Dear Bob,
Below are some figures that you might find useful. I compiled these
originally, but they come with emendations from others on the USMA listserv.
Cheers,
Pat Naughtin
CAMS - Certified Advanced Metrication Specialist
- United States Metric Association
ASM - Accredited Speaking Member
- National Speakers Association of Australia
Member, International Federation for Professional Speakers
--
on 2002/02/15 14.39, Bob Price at [EMAIL PROTECTED] wrote:
> I am heading up a public event to promote astronomy in the Chicago area and
> I am hoping to find a way to encourage metric units in astronmy. We
> ususally have free handouts that give info on planets, but it is in miles
> only. I will have to work on that.
> Does anybody know where I can get freebies to hand out to the public? Are
> there any cheap metric only rulers I can get my hands on? I would love to
> include those in my package of free handouts. Perhaps I can sneak a little
> metric into this event. (After all, astronomy should be metric.)
Earth - megametres
When I ask friends how far it is from Geelong to London or to New York, they
reply automatically with something like 20 000 km to London or 12 000 km;
they don't say 20 megametres to London or 12 Mm to New York.
One way to develop a mind image for a megametre is to take an atlas and
picture the places that can be measured in megametres from your hometown. In
my case - from Geelong - Sydney is about 1 Mm away, Eucla is about 2 Mm,
Cairns is a little over 3 Mm, and Geraldton is about 4 Mm from here.
Earth - surface area
This is a delightfully simple calculation and it shows one of the best and
simplest illustrations I have seen that argues for the use of megametres. I
have always liked megametres and would like to encourage their use, but I
seem to be constantly stymied by the 1000 kilometre alternative.
To calculate the area of the Earth you can use these two standard
mathematical formulae.
The surface area of a sphere is: A = 4�r2 and the circumference of a circle
is: C = 2�r
We also need to know the circumference of the Earth. This is the easy part,
because the people who first defined the metre did so using the Earth as a
model. They made the distance from the equator to the North Pole equal to 10
000 km so the circumference of the Earth is four times that, or 40 000 km.
For ease of calculation we can think of this as 40 megametres, and we can
write it as 40 Mm.
Rewriting the second equation (C = 2�r) we get r = C/2� and we can
substitute in the first equation (A = 4�r2) by replacing r with C/2�
This gives us a new equation A = 4�(C/2�)2
And this can be reduced to A = C2/�
So the surface area of the Earth is:
40 Mm x 40 Mm � � = 1600 � 3.14159 = 509.3 square megametres (Mm2)
It would be wise to round this value to about 500 Mm2 for two reasons: it's
much easier to remember, and modern measurements of the Earth show that its
circumference varies at different places around the world. It's very close
to, but it's not exactly, 40 000 km.
If you wish you could change the Mm2 to square kilometres by multiplying by
1 000 000 and this would give you 509 300 000 km2; but, personally, I find
500 square megametres easier to say than this.
Earth - volume
You can use the same technique to find the volume of the Earth. In this case
the formulae that you need are:
The volume of a sphere is: V = 4/3 �r3 and the circumference of a circle is:
C = 2�r
We rewrite the second equation to get r = C/2� and then we substitute this
in the first equation.
V = 4/3 �r3 becomes V = 4/3 �(C/2�)3 and this reduces to C3/3�2
So the volume of the Earth is:
V = C3/3�2 = 40 Mm x 40 Mm x 40 Mm � 3 x �2 = 64000 � 3 x 3.141592 = 64000 �
29.608 763 = 2161.5 Mm3
We could remember this number as about 2000 cubic megametres. Changing this,
by multiplying by 1 000 000 000, gives us 2 161 500 000 000 cubic kilometres
(km3) but this doesn't make anybody's life any easier; so we best forget it,
and stick with 2000 Mm3.
Universe estimations
The circumference of the Earth is 40.0 megametres, so its diameter is about
12.7 megametres, and its radius is about 6.37 megametres.
The average distance from the Earth to the Sun is about 150 000 000 000 m or
150 gigametres (150 Gm).
The average distance from the Earth to the Moon is about 380 000 000 m or
380 megametres (380 Mm).
In a year, the Earth intercepts about 4 yottajoules of solar energy (4 YJ)
from the Sun.
>From the Earth to the next nearest star (after the Sun), is about 40
petametres (40 Pm). The next nearest star can refer to either Proxima
Centauri or Alpha Centauri, depending on their relative positions in their
orbits around each other.
>From the Earth to the nearest galaxy, M 31 in Andromeda, is about 20
zettametres (20 Zm)
>From the Earth to the furthest, normal, galaxies is about 40 yottametres (40
Ym).
>From the Earth to the furthest objects detected in our observable Universe
(quasi-stellar objects or quasars) is a little more than 100 yottametres
(100 Ym). As the distance from Earth to the furthest Quasars that have been
studied is about 100 yottametres, this means that the diameter of our
observable Universe is about twice this value or 200 yottametres (200 Ym).
Pat Naughtin
Geelong, Australia
