```From: henry@spsystems.net (Henry Spencer)
Newsgroups: alt.sci.astro,alt.sci.physics,sci.physics,sci.space.science
Subject: Re: The Size Of The Sun
Date: Sun, 14 Feb 1999 05:09:01 GMT

In article <7a4p3m\$qqf\$1@news6.svr.pol.co.uk>,
theresa knott <theresa@knott16.freeserve.co.uk> wrote:
>>The Sun's angular width is about 31 minutes of arc, so multiply be 60 to
>>get arcseconds, then put in the distance to the Sun.
>
>How do you find out the distance to the sun?

That's a lot harder, and was a significant preoccupation of astronomy for
a long time.  Conventional observational astronomy is all angles, which
gives you proportions just fine, but no absolute distances.  Getting a
good reading on *one* distance is enough, but that's hard.

A variety of schemes were tried, including direct triangulation of various
astronomical objects using the Earth's diameter as a baseline (the most
successful work being done on Eros, which has the twin advantages of
having no atmosphere and passing fairly close to Earth), and assorted
indirect approaches such as measuring Doppler shifts of starlight to
determine Earth's orbital velocity.  None worked terribly well.

What finally did the trick in about 1960 was interplanetary radar -- and
just in time, because an accurate value was urgently needed for spacecraft
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)

```

```From: Ned Wright <elwright@ucla.edu>
Newsgroups: alt.sci.astro,alt.sci.physics,sci.physics,sci.space,
sci.space.science
Subject: Re: The Size Of The Sun
Date: Sun, 14 Feb 1999 06:25:17 -0800

theresa knott wrote:
> How do you find out the distance to the sun?

Note that Kepler's Third Law, D^3 = P^2, where P is the
period of a planet's orbit in years, and D is its distance
in au (D=1 for the Earth), gives the relative distances
of all the planets. Thus measuring the distance to any planet
in meters gives the values of the au [astronomical unit] in
meters and hence the distance to all planets in meters.

Modern: use radar to measure the distance to Mercury at many
places on its orbit.  The Sun is at one focus of this ellipse.

18th century: mount great expeditions to observe transits of
Venus from widely separated spots on the Earth.  Use the size
of the Earth as the base of a triangle, and the small angular
difference in the position of Venus relative to the Sun to
determine the distance to Venus which gives the scale of the
Solar System.

Once the distance to the Sun is known, the Earth's orbit is
used as a baseline for surveying the Universe.  See
http://www.astro.ucla.edu/~wright/distance.htm

--
Edward L. (Ned) Wright, UCLA Astronomy, Los Angeles CA 90095-1562
(310)825-5755, FAX (310)206-2096   wright@astro.ucla.edu
http://www.astro.ucla.edu/~wright/intro.html

```

```From: henry@spsystems.net (Henry Spencer)
Newsgroups: alt.sci.astro,alt.sci.physics,sci.physics,sci.space.science
Subject: Re: The Size Of The Sun
Date: Tue, 16 Feb 1999 15:37:25 GMT

In article <36C6DCCD.2877@ucla.edu>, Ned Wright  <elwright@ucla.edu> wrote:
>> How do you find out the distance to the sun?
>
>18th century: mount great expeditions to observe transits of
>Venus from widely separated spots on the Earth...

The transit-of-Venus approach, alas, never worked terribly well.  The
problem is that since Venus has an atmosphere, which refracts and diffuses
light, it's difficult to decide exactly when Venus has crossed the edge of
the Sun.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)

```

```From: sbharris@ix.netcom.com (Steven B. Harris)
Newsgroups: alt.sci.astro,alt.sci.physics,sci.physics,sci.space,
sci.space.science
Subject: Re: The Size Of The Sun
Date: 17 Feb 1999 06:32:45 GMT

In <36c94354.0@news.uni-bielefeld.de> Kresimir Kumericki
<kkumer@post.uni-bielefeld.de> writes:

>3rd century BC: Measure the angle between the Moon and the Sun when
>the Moon is in its first or last quarter (so that the angle
>Earth-Moon-Sun is 90 degrees. Knowing the distance to the Moon
>you have all that you need to determine all parameters of
>this triangle, including Earth-Sun distance. (Not a very
>precise method, though.)

Since the distance ratio is 400 to 1, you have to tell a difference
between a moon that is exactly half illuminated, and one that is
illuminated at an angle off that by artan(1/400) = .14 degrees.  Given
the fuzziness of the terminator and lack of telescopes, I really don't
think you can see the teminator well enough to see when the angle of
illumination moves 0.14 degrees.  You'd be lucky to tell 5 degrees.

```

```Newsgroups: alt.sci.planetary
From: henry@spsystems.net (Henry Spencer)
Subject: Re: Can anyone simply explain something to me?!?
Date: Wed, 17 Feb 1999 15:08:55 GMT

In article <36CA22FC.C00388FC@hotmail.com>,
William Giger  <lordsabiath@hotmail.com> wrote:
>Okay,  I guess I'm just stupid, but I really don't get exactly how they
>tell the distance of stars from the Earth...

It's not easy.

For nearby stars, you use parallax, measuring the star's exact position
against the "background" stars (which you hope are far away), and then
doing it again six months later, from the opposite side of Earth's orbit.

Hold your thumb up at arm's length.  Close your left eye, and note the
thumb's position against the background.  Open your left eye and close
your right, and note the thumb's position again.  It seemed to move,
because your eyes are a few centimeters apart and are viewing it from
slightly different angles.  If you measured the angle, and measured the
horizontal distance between your eyes, you could determine how long your
arm is without measuring it directly.

It's the same story with a star observed from opposite sides of Earth's
orbit:  it shifts its apparent position slightly, and by measuring how
much, and knowing the size of Earth's orbit, you can calculate the
distance.  Early attempts to do this were troubled by the fact that some
of the brighter stars are not, in fact, particularly close -- they're just
really big and bright -- but it was eventually accomplished by Bessel.  If
you do it from space, with cost-is-no-object optics and elaborate data
analysis, as ESA's Hipparcos satellite did, you can make it work out to
1000 light-years or so as I recall.

Beyond that, you're stuck with using less direct methods.  Mostly, you end
up looking for objects whose inherent brightness you can guess, and then
comparing that to their apparent brightness to determine distance.  A
candle a meter away and a 100W light bulb twenty meters away have about
the same apparent brightness, but if you know how bright they'd look at
the same distance, you can estimate their relative distances.  The trick
is finding "standard candles", whose inherent brightness is known somehow.

One particularly popular choice is Cepheid variables, a type of variable
star whose period of variation (easily observed) is related to its
inherent brightness.  (There was one minor problem with this, in that
until Hipparcos, there was no Cepheid within range of parallax methods, so
the relationship between Cepheid distance and real distance was slightly
uncertain.  The data from Hipparcos has caused some recalibration of the
Cepheid distance measurements.)  The first absolute proof that "nebulas"
like the Andromeda Nebula were really separate galaxies, not star clusters
within our own galaxy, came when Baade managed to pick out Cepheids in
Andromeda.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)

```

```Newsgroups: alt.sci.planetary
From: henry@spsystems.net (Henry Spencer)
Subject: Re: Can anyone simply explain something to me?!?
Date: Wed, 17 Feb 1999 20:38:58 GMT

In article <36CAF95E.F5F421F1@dod.no>, BĂ¸rge Berg-Olsen <azoth@dod.no> wrote:
>> One particularly popular choice is Cepheid variables, a type of variable
>> star whose period of variation (easily observed) is related to its
>> inherent brightness.
>
>Another "standard candle" that we know the inherent brightness of would
>be a supernova, or am I totally off track now?

There are several different types of supernova, and some of them can be
quite variable in brightness, depending on things like how big a star was
involved.  *However*, "type 1A" supernovae are thought to be pretty much
all alike, and they have been used in some recent work on measuring really
large distances, to calibrate the cosmic distance scale and measure the
expansion of the universe.  They have the advantage that they're visible
at really long distances, too far for any normal star to be picked out.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)
```