{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Parallaxes from GAIA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this exercise, we will download some data from the GAIA archive on parallaxes of stars. The parallax, $p$, of a star is half the change in the angular direction of a star as seen from opposite points of the Earth's orbit, as shown here:\n", "\n", "\n", "\n", "\n", "It can be used to determine the distance to a star: simple geometry gives \n", "$$tan(p) = 1 / d$$\n", "where $d$ is the distance in units of the earth-Sun distance, which is called an astronomical unit (and is equal to $1.496 \\times 10^{13}$ cm\n", "\n", "Since stars are very far away, the parallax is always a very small angle, so\n", "$$tan(p) \\approx p = 1/d$$\n", "where $p$ is in radians.\n", "Astronomers have defined a distance unit called the parsec, such that the distance in parsecs is:\n", "$$d({\\rm in\\ parsec}) = 1 / p ({\\rm in\\ arcsec})$$\n", "where 1 arcsec = 1/3600. degree. With this definition, \n", "$$1 parsec = 1 astronomical unit \\times 3600 arcsec/degree \\times 180 / \\pi = 3.086\\times 10^{18} cm$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The GAIA mission is currently measuring parallaxes to billions of stars. They release data to the public through a relational database in the GAIA archive. We will download some data from the database, using a Python package called astroquery . Once astroquery has been installed in your Python distribution, we can import it:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import astroquery" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Many quantities are available in the GAIA archive database. These are described by the database schema. You can find the schema for GAIA at the GAIA archive: click on the Search link at the top, and then the Advanced (ADQL) link, and finally expand the gaia.dr3.gaia_source description on the left by clicking the +. This will show you all of the information in this database table. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will query the database using the Astronomical Data Query Language (ADQL) which is a superset of the standard Structured Query Language (SQL). The basic format of queries is relatively simple:\n", "\n", "
\n",
    "SELECT selectList \n",
    "FROM fromClause \n",
    "[WHERE conditions] \n",
    "
\n", "\n", "Basically, the selectList gives the quantities you want to download, the fromClause gives the table where the quantities are located, and the optional WHERE clause gives some conditions for which objects you want to download.\n", "\n", "\n", "ADQL is an extension of SQL, in particular, defines some useful geometric functions, e.g. CONTAINS() can be used to select objects within some distance of some point in the sky, e.g.\n", "
\n",
    "WHERE 1=CONTAINS(POINT('ICRS', ra, dec), CIRCLE('ICRS', tablera, tabledec, radius)\n",
    "
\n", "would select points where the database coordinate variables (tablera and tabledec, but you will need to use the appropriate column names) fall within some distance of the ra/dec specified in the query.\n", "\n", "For a little more information on ADQL/SQL see https://www.cosmos.esa.int/documents/915837/915858/ADQL_handson_slides.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Let's write a query to get the parallaxes of all stars within 0.5 degree of the north Galactic pole. Look at the schema to get the column names for ra, dec, and parallax, and try to complete the following SQL query. Give it a quick try, then move on to the next cell to see a valid query:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SELECT\n", " FROM\n", " WHERE \n", " \n" ] } ], "source": [ "# get RA/DEC at the Galactic pole, which has l=0, b=90\n", "from astropy.coordinates import SkyCoord\n", "import astropy.units as u\n", "coord = SkyCoord(0, 90, unit=(u.degree, u.degree), frame='galactic')\n", "ra=coord.icrs.ra.value\n", "dec=coord.icrs.dec.value\n", "\n", "query=\"\"\" SELECT\n", " FROM\n", " WHERE \n", " \"\"\"\n", "print(query)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell gives and implements the query" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/holtz/anaconda3/lib/python3.7/site-packages/requests/__init__.py:91: RequestsDependencyWarning: urllib3 (1.26.9) or chardet (3.0.4) doesn't match a supported version!\n", " RequestsDependencyWarning)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "SELECT ra, dec, parallax, parallax_error\n", " FROM gaiaedr3.gaia_source\n", " WHERE 1=CONTAINS(\n", " POINT('ICRS', 192.859478, 27.128252),\n", " CIRCLE('ICRS',ra, dec, 0.500000))\n", "INFO: Query finished. [astroquery.utils.tap.core]\n", "Returned 2052 objects\n" ] } ], "source": [ "from astroquery.gaia import Gaia\n", "from astropy.coordinates import SkyCoord\n", "import astropy.units as u\n", "\n", "# get RA/DEC at the Galactic pole, which has l=0, b=90\n", "coord = SkyCoord(0, 90, unit=(u.degree, u.degree), frame='galactic')\n", "ra=coord.icrs.ra.value\n", "dec=coord.icrs.dec.value\n", "\n", "# search radius\n", "rad=0.5\n", "\n", "#form the SQL query\n", "query=\"\"\"SELECT ra, dec, parallax, parallax_error\n", " FROM gaiaedr3.gaia_source\n", " WHERE 1=CONTAINS(\n", " POINT('ICRS', {:f}, {:f}),\n", " CIRCLE('ICRS',ra, dec, {:f}))\"\"\".format(ra,dec,rad)\n", "print(query)\n", "\n", "# run the query and get the results\n", "job = Gaia.launch_job_async(query)\n", "tab = job.get_results()\n", "print('Returned {:d} objects'.format(len(tab)))\n", "\n", "# FYI, here's an alternate way to use astroquery for a simple cone search that bypasses the SQL, but is less flexible\n", "#coord = SkyCoord(ra=ra, dec=dec, unit=(u.degree, u.degree), frame='icrs')\n", "#radius = u.Quantity(rad, u.deg)\n", "#job = Gaia.cone_search_async(coord, radius)\n", "#r = job.get_results()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results are returned in an astropy table. You can display them in a convenient notebook interface. Individual columns can be referenced using tab['columnname'], e.g. tab['parallax']. If you are more familiar/comfortable with pandas data frame, tables can easily be converted to pandas." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parallax of row 100: 0.294\n" ] }, { "data": { "text/html": [ "Table length=2052\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", 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idxradecparallaxparallax_error
degdegmasmas
0192.364122479850827.170031430014568----
1192.3896313252340627.1932916447179450.82384839096817290.7112348
2192.3660526014190327.19754313280102----
3192.3700837641190427.209544055454970.29908522664797270.66879827
4192.319348815374427.194094769490170.78166337410633510.4147468
5192.3108113831370427.200340385134331.45331846885513531.1174845
6192.3064325537483227.210527793266551.0912003886926450.1020728
7192.308465488678227.218095184011474----
8192.3261143509931227.2345550336434670.110233928687797120.42845914
9192.317998566799427.2620621041545020.335526518018960830.11267472
10192.3972235436537227.197618349630204----
11192.4906875715970827.1406527283642660.63434424282995820.038752172
12192.4982531084617727.140547444508314-0.79294039938298160.8093335
13192.4958035151156327.15265890469925----
14192.4723817892817427.1528552701394942.04947124717387030.0907048
15192.475647105314827.1533976516431320.474577485897807960.07928828
16192.4720348695260627.162599578518690.075576729898751220.39977738
17192.523889361154827.160006032270862.44494110112260140.81470805
18192.5400103973202327.170610243621702----
19192.511399189995527.20352528084393.25107367581635741.6075095
20192.4363639919098127.158564635974383----
21192.4680683402439727.1901256373814561.53533643408969360.12974222
22192.439398414454727.1982642083249541.61847666253892640.39045492
23192.4419247857842427.1980128509687380.34574211004300680.60997766
24192.456151460888127.1992791951802250.03596497935083390.8949397
25192.416504461328427.1881006363907822.02103035210195130.42272574
26192.4230103019380427.2031694637649970.26480030217997730.37509325
27192.648258261729827.275327633400828----
28192.3992699072883327.196203351373162.1814779897318360.14366148
29192.48228463072327.22648189381898-0.069785386769332630.30917543
30192.5201689896168827.2371445697017831.737940605512590.82069486
31192.4896199584414427.242631681760811.78928424750393370.09227437
32192.465560740548727.239987611465441.80796365160551330.14972168
33192.467737195685927.2398919372691570.7341164011064571.2075833
34192.5782608294520627.210987621774671.25994547362054980.03157514
35192.57190904934627.2257072521529760.201847092699394160.63668346
36192.5383749424797227.2503717505151140.00252739454160963440.70338905
37192.5488449471080227.25044751735711----
38192.5408556967245527.243231812163491.62301741608362440.028623845
39192.550408746823427.2587830763624023.49158577635763120.33538312
40192.565976500618627.277284486657430.39803653363838120.43420827
41192.6020545071104427.2673986313698830.052537398661312130.4622145
42192.6121127640149727.2606120525443740.73145366533108560.05489267
43192.6431715673000427.2674205669723342.2571754495881090.14796008
44192.6488316374210427.283911774768742.07687665788179741.2133338
45192.6369474732544527.287107116993662.9797023044473280.1712976
46192.574739830757727.2830889933382470.53170532033236580.49238777
47192.5806037517430427.290315038386----
48192.615485665349727.291208626776555----
49192.5262329763317627.2593210677911130.32707779320400470.35255346
50192.5605598538996627.275792967833734-0.78950900269019570.6228187
51192.5292915837736727.2761154748037244.3587715529405760.25528818
52192.5093158778259427.2883432766131943.3381236450526750.09111057
53192.499011407655327.295352780672665-0.98704226486093190.9813594
54192.5415394352155527.304674322922870.41022249419846630.21589251
55192.5268646668377227.3096932476713870.1118363151612610.16284308
56192.569849426740227.283619876117091.10950656540860960.24345638
57192.5710253825910227.3001969440368980.69782580249637740.12271262
58192.5616884953004727.3028686654458----
59192.548849475098527.2990549290223221.71490960442525451.2558198
60192.5863644732335727.310124841566243-0.2396916220130920.6477802
61192.5976325245216927.3263545895517----
62192.582961404973327.323987717998698----
63192.5575113942801727.3166796250345530.351868713759991240.43076825
64192.549579229026927.3213483645609260.52688231697513790.46579158
65192.5619215156301627.325238673792512-0.59155539325144251.627155
66192.5613014996207827.327120484063656----
67192.5288861878201227.3216591119863643.3614951618793080.15679714
68192.531905740800227.321019291542022----
69192.5457382652079727.33440940205794-0.43847130341562950.3809733
70192.5692482584817427.356901864714832----
71192.4089552771996227.2325604067735550.60701626098983690.33407697
72192.4162958371776727.2479430951863470.71083837230618420.78992623
73192.399636912005227.2466488467258580.81286108669042530.020781307
74192.3801474179827627.256572614362062.68391999055586130.26570737
75192.3903013308861627.271112305691320.59799355798291420.057883453
76192.4372421475961827.243749558966931.31636185786092690.016706623
77192.4425227150529727.2548367886537332.31821959111368470.019256683
78192.4722541621681827.2839718010339461.3931149807431130.56912935
79192.4224207852314227.2679739419420740.84558758099870380.085596666
80192.4093153609066527.263972530663911.16363204872285860.026564002
81192.406299309197427.2819118601070620.197378770801839520.08269813
82192.4090516016612827.2893535157515360.249316312537736950.4612973
83192.4509360111729827.2959010869242920.58125764625475870.3782572
84192.4489410406643227.293295398408237----
85192.3428586072464327.263177837641811.11068625499732240.51028115
86192.3654834248544627.26763386356787----
87192.3890193544481227.281539012357072-0.33909037501088541.1756742
88192.3714768919004127.290437791311586-0.35825118184801050.46082795
89192.3658366137989627.292761115841970.88719317508451310.33716863
90192.3331998573957327.2714752996948850.420496540555120760.85069126
91192.334170735476927.28911969385810.228925651634077520.23437227
92192.3502599549101727.284034457703770.54626585569358180.19812028
93192.3597300063060227.3042211025199140.5013259342354050.04313093
94192.3968107219161327.284071196003-0.46508057613082270.7086895
95192.404945310522527.29385450944681.31283572641973880.24840128
96192.3834618617681527.2983885457330761.33072707816101480.48822427
97192.3926549329269227.3197845435302331.68036853410214170.9557062
98192.3859160456625827.3276846014539851.10718545228327910.13380633
99192.4007078039190327.342738228362258.6302281548915140.6376197
100192.389165189295127.3505730270061170.293872591836903560.3674331
101192.3880647707758327.356171006521492----
102192.4834669910388227.300701558395463-1.87427112615215591.1815611
103192.4973393252597327.301292088871431.63078341614828970.5568462
104192.5049912395817827.303421151706080.91731704723621640.0662718
105192.5128004910675727.3277626143683040.65073642006683170.40799654
106192.4949041416247227.319163475397632.08974147397185250.23647495
107192.508913295396427.3283602769589251.87288455576355450.0344368
108192.481079832242827.3295192856524742.67793953502287430.024297062
109192.5172424314124827.341718737879784.2196490672739950.4853872
110192.5383042564966227.352133809461012----
111192.5611584939065327.361880291727587----
112192.554035951418527.362214697812245----
113192.5351251364509227.39195478155372-0.18170976459315610.35625455
114192.420541296604227.353803569619487----
115192.40079485621827.361876316369981.40378117586425550.109749734
116192.414879690076327.372737146129936----
117192.4392819165732627.37981556726668----
118192.44107911135327.369078477848923----
119192.430447974055127.394980878563512----
120192.480476395197327.3718423574906140.1381349624685020.13172804
121192.4811200409545527.39421704043421-0.03291394378980360.27559903
122192.475490724860427.394566408829508----
123192.4591801718517327.40380616943294-1.67651465841511781.3984381
124192.4549331683474827.4208892406007581.96903844990078310.27537134
125192.4522129895622727.4130965755507352.5842373681834040.069471344
126192.479210266660527.4116349994456632.1627268447629010.16221452
127192.4147906931487727.407788594288736----
128192.3903415238327.3646656910939220.72671577100379940.727887
129192.383434139227827.3631489179901952.12725250450816230.04218704
130192.3971701990981827.377695921229627-0.64274386243789880.5847021
131192.3971588338900727.376942931670560.208932731627863520.71648717
132192.399693597719927.3947613252905951.30925012767368480.018128952
133192.4281354635163327.400907128089838-2.17192745208983951.595387
134192.4175516560322627.40831281361949----
135192.4027815667613827.3971504019413460.37405656170408110.07751725
136192.4114869734042727.40408941655044----
137192.4436522253433827.4153918171996050.78599649983004780.07236411
138192.4367297006458827.420792032762560.316938175867402140.10234196
139192.4401890934913427.4337129705107260.79556187999167980.16861713
140192.4362085530519827.444209457132196----
141192.4540543228696427.44657067965370.213131287154561060.7150383
142192.4604769387154627.451876004511250.67641568365246020.13622285
143192.4375056415768827.45022473196844-0.205483732783736270.2255534
144192.4368267977302227.4524408588319840.431651415866333431.6477929
145192.4493657241128527.468293553724230.3528891322681920.12054172
146192.4552382067628927.46964798907312-0.382784441553714050.6375971
147192.6599056226463327.292751781802133.3177986878304030.062192056
148192.663038125669927.302869543929994----
149192.6455801984479627.29843707101804-0.66126506567464061.3037262
150192.6449554152764627.2909802820828171.42631328185512070.39383548
151192.6508254800091627.31207174885947-0.28212551023891350.56158763
152192.6769923389484827.307405079357572.385754755836880.91924626
153192.6917873121769327.3234685465898----
154192.6832838655958327.3261998943842630.225951276685122130.4786978
155192.6625146183138227.322454087102702-0.350270029755481550.9925099
156192.6635138164916227.3226682368503871.28305144555520250.04008015
157192.6382973931128227.320387871536557-0.83329170598688230.76168054
158192.6352739276699427.337411670482170.491023915289662940.57090235
159192.6508921868181727.337611808278332.1038256768046850.16563411
160192.6537737222384427.344536955268950.467330402158069760.3055561
161192.6524678135358227.3527774047211770.35086426052691321.7114662
162192.6599466716573727.348809409675464----
163192.7340885777911427.35459480540250.484048111404812850.33044717
164192.6480159864755427.425604622166812----
165192.70899590703327.3713952371541220.98366875295478740.21371199
166192.7182095679952527.3703058395246654.7056780530795110.08468468
167192.7005859506280427.3947827487967073.77650932925853941.2760242
168192.6053518886629727.3358776509613330.409279558314952050.20512794
169192.624530321874527.3441374173308350.88350148741127410.72125506
170192.620932522878327.3588244941870082.46116638400667350.068524174
171192.606269532871427.380732369086413----
172192.602418132055627.3809610958350334.7404828443057550.019668732
173192.6364515492403527.385634760532202-0.70903171279834950.27930143
174192.654868866647227.3923419822158820.99693290478884010.46159172
175192.6768108146490327.411229527794013.3715857630199991.7250566
176192.636463864317827.39430595944603----
177192.6361766891440427.39421626982631-0.50781681530627130.28716832
178192.6468336687928227.405927845432650.4317435437114541.013857
179192.6196749137037627.4078660775890550.58734629207138570.14637884
180192.6400140279440327.417895401180818----
181192.6347703264442327.407409054952595----
182192.656319996027927.424788380980704----
183192.647802868674227.425558020532318-1.15608713957401580.5013985
184192.7582899151527427.380431121534751.6645280884880051.119963
185192.758480252016527.3801456689259841.61514663965586941.2562157
186192.757822644561427.38454851853389----
187192.7430191223289527.3979949039757-0.2599785517277710.21383522
188192.7736753374434527.40717009385885-1.9488883083546112.3007138
189192.7776042460831727.3988668661910671.0822255446969790.040191554
190192.778026157359327.3985355010803741.01517438831016580.04169303
191192.7496742877652627.40117135890243----
192192.766212609147427.4205864864446620.48810198210453110.06991914
193192.7122990878364427.39454489881983----
194192.7093191972547627.4134451879545970.69851111948237830.6929934
195192.7521722195049627.435941608646652.94173900524129640.6496761
196192.7938561911895227.424632047032554.366686119884472.1821046
197192.7972990726737827.426870154694036----
198192.8122354530952427.43238661485408----
199192.769584175371627.430644346951143.3455132888008730.018217271
200192.7729346547917327.4530134125293732.4919794863782230.12652099
201192.7513387845434427.443363706290380.2127450453586160.36891094
202192.7465772479512827.4461613857757420.57099276097237520.043913808
203192.7661032750871527.456806356998417----
204192.8001691851143327.4747339089323472.13929270256789740.3493675
205192.6994355202954227.4091966866779120.93306820405733080.10652853
206192.6968746158554527.4212616227970081.5636208191150850.034941744
207192.697242988689827.4397194590719881.67804956940783350.8942365
208192.7306029671220227.4437894082644860.430279867239132030.08184681
209192.7111621550074627.4476555797009921.27373141680113040.89827096
210192.719084529682927.4497790248672653.48588183690861531.471572
211192.6764971360652527.43645995245119-0.38728602774514261.2101308
212192.6854760884387827.454606861997096-0.454663289161417960.6347142
213192.7050905059175227.480934376912110.66397717097297291.1822629
214192.7415087178777627.464442885768523-0.50596344516611350.68009734
215192.7350280498558327.4733817900013830.92662615630527290.056381434
216192.7710594724609327.4865005245697241.23949087182822031.1871048
217192.7639375294140827.4959465955584931.82259831236799871.2661413
218192.5664096527479227.43996952489847----
219192.72605901669627.4806234028199970.4606947010705690.6640772
220192.7418111354155627.4912894976717474.9266142380832390.108539596
221192.7125215021885727.4907209710697240.447495101829398560.07130212
222192.5673989641491327.3799992434642----
223192.5780092955582227.3826338506237550.6437901051741522.1581254
224192.5713595056275827.3854480597133331.60889415695824110.01590749
225192.554237175841327.377545757449631.49832965108225861.00458
226192.562770972316327.399055402840172-0.49306992495336750.16989784
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1046192.5692514643318727.149233750870373----
1047192.6023830328994427.1534138630774430.88075359403456680.31041935
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1054192.6406882523586127.134633886950454----
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1080192.638817590201427.200972853723723----
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1086192.6573345938826427.2292782406043051.71433757116565480.7581975
1087192.6543164815458627.22101760536722----
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1095193.1885462947686826.774931842012382----
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1100193.2726362537447626.80988731828042----
1101193.2816493320255526.823038513664540.38626923562229190.17401507
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1107193.2876343831649426.835288781844028----
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1113193.2764830627559126.858515541910194----
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1123193.1563321919172226.812153436874734----
1124193.18985887018626.8357879317594731.57683990728752140.31436592
1125193.195349442075326.835441854139933----
1126193.1705664604055526.842189750098683-1.18374870128173121.2238967
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1136193.125613855731926.873608952767597----
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1138193.1364844764166326.885107431474825----
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1140193.162716041186526.881394052276760.84991516178539730.060146958
1141193.1832255445770826.896784770117527----
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1145193.1619775803644626.89915701241425----
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1157193.2462224224959826.899602244531714----
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1290193.375440635408727.0392462063708621.25260916599620620.082091525
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2050192.343716413859227.15999098954011-0.06474540537944060.21915136
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\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#display the results\n", "print('parallax of row 100: {:.3f}'.format(tab['parallax'][100]))\n", "tab.show_in_notebook(display_length=10)\n", "\n", "#if you prefer to convert to pandas, use the following\n", "#ptab = tab.to_pandas()\n", "#print(ptab['parallax'][100])\n", "#print(ptab)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the output of the query, what is the least and most distant star?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Does anthing seem unexpected?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Response:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How would you present the distribution of distances graphically? Are there any choices to be made?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What might you need to consider if you wanted to make a model of the density distribution?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Response:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.11" } }, "nbformat": 4, "nbformat_minor": 2 }