The distance to the Moon has been measured by Lunar Laser Ranging,
utilizing lasers that are transmitted through telescopes on Earth to
reflectors that had been placed on the lunar surface by Apollo
astronauts and a Russian lunar lander. The distances have been
calculated so precisely that fractional differences in centimeters
have been measured. The Moon is receding from the Earth at a rate of
3.8 cm per year.
Gravitational and Relativistic Physics (GRP)
"Ranging has provided the most accurate technique available for
measuring the Moon's rotation and orbit. It has also determined that
the length of an Earth day has distinct small-scale variations. Also
observed are crustal plate drifts on Earth. Measurements show that the
Moon is moving away from the Earth at a rate of about 3.8 centimeters
per year. Laser ranging has also made possible a wealth of new
information about the dynamics and structure of the Moon."
ILRS Satellite Missions
Distances to the inner planets of the Solar System have been
determined by radar ranging, in a manner similar to that used in laser
ranging of the moon. The distances to the outer planets Neptune and
Pluto are such that traditional means of measurement by triangulation
are used. Observations from widely spaced Earth observatories provide
parallax measurements from which the distances to the most distant
planets can be calculated. Calculations are based upon tables for
planetary ephemerides, the most accurate being produced by the Jet
Propulsion Laboratory, which directs many interplanetary missions and
must have precise figures by which navigation of spacecraft can be
accomplished. The margin of error for the planets Neptune and Pluto
are such that respective errors of 4000 and 10000 km are normal.
The Solar System
"Pluto, normally the most remote planet, has an average distance of
5,913,520,000 km from the Sun."
"One of the most accurate ways to measure the distances to the planets
is by bouncing radar off them, or sending a spacecraft there, which
can send a radio signal back to the Earth that can be timed. Radar is
essentially microwave electromagnetic radiation (microwaves fall under
the radio spectrum). Since electromagnetic radiation, in all of its
forms, is light, we know that radar travels at the speed of light - 3
x 10^5 km/s. We know that a distance traveled is equal to the time it
takes to travel that distance, times the velocity used to travel that
distance (x=vt). If we bounce radar off a planet, and measure the time
it takes the signal to get there and back, we can use this information
to calculate the distance of the planet.
In the absence of spacecraft or radar, one can, in principle, use
triangulation to measure the distance to a planet. That is, measure
the celestial position of a planet from two different points on Earth
simultaneously; knowing the difference in the angles that were
measured, and the distance between the two points on Earth, the
distance to the planet can be calculated. Even with modern technology,
this is not trivial - even with a baseline of 10,000 km (about as long
a baseline that is possible on Earth), the angular offset at two sites
must be measured to be accurate to 4 seconds of arc (1/450th of the
diameter of a full moon) to achieve ~10% accuracy in the distance to
Venus, our nearest neighbor."
"This method has been used in one form or another to determine the
distances to all of the planets in our solar system (except Pluto,
which we have not visited)."
Description of JPL Solar System Ephemeris
Help for EPHEMERIS
"One method of describing the accuracy of the positions provided in
DE403 is to consider the angles between various ephemeris objects as
viewed from Earth.
If the two objects observed are taken from the list (Sun, Mercury,
Venus, Mars, Moon) the angles computed from the ephemeris positions
are accurate to one or two milli-arcsecond.(This assumes all
appropriate corrections are applied for light time, stellar
aberration, and relativistic effects to the ephemeris derived
positions.) If you add the barycenter of Jupiter to this list,
uncertainty in ephemeris derived angles may grow to a few hundredths
of an arcsecond. Adding Saturn, Uranus and Neptune will raise the
uncertainty level to approximately 0.1 arcseconds. Finally, adding
Pluto to the list raises the observable errors to 0.3 arcseconds for
the present and increasing into the future.
Radial distances to the centers of objects follow a similar trend. The
radial distances between the inner objects of the solar system as
computed via the ephemeris are accurate to 1 to 2 km. The distance
between the Earth and the Jupiter Barycenter is accurate to better
than 10 km.
The uncertainty in the distances to Saturn, Uranus and Neptune are
approximately 1000, 2000 and 4000 km respectively. For Pluto, the
radial distance from earth may be in error up to 10000 km for the
present and growing into the future."
New Accuracy Levels for Solar System Ephemerides
The JPL HORIZONS
"The JPL HORIZONS /On-Line/ Solar System Data and Ephemeris
Computation Service provides access to key solar system data and
flexible production of highly accurate ephemerides for solar system
objects (163000+ asteroids and comets, 128 natural satellites, 9
planets, the Sun, L1, L2, select spacecraft, and system barycenters)."
The Hipparcos Space Astrometry Mission
The Hipparcos and Tycho-1 Databases
The Tycho-2 Database
The Guide Star Catalog
Based upon the observations of the European Space Agency's (ESA) High
Precision Parallax Collecting Satellite (HIPPARCOS), within 30 light
years of Earth, the accuracy of distance measurements is about 1 per
cent. Within 150 ly, the accuracy is about 5 per cent. Within 300 ly,
the accuracy is about 10 per cent. Beyond those distances, however,
the error and be as high as 50 percent, the greater the measured
distance from our solar system.
Extremely large distances are calculated by measuring the Doppler
shift of spectra, and this requires an accurate value for the Hubble
constant. The different means by which a value for the Hubble constant
can be determined can yield differing numbers, and thus differing
results from the calculations for distance can result. The standard
means of getting a value is to find some distant object to which a
reasonably firm distance can be attached. Choosing such an object is,
however, contentious. One generally accepted means uses Cepheid
variable stars. This method is itself disputed, however, by some
astronomers, because of the underlying assumptions, themselves of
doubtful validity. A second method relies upon masers, and has fewer
assumptions. It gives a significantly different value. There is no
agreement on the better method. Therefore, even distances within the
Milky Way galaxy have a large margin of error built into them.
Distances to the Sun and Stars
"Hipparcos worked by observing stars through two telescopes aimed 58
degrees apart. The light from the two telescopes was merged into a
detector with a fine grid of wires. As the satellite rotated,
different stars passed through the field of view of each telescope and
blinked on and off as the stars passed across the grid of wires. These
observations allowed extremely accurate relative positions of the
stars to be determined. The relative positions of all the stars could
then be combined into an extremely accurate catalog of star positions
across the entire sky.
For 118,000 selected stars, Hipparcos measured their parallax accurate
to .001 second of arc. That's the apparent diameter of a quarter at a
distance of 5000 kilometers, or putting a quarter in New York and
viewing it from San Francisco. It's also the amount the hair on a
person a meter away appears to grow in one second. A secondary mission
named Tycho measured another million stars to an accuracy of "only"
"Accuracy Level Earth-Based Data Hipparcos Data
1 percent 50 stars 10 light years 400 stars 30 light years
5 percent 100 stars 20 light years 7,000 stars 150 light years
10 percent 1000 stars 50 light years 28,000 stars 300 light years"
"When we say that the bright star Deneb is 1600 light years away, for
example, the distance is an estimate based on its brightness and
spectral type. The distance could easily be 25% larger or smaller.
Deneb is still too far away for even Hipparcos to measure accurately."
The cluster method works out to a thousand light years or so.
Fortunately, within that distance are stars that give us a yardstick
to distant galaxies. These are the Cepheid Variables. Cepheids are
named for a star in the constellation Cepheus, the first star of this
type discovered, but the most famous Cepheid, and also the nearest, is
Polaris, the Pole Star. Polaris is about 300 light years away and
varies in brightness too slightly to be obvious to the unaided eye.
Before Hipparcos, the distance to Cepheids had to be determined
indirectly by the cluster method, but now the distances to several
have been determined directly."
Cosmic Yardsticks: Pulsing Stars Unlock Universe's Secrets
"Astronomers calculate the Hubble Constant by observing the "Doppler
shift" in the color of light galaxies emit, determining how fast
galaxies are moving away from us. Then, they combine that with the
distances to those galaxies, as measured using Cepheid stars.
Existing methods have a 30-percent to 50-percent margin of error for
measuring the distance to a single Cepheid, although measuring
numerous Cepheids sharply reduces that margin, Lane said.
The new method now has a 15-percent maximum error margin for measuring
distance to one Cepheid, but that should drop to less than 3 percent
when the method is used with bigger, advanced interferometers, he
The Distance to the Galactic Center
"The distance between the Sun and the Galactic Center, referred to as
R_o , is an important one. Many of the measured parameters of galactic
objects such as distance, mass and luminosity are directly related to
R_o , which has an estimated value of 8.0 kilo parsecs (~26,000 light
years), with a standard error of about 0.5 kilo parsecs."
"Salim and Gould expect to be able to determine R_o to an accuracy
within 4% as early as the year 2002. While this is indeed an
improvement over the current standard of error, it is a slight one.
Nonetheless, the astronomical community awaits their results."
NASA's measure of the universe questioned
"A technique using a radio-telescope is a "golden ruler" for measuring
cosmic distances and calls into question the conclusions announced by
astronomers using the Hubble Space Telescope who were supported by the
National Aeronautics and Space Administration, a researcher said
"Ours is a direct measurement, using geometry, and is independent of
all other methods of determining cosmic distances," said Jim
Herrnstein of the National Radio Astronomy Observatory. "It is the
most precise distance ever measured to a remote galaxy.""
"He said the new technique shows a 15 to 20 percent margin of error in
the results announced last week by a NASA team led by Wendy Freedman
of the Carnegie Institute of Washington.
The NASA team using the space telescope said last week that it had
successfully achieved the goal of measuring within an uncertainty of
only 10 percent the speed at which the universe is expanding, a value
called the Hubble constant.
Herrnstein said this calculation is off by 15 to 20 percent. He based
his conclusion on the difference in calculated distance to a specific
galaxy using his technique compared with the calculation method used
by the NASA group."
"But Herrnstein said the technique using Cepheids is far less accurate
than his new method that directly measures the motion of gas around a
galaxy. NGC 4258 is surrounded by a rotating cloud of gas. Within this
gas cloud is water vapor, which tends to amplify radio signals. This
creates radio "hot spots" called masers.
The orbital speed of masers between NGC 4258 and Earth was measured in
1994, and again every few months over the following three years. By
determining the speed at which the masers were moving, the astronomers
created a triangle with the first maser position at one angle, the
latest position at a second angle, and the galaxy center at the third
angle. Measuring the angles gives the distance.
The distance to NGC 4258 was calculated at 23.5 million light years,
with an accuracy to within 4 percent. This distance has been
calculated using the Cepheid star technique at 27 to 29 million light
Herrnstein said that the distance measure using Cepheid stars is based
on a series of assumed values, such as the distance to the Large
Magellanic Cloud, a galaxy neighbor to the Milky Way. These assumed
values, said Herrnstein, have a greater margin of error than does the
direct measuring technique he is using."
Astronomers dispute NASA gauge of universe's age
Thus, the margins of error:
Moon - fractional centimeters
Neptune and Pluto - thousands of kilometers
Proxima Centauri (4.22 ly) - ~ 1 per cent
The star Rigel (910 ly) - greater 10 per cent less 25 percent
Globular Cluster in Hercules (There are four globular clusters in
Hercules, the nearest, M13, is 13000 ly from the Sun: M93 is 25000 ly
away: 6229 is 102000 ly distant.) - margin of error greater than 25
Spiral Galaxy in Andromeda, M31 (~2 million ly) - greater than 25 per cent
A Galaxy in the Virgo group (3000 galaxies, ~65 million ly) - greater
than 25 per cent
The Quasar 3C273 (~2.5 billion ly) - greater than 25 per cent,
possibly as much as 40 percent