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Former PARI students
shine at AAS
Volume 15 Number 1 Winter 2015
PARI Calendar
January 24-25
Astronomy Days at
NCMNS, Raleigh
February 10 - 11
Western Regional
Science Fair
February 13
Evening at PARI
February 14
Valentine's Day
Special Event
March 13
Evening at PARI
April1 1
Mitchell County CC
STEM event
Several former PARI students were front and center
with their research projects at the 225th meeting
of the American Astronomical Society in Seattle.
Shown in this photo with PARI Science Director Dr.
Michael Castelaz, they are (left to right):
•
Rosalie McGurk, Duke TIP 2004 and a 2006
Richard and Sherry Austin Intern, presented her
Ph.D. thesis on colliding galaxies and black holes. Rosalie will receive her Ph.D. in Astrophysics from
the University of California-Santa Cruz this spring.
•
Dillon Dong, Duke TIP 2009, is now
a senior physics and math major at Pomona
College and is applying to graduate schools.
Dillon presented a paper on star formation using
observations he obtained from the Very Large Array
radio observatory.
•
Cameron Lemley, Duke TIP 2010 and 2013
J. Donald Cline Intern, is a junior at Columbia
University majoring in physics and astrophysics.
He presented his research of the Milky Way Galaxy
from data obtained from the GALEX space-based
telescope.
April 10 - 26
NC Science Festsival
April 10 Evening at PARI
April 11
Mountain Science EXPO,
NC Arboretum, Asheville
April 23
Homeschool Day
April 24
NC Star Party event
at PARI
May 2
PARI Space Day
“Not only is it fun seeing these students again,” said
Dr. Castelaz, “it provides a sense of pride about what
we are doing at PARI and the quality of students we
serve. Each one told me independently how their
Duke TIP and internship experiences at PARI has
positively influenced the tracks they are now on. They also send their thanks to Don Cline and PARI.”
Radome removed from PARI’s 12m radio telescope
Like a butterfly emerging from a cocoon, a
long-dormant asset at PARI has shed its outer
covering and is evolving into a major new
research-grade scientific instrument.
PARI’s 12m radio telescope
inside the radome.
Step one in the radome
removal, securing the structure
with a crane.
Step two, after being detached from its pad,
the radome was carefully hoisted away from
the antenna.
The radome removal team.
Step three, with the
radome safely away
from the antenna,
workers began the
process of disassembly.
For decades a 12m (40 ft.) radio telescope
on the west side of the PARI campus has
been hidden from view by a radome. The
covering was essentially a Cold War relic,
designed primarily to keep prying eyes from
determining where the antenna was pointed
and what it was monitoring. When PARI took
over the site from the Department of Defense,
the instrument had been decommissioned.
For the antenna to assume its new role at
PARI the radome needed to be removed, and
that was no small task. The structure weighed
23,000 pounds and was composed of 340
panels held together by an estimated 6,000 ⅜”
bolts and about 2,000 ¾” bolts. In addition to
the safety of the men, great care was necessary
to prevent any damage to the delicate surface
of the antenna housed beneath the massive
structure. PARI’s Executive Director Ken
Steiner served as project engineer, supervising
the work of 22 men and women who were
aided in their work by a 130-ton capacity
crane.
With the successful removal of the radome,
PARI astronomers and engineers are
provisioning the antenna for its new mission:
a survey of the Milky Way Galaxy at
22.35GHz for water masers, which are regions
of star formation. A similar survey has been
completed in the Southern hemisphere but
none have been conducted for the Northern
hemisphere. The survey itself will take
about seven years to complete and requires a
dedicated precision surface telescope like the
PARI 12m.
Homeschool Day brings students to campus to
study earthquakes
Students being schooled at home were treated to a special
day of learning on the PARI campus. PARI astronomers
and educators designed and taught grade-appropriate
(K-2, 3-5, 6-8 and 9-12) modules on earthquakes in North
Carolina. The day also included a visit to PARI’s StarLab
planetarium for each student.
“Although usually quite minor, earthquakes are fairly
common in North Carolina,” said PARI Education
Director Christi Whitworth. “During our sessions we
explained why earthquakes occur and how seismometers
are used to measure their intensity. We also showed the
students how they can access PARI’s seismometer online
and continue their education from home.”
PARI conducts Homeschool Days each spring and fall, each time developing a new educational experience.
Blade center donation
PARI CIO Lamar Owen shows President Don
Cline a blade server from one of 19 blade centers
recently donated to PARI. Each blade center
contains 14 blades and each blade is is equivalent
to a mid-range PC. In effect, the blade centers
provide the combined computer horsepower of 266
PCs. The donation substantially increases PARI’s
computational power and will be used in multiple
programs, including 3-dimensional modeling.
Orrery loaned to PARI
The Barnard Astronomical Society in Chattanooga, TN, has
loaned PARI an orrery for display and educational purposes.
An orrery is a mechanical model of the solar system used to
represent the relative positions and motions of the planets
as they orbit the Sun. This orrery also accurately displays
the angle of Earth during each position of its orbit. And, as
can be seen in this photo, it is already providing hands-on
learning for young visitors.
PARI in Pictures
Friends of PARI Volunteer Alex Armstrong is a professional photographer who graciously provides
stunning photos for PARI literature and public outreach. Here are a few of his recent works.
RESEARCH UPDATE
Michael Castelaz, Science Director
Discovery of a Third Star in the Eclipsing Binary Star System V523 Cassiopeiae
V523 Cassiopeiae is a 10th magnitude eclipsing binary where the two stars orbit each other in about 5 hours
and 36 minutes. To orbit each other so fast, the two stars must be nearly in contact. Imagine our Sun being two
stars like this orbiting each other! In 2004 a paper was published by astronomer Dr. Ron Samec suggesting that
a third star is present orbiting the pair once every 101 years. But, according to Dr. Samec, observations would
be needed in 2012-2013 to really observe the presence of the third star. We set out to observe the V523 Cas
through many orbits in 2012 and 2013 to definitively detect the presence of a third component.
V523 Cas was observed using the Pisgah Astronomical
Research Institute 0.4-m telescope equipped with an
Apogee E42 2048x2048 CCD camera and Visual (V), Red
(R), and near-Infrared (I) filters. Exposure times were 40
seconds in each filter. The number of images per filter per
night varied from 80 to 120. Observations were made on
UT 2012 October 22, 23, 24, 25, November 2, 9, 11, 14,
16, 18, 19, 21, 22, 25, 26, 29, and UT 2013 October 10,
11, 12, 24, November 4, 8, 11, 14, 15. A total of 1,833
images were made in each filter over the two year period. The telescope and camera have a 30 arcminute field of
view, about the same angular size as the Moon. Three
stars in this field of view were selected to compare the
brightness of V523 Cas over time. Figure 1 shows the
field of view and marks the location of V523 Cas and
comparison and check stars. Figure 1. One image of V523 Cas taken with
the PARI 0.4-m telescope. The variable and
comparison and check stars are circled
As the two stars nearly in contact orbit each other,
the brightness varies over the 5 hours and 36 minutes
of their orbit. We observe the change in brightness
as a light curve. Measuring that brightness and
comparing it to the Comparison and Check stars, we
plotted the light curve in each of the V, R, and I filters.
Figure 2 shows the light curve of V523 Cas from all
observations made in 2012 and 2013. We observed 30 complete orbits. We observed the
time each orbit reached minimum brightness. The
minima that we observed should have occurred at a
very precise predictable time that we can calculate
from knowing the orbital period. The difference
Figure 2. The light curve of V523 Cas
RESEARCH UPDATE
between the observed and computed times of minima is called O-C. Figure 3 shows the O-C versus Epoch (the
number of orbits). The dots are the measured O-C from our data. The dashed line is where those dots should
be. The dashed line is where the dots would be if we put a third star orbiting the close pair of stars. The third
would need to be in a 70 year orbit and have a
mass of about 0.6 that of the Sun. Including this
third stars matches the data very well.
This is a lot of information from 2 years of
observations. We checked to see if anyone
imaged this star at extremely high resolution. One
group in 2009 tried but did not detect it. So, we
think third star is nearly along the line-of-sight of
the close pair. So, in a 70 year orbit, we should
be about to image it in 15-20 years when it is not
along that line-of-sight. We’ll report back then.
Figure 3. The O-C versus orbits of V523 Cas. The
observed (dots) O-C match the model that includes a third
component (solid line) very well. The dashed line is the
model without a third star.
The paper describing this research has been
accepted for publication in the refereed journal
called The Information Bulletin of Variable Stars,
volume 6120.
Astronomical Photographic Data Archive
The Astronomy Legacy Project to digitize astronomical photographic plates in APDA is underway. Thanks
to contributions through our Indiegogo crowdfunding campaign ($20,000 was raised), the Astronomy Legacy
Project equipment has been purchased and is now installed and operational. We have now started the digitizing
phase of the project. We are beginning with 3 collections: 1.) Harvard All-Sky Survey: There are 55 plates
in this collection; 2) 200 plates taken in November and December 1972 of the Large and Small Magellanic
Clouds; and 3) 513 plates taken in 1961 of a wide variety of older, very red stars – we called this the red star
survey. We will have these collections completely digitized by the end of 2014.
Meetings
On October 4, 2014 we presented at the annual North Carolina Astronomers Meeting at Guilford Tech
Community College for PARI. Five posters were presented. The posters included: “PARI: Site for the 2017
Total Solar Eclipse” author Don Cline; “The Astronomy Legacy Project” authors Castelaz, Cline, Barker,
Boehme, Armstrong, and Rottler; “SCOPE” authors Barker, Castelaz, Cline, and Owen; “PARI Programs”
authors Whitworth, Cline, and Castelaz; and “A Third Component in the V523 Cas Eclipsing Binary System”
author Castelaz.
On October 17-18, 2014 we attended the Appalachian College Association Summit and presented an hour
long seminar about PARI entitled “The Lab and Classroom Resources at the Pisgah Astronomical Research
Institute.” This generated interest from several ACA member colleges.
Update on Comet Research
astronomer's corner
Dr. Bob Hayward, Astronomer/Educator
INTRODUCTION: Comets have always
fascinated people whenever they are spotted in the
sky. In earlier times we didn’t understand what
they are or even where they are. At one time they
were considered to be atmospheric objects rather
than objects out in space. They have often been
suggested as a possible explanation for the nature
of the Star of Bethlehem since they do hang in
the sky for extended periods of time from days
to weeks to even months. For the superstitious
among us they have been seen as omens of evil
things about to happen usually to our rulers.
For example the Bayeux tapestry supposedly
foretold the demise of King Herald at the Battle of
Hastings.
Now, however, our fascination with comets is simply in the beauty of these visitors to our skies since we know
what comets are, how they move, and what they are made of. Or do we?
Obviously, we have come a long way from our views of comets as the swords of the gods. We know, for
example, that these are frozen objects that, as they come into the inner regions of our solar system, they “melt”
and give off their gases to form the spectacular tails that make them so beautiful. Technically, we should say
the ices on the comets don’t melt, they sublimate, meaning they go from a solid ice directly to a gaseous form
without ever becoming a liquid in those cold reaches of the solar system.
We also know that comets are composed, not of pure, clean ices, but rather
of dirty ices, frozen gases such as water, carbon dioxide (dry ice), methane,
ammonia and others, with solid materials trapped within the ice. Thus,
astronomer Fred Whipple in 1950 characterized comets as “dirty snowballs”
and that appellation has stuck. In fact, it may be that some or all comets
have a solid core beneath their outer surface of frozen gases.
In recent years, the dividing line between icy comets and rocky asteroids
has become blurred. There are some bodies that appear more like asteroids
with ice on them than the generally assumed structure cometary bodies med
up of pure dirty ice. The surfaces of comets may be coated with a layer of
organic material and this has given rise to theories that the earth received
the building blocks of life from outer space, i.e., comets and meteoroids that
have impacted our home planet throughout the age of the solar system but
especially in its formative years billions of years ago.
Fred Whipple
(1906-2004)
Inducted into the International
Space Hall of Fame in 1984
in part for his “Dirty Snowball”
theory of comets in 1950.
Dynamically, comets are the oddballs of the solar system. Solar system
bodies, i.e., planets, asteroids, dwarf planets, gas and dust, generally follow
orbital paths that keep them close to the plane of the solar system, defined
as the plane of the earth’s orbit, i.e., the ecliptic. Since most of our solar
system exploration missions have been designed to study these objects, even
our satellites and spacecraft follow orbits in the plane of the solar system.
Update on Comet Research (continued)
Also, most bodies orbit their hosts in a prograde direction, i.e., clockwise when viewed from above the solar
system. Those objects that don’t follow this pattern present challenges to dynamicists trying to explain their
unusual behavior.
But comets don’t follow these rules. First of all, most, but not all, comets have extremely elliptical orbits;
they swing far out in the solar system, spend a long time in the cold, dark depths of space, and then, under
the influence of the gravity of the sun, periodically fall into the inner solar system to quickly whip around the
sun and once again disappear into the depths of space. Some come back in a short period of time, just a few
years. Some, like the famous Halley’s comet may take decades to return. These comets are termed periodic for
obvious reasons and probably have originated within the inner solar system itself. It’s possible they originated
elsewhere and were “captured” by the gravity of those massive gas giant planets out beyond Mars and the
asteroid belt.
However, some comets don’t’ return; their orbits are extremely elongated to indicate they originated far beyond
the outer planets in a region of space postulated by the late Dutch astronomer Jan Oort to be roughly 1000 times
farther away than even the former planet Pluto. These comets have probably been there since the formation of
the solar system and, thus, when they fall into the inner solar system react to the sun’s energy in different ways
than the periodic comets for whom passing by the sun is old hat. Also, these Oort comets are composed of
material dating from the original formation of the solar system. What a boon it would be for cosmologists to be
able to determine what they are composed of.
While astronomers can observe comets with telescopes and even determine some things about their
compositions by using spectral imaging of the gases in their tails, they would really appreciate close up looks
and these bodies and even information directly obtained by sampling the composition of the ices of the comets.
We have made great strides in the past thirty years in doing just this.
International Cometary Explorer – Giacobini-Zinner 1985 & Halley 1986
In 1982 NASA’s International Sun/Earth/Explorer 3 (SEE-3) was redirected from its station keeping orbit in the
Earth’s L1 Lagrangian point. Renamed the International Cometary Explorer (ICE), it flew through the plasma
tail on Comet Giacobini-Zinner on September 11, 1985. In late March 1986 it flew through the tail of Comet
Halley at a distance from the comet of 28,000,000 km.
Vega 1 – Halley 1986
Launched by the Soviet Union in 1985, Vega 1 was designed as a Venus mission with a follow-up fly-by of
Comet Halley. On June 11, 1985 a lander was released to land on Venus. The mother craft used the gravity of
Venus to redirect it to Comet Halley. Its closest approach to the comet was at 8,889 km on March 6, 1986. The
low resolution photographs obtained showed two bright spots on the nucleus of Halley which were initially
thought to indicate a double lobed body. However, later it was determined that what Vega 1 had seen were two
areas of outgassing of material from the comet as it closed in on the sun and, thus, warmed up.
Vega 2 – Halley 1986
As the name implies, Vega 2 was a sister craft of Vega 1. Its lander was landed on Venus four days after the
Vega 1 lander. Closest approach to Comet Halley was on March 9, 1986 at a distance of 8,030 km. It did take
700 pictures of the comet but a power deficit limited its operation.
Update on Comet Research (continued)
Suisei – Halley 1986
This spacecraft, named with the Japanese word for comet, was launched on August 18, 1985 by the Japanese
Institute of Space and Astronautical Science (now part of the Japanese Aerospace Exploration Agency, or
JAXA) and flew by Comet Halley at 150,000 km on March 8, 1986. Originally, it was to fly to Comets
Giacobini-Zinner and Tempel-Tuttle but plans had to be cancelled due to a depletion of hydrazine in the
spacecraft. (Comets are named after their discoverers with the names of up to three persons who first spotted
them.
Sakigake – Halley 1986
Sakigake was developed and launched on January 7, 1985 by the Japanese Institute of Space and Astronautical
Science and flew by Comet Halley on March 11, 1986 at a distance of 6,099,000 km. It was also originally
planned to fly by Giacobini-Zinner but, again, that mission was cancelled due to a lack of propellant.
Giotto – Halley 1986 & Grigg-Skjellerup 1992
Launched in 1985 by the European Space Agency, Giotto made the
first close (596 km) encounter with a comet on March 14, 1986. This
pass was so close that the spacecraft was pelted by pebbles from the
comet that destabilized its pointing in space and actually destroyed
a camera (thankfully, after it had already taken valuable pictures). Results showed that Halley was 15 km long with a diameter ranging
from 7 to 10 km. Comets are not large enough to have enough
gravity to retain a spherical shape.
Comet Halley as viewed from the
Giotto spacecraft
Following its encounter with Halley, Giotto went into a sleep only to
be retargeted to another comet, this one Grigg-Skjellerup. Giotto flew by this comet in June 1992 at a distance
of only 200 km but did not obtain any pictures due to the damage to the camera by Halley.
Stardust – Wild-2 2004
As the name implies the Stardust spacecraft was basically a solar system vacuum cleaner. Its mission was
to scoop up the dust known to exist in the plane of the Earth’s orbit, the ecliptic (defined above). Launched
by NASA on February 7, 1999, Stardust collected this material as it looped throughout the solar system. On
January 2, 2004 it flew close to Comet Wild-2 and collected a sample of the material that was being expelled by
the comet. This material was placed in a capsule which landed in the Utah desert on January 15, 2006.
Deep Impact/EXPOXI -Tempel 1 2005 & Hartley 2 2010
Launched in January 2005 NASA’s Deep Impact was designed as the first spacecraft to actually go out and
touch a comet. On July 4, 2005 a fortified probe released from the mother ship was sent into the comet to see
what would happen and to disperse cometary material for the mother ship to sample. The event was not only
spectacular for the viewer but also provided very valuable information regarding the composition of this comet.
Following this successful encounter the mission of the mother ship was renamed EPOXI, a combination of
the names for the two extended mission components: the extrasolar planet observations, called Extrasolar
Planet Observations and Characterization (EPOCh), and the flyby of comet Hartley 2, called the Deep Impact
Update on Comet Research (continued)
Extended Investigation (DIXI). This flyby of
Hartley 2 occurred on November 4, 2010. The
views of this comet clearly showed the jets of
gases being expelled by the comet due to the
heating of the sun.
Image of comet Tempel 1 taken 67 seconds after it obliterated
Deep Impact's impactor spacecraft.
Plumes of gases photographed by the EPOXI
spacecraft in 2010.
Stardust-NExT: Tempel 1 2011
Well, if you poke a hole in a comet,
surely you want to see what you
have done. Stardust-NexT (Stardust
– New Exploration of Tempel) was
the spacecraft chosen for this juicy
mission. Directed to fly by Comet
Tempel 1 and take pictures of the
“damage” done by the Deep Impact
probe, Stardust-NExT returned a
picture of the 150 m wide new crater
on the surface of the comet at 110 km
distance on February 14, 2011.
Rosetta and Philae: ChuryumovGerasimenko 2014
So, we have photographed a multitude
of comets; in the case of Halley and
Tempel 1 even several times. We have Impact crater on Comet Tempel 1created by the
sampled the materials given off by
Deep Impact probe as recorded by Stardust NExT
these ancient bodies as they feel the
heat of the sun. And, we’ve shot a
hole in one of them. What’s left to do? Of course, landing a probe on the surface of a comet is the next logical
step. That was accomplished just a few months ago by the European Space Agency. Launched on 2 March
2004, Rosetta, the mother ship with a lander attached, flew by two asteroids, Stein in 2008 and Lutetia in 2010,
on its way to a rendezvous with Comet Churyumov-Gerasimenko. On August 6, 2014 it arrived in the vicinity
of the comet and began an orbit of the comet that continues as of this writing.
On November 12, 2014 Rosetta released the lander Philae which then went into a freefall to the surface of
the comet. Since a comet of this size has very little gravity, Philae was designed to attach itself to the surface
Update on Comet Research (continued)
with a set of probes. Unfortunately, these did not deploy and the lander ended up bouncing back into space
twice before finally settling on the comet on its third landing. It ended up instead of on a flat area as planned
but down in a bit of a hole in the shadow of a cliff. While it did complete its initial scientific tasks before
its batteries ran out, this location limits how much it will be in the sun during the comet’s 12-hour day for
recharging its batteries.
In the meantime, the mother ship continues to orbit the comet
and make observations. It will do so through the comet’s
perihelion, its closest approach to the sun, in August 2015.
SUMMARY: We have come a long way from when we
thought comets were in the earth’s atmosphere or they were
portents of disasters to come. In fact, we have come a long
way to understanding the nature of comets from what we knew
just a few short years ago. Observations continue with Rosetta
and with ground-based telescopes. Ironically, the observations
will help to unlock the secrets of these magnificent celestial
wonders just as the Rosetta Stone of so long ago gave us a clue
to the ancient Egyptians writings.
Philae lander is in a precarious spot on Comet
Churyumov-Gerasimenko.
References:
European Space Agency.
“Rosetta”: http://sci.esa.int/rosetta/
National Aeronautics and Space Administration (NASA).
“NASA’s Deep Impact Produced Deep Results”: http://www.nasa.gov/mission_pages/deepimpact/
media/deepimpact20130920f.html#.VKrdIdGAg
Space.com.
“Comets”: http://www.space.com/53-comets-formation-discovery-and-exploration.html/
“Photos of Comet Tempel 1 from NASA Space Missions”: http://www.space.com/10814-comet-tempel1-photos-nasa-spacecraft.html
Wikipedia: “Giotto (spacecraft)”: http://en.wikipedia.org/wiki/Giotto_%28spacecraft%29
“26P/Grigg-Skjellerup”: http://en.wikipedia.org/wiki/26P/Grigg%E2%80%93Skjellerup
“Vega 1”: http://en.wikipedia.org/wiki/Vega_1
“Vega 2”: http://en.wikipedia.org/wiki/Vega_2
“Suisei (spacecraft)”: http://en.wikipedia.org/wiki/Suisei_%28spacecraft%29
“Sakigake”: http://en.wikipedia.org/wiki/Sakigake
Bob Hayward's column is a regular feature of our newsletter. For additional information, or if you'd like to ask Dr. Bob a question,
e-mail [email protected] or, write Dr. Bob at One PARI Dr., Rosman, NC 28772.
PARI needs your help!
PARI is a public not-for-profit foundation. Financially, we are dependent upon contributions and grants for our educational and research programs, and
for the many operating expenses associated with maintaining the campus and our facilities.
If you have recently contributed, we thank you for your support. If not, please help support PARI and our mission with a contribution. PARI is a
501 c(3) organization and all donations are tax deductible to the full amount allowed by law.
A financial contribution automatically makes you a member of Friends of PARI. Membership levels include: Student Member $10.00, Associate
Member $50.00, Member $100.00, Family Membership $200.00, Supporter $500.00, Mentor $1,000.00, Advisor $2,000.00, Benefactor $5,000.00. All donors at the level of $5,000 and above will receive recognition on a permanent plaque at PARI.
Please provide the requested information below and mail it with your contribution to:
Pisgah Astronomical Research Institute
One PARI Drive
Rosman, North Carolina 28772
Name: ___________________________________
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Email address _______________________________
Pisgah Astronomical Research Institute
One PARI Drive, Rosman, NC 28772
Phone: (828)862-5554 Fax: (828)862-5877 Web: www.pari.edu
Don Cline
Ken Steiner
Michael Castelaz, PhD
Christi Whitworth
Bob Hayward, PhD
Lamar Owen
Mark Krochmal
Ben Goldsmith
Thurburn Barker
John Avant
Ann Daves
Thad McCall
Joe Phillips
John Boehme
John Halsey
Alex Alexander
John Sinclair
President
Executive Director
Science Director Education Director
Astronomer/Educator
Chief Information Officer
Manager of IT Support
Site Support Engineer
Director of the Astronomical Plate Data Archive
Communications Director
Accountant & Assistant Treasurer
Facilities Manager
Director of Public Outreach
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Director of RSAS
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Curator of Meteorites
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The Pisgah Astronomical Research Institute (PARI) is a public not-for-profit 501 (c)(3) foundation established in 1998. Located in the
Pisgah Forest 30 miles southwest of Asheville, NC, the PARI campus is a dark sky location for astronomy and was selected in 1962 by
NASA as the site for one of the first U.S. satellite tracking facilities. Today, the 200 acre campus houses radio and optical telescopes, earth
science instruments, 30 buildings, a fulltime staff and all the infrastructure necessary to support STEM (science, technology, engineering
and math) education and research. PARI offers educational programs at all levels, from K-12 through post-graduate research. PARI is
home to the Astronomical Photographic Data Archive and a member of the NC Grassroots Science Museums Collaborative. PARI's Exhibit Gallerydisplays a collection of rare meteorites as well as NASA Space Shuttle artifacts, many of which have flown in space. For more information about PARI and its programs, visit www.pari.edu. Follow PARI on Twitter at http://twitter.com/Astronomy_PARI.
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