.5 x 1011m)
D = 1 AU/tan p
 This
equation comes
from the trigonometric
relationship between
our 3 variables.
 Even the closest stars
are really far away and
as you can see, p gets
smaller for more distant
stars.
 Parallax angles as small
as 1/360000o can be
measured which
equates to a distance of
about 100 light years
 This
can also be worked
using the total
displacement of the
Earth over 6 months.
 This would make the
parallax equation –
2 𝐴𝑈
sin 𝜃 =
𝑥
 In Radians for small
angles, this then
changes to –
2 𝐴𝑈
𝑥 =
𝜃
 The
parsec is defined as
the distance between a
base of 1AU at an angle of
1 arcsecond.
 This means that
1pc = 3.086 x 1016 m
 This
is NOT a definition of time.
 It is the distance that light can travel
through a vacuum in 1 year.
 If you work it out it is –
9.461 x 1015m
When you consider the ridiculous distance
involved in astronomy, it makes sense to have
large units!
 Olbers
showed that in an infinite, uniform
Universe the sky at night would be bright,
but this is not so.
 BUT … the Universe must be infinite or it
would collapse under its own gravitational
forces.
 This is the paradox.





Imagine a thin shell in space
at radius r from Earth.
Radiation from these stars
reaches Earth with small, yet
definite intensity.
Another shell, at 2r, has the
same density of stars, so has
4 times as many star in the
shell but we receive ¼ of the
light from each star due to
the inverse square law.
Therefore, we receive the
same intensity of light from
each shell.
This means that we receive
starlight from all directions
at all time, so the sky should
be infinitely bright.
All of this stems from logical mathematics yet is
clearly not true.
 Therefore Olber deduced that the Universe is not
infinite.
 He did however make some assumptions –

that the Universe is infinite and uniform
 the space extends indefinitely in all directions,
independent of any matter
 That the Universe is static

The paradox is –
‘With an infinite number of stars in an infinite
Universe, it does not matter where you look, there
will always be a star in your line of sight.
Therefore the night sky should be as bright as day.’