As far as I know, Peter David has
written 95 novels, mostly SF, and won 10 awards. I know him from his
Star Trek books, of which, between 1997 and 2002, I read 19. I am now
reading

*After Earth*, the novelisation of the recent film with Will Smith, and discovered in it an appalling (and certainly unexpected) mistake.
On page 101, he wrote:

*A parsec, she recalled, was a measure for the speed of light, how far it would travel over one hundred years*.
The sentence is at best awkward. What
does it mean “A parsec [...] was a measure for the speed of light”
when in fact a parsec is a measure of distance, as David writes in
the next sentence?

But the problem is that a parsec is
only 3.26 light years, not 100!

If you draw two lines from a point in
interstellar space, one passing through the sun and one passing
through Earth, when the amplitude of the angle between the two lines
is one second of arc, the object’s distance is by definition 1
parsec. The “par” in parsec stands for “parallax” and the
“sec” for “second”.

Imagine making two observations of a
star with a six months period between them. During the six months,
Earth will have moved half of its orbit. As a result, you will have
to point the telescope in two slightly different directions. If you
know the radius of Earth’s orbit, you can use the angle between the
two directions to calculate the star’s distance.

Here is how you do it.

Earth’s distance from the sun (i.e.,
the radius of Earth’s orbit) is approximately 150 million km = 1.5
x 10

^{8}km.
A second of arc is 1/3600 of a degree
and there are 360 degrees in a full circle, which is 2π times the
radius R of the circle. This means that 2π x R / 360 / 3600 is the
length of a second of arc = R x 4.85 x 10

^{-6}.
If a star has a parallax angle of two
seconds (not one second because the two lines of view are through
opposite points of Earth’s orbit, rather than one though Earth and
one through the sun), to calculate its distance in kilometres you
only need to imagine a circle of radius D centred on the star and
passing through the sun. Then, the diameter of Earth’s orbit is
given by:

1.5 x 10

^{8}km x 2 = 2 x D x 4.85 x 10^{-6}
That distance will be 1.5 x 10

^{8}km / 4.85 x 10^{-6}= ~3.1 x 10^{13}km.
As the speed of light is 300,000 km/s =
3 x 10

^{5}km/s, 1 light year is 3 x 10^{5}km/s x 3600 s/h x 24 h/d x 365 d/y = ~ 9.46 x 10^{12}km (actually, the light is 0.07% slower, but the year is 0.07% longer, so it works out just fine! :-) .
Then, 1 pc = ~3.1 x 10

^{13}km / (9.46 x 10^{12}km/ly) = 3.28 ly. Close enough, considering the approximations.
There is no star at 1 pc from Earth,
but Proxima Centauri, the closest star to Earth, is 1.3 pc away.

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