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Jupiter’s Moons and the Speed of Light

JUPITER’S MOONS AND THE

SPEED OF LIGHT

Student ManualA Manual to Accompany Software for the

Introductory Astronomy Lab Exercise

Document SM !" #irc$%ersion $&

Department of 'hysics

(ettysburg #ollege

(ettysburg) 'A *+,!

-elephone" .**/ ++*01&,2email" clea3gettysburg$edu

Database, Software, and Manuals prepared by:

Jan 'aul Dabrows4i) Marylhurst 5ni6ersity) (lenn Snyder and LaurenceMarschall . Project CLEA) (ettysburg #ollege/

#ontemporary Laboratory

Experiences in Astronomy

mailto:[email protected]:[email protected]:[email protected]


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Contents

Learning Goals.....................................................................................................................................................................

Proe!"ral O#$eti%es..........................................................................................................................................................

Use&"l Ter's.........................................................................................................................................................................

Intro!"tion( Historial )a*gro"n! o& t+e Roe'er E,-eri'ent...................................................................................

Starting t+e Progra'...........................................................................................................................................................

Aessing Hel- Files.............................................................................................................................................................

S"''ar o& t+e La# Ati%it..............................................................................................................................................

O%er%ie/ o& t+e O#ser%ing Proe!"re.............................................................................................................................

)e&ore o" )egin.................................................................................................................................................................

O#ser%ing Proe!"re000A 1or*e! E,a'-le....................................................................................................................

2o"r O#ser%ations an! Cal"lations................................................................................................................................

3"estions an! Dis"ssion...................................................................................................................................................

,


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Goals

7ou should be able to use the obser6ations of eclipses of Jupiter’s moon Io by

Jupiter’s shadow) ta4en at different points in Jupiter’s orbit) to determine thespeed of light$ 7ou should be able to understand how 8le 9oemer) in the *th

#entury) was able to notice that light did not tra6el through space instantaneously)

but had a finite speed$

O#$eti%es

I& o" learn to 44.

8bser6e Jupiter’s Moons as they orbit the planet$

9ecogni:e eclipses and record precise times for them$

'redict the timing of future eclipses of Io by Jupiter using the 4nown period of Io

around Jupiter and obser6ations of the time of one eclipse$

8bser6e eclipses of Jupiter’s moon Io) once when it is close to Earth) and once

when it is much further from Earth .when Jupiter is on the opposite side of

the Sun$

2o" s+o"l! #e a#le to 44.#ompute the time difference between an expected eclipse and your obser6ations$

Determine the speed of light due to the difference between the obser6ed andexpected time of eclipse$

USEFUL TERMS 2OU SHOULD RE5IE1 IN 2OUR TE6T)OO7 AND IN THIS

MANUAL Astronomical

Unit

Conjunction Eclipse Ephemeris Galilean

Satellites

Julian Day

Jupiter Latitude Longitude Opposition Orbit Percent

Dierence

Period o an

Orbit

Satellites Shado! Speed o light Uni"ersal #ime

+


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INTRODUCTIONOle Roe'er an! t+e First Meas"re'ent o& t+e S-ee! o& Lig+t

-he #LEA Moons of Jupiter simulation can be used to duplicate an experiment

performed three centuries ago to determine the speed of light$ In this acti6ity you will be

able to recreate that feat and find the speed of light$

Introduction

-he first accurate determination of the speed of light . c / was made in 1*1 by Danish

astronomer 8le 9oemer$ ;e did this using timings obtained by (io6anni #assini of theeclipses of Jupiter’s moons$


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Jupiter the Clock

(alileo disco6ered that Jupiter had four moons in 1&) which went around the planetwith remar4able regularity$ It didn’t ta4e long before astronomers had highly accurate

measurements of the orbital period of these satellites$ Io orbited in about $2 days$ Europa

too4 +$! days$ (anymede’s orbital period was @ust o6er * days$ And #allisto) the mostdistant of the (alilean moons) went around Jupiter in 1$* days$


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considered as an important way to tell time precisely) especially for na6igation at sea)

where a few miles could ma4e the difference between safe passage and shipwrec4$

Finding Latitude and Longitude: he need for accurate ti!ekeeping

-he main purpose of na6igation is to determine a ship’s position on the surface of the

earth so that the ship can get safely to its destination$ -he system of latitude and longitude

is used for this$

Latitude) the angular distance north or south of the euator) is easy to determine$ -he

angular altitude of the Corth #elestial 'ole .C#'/ is eual to a person’s latitude$ 'olarisis close to the C#' so for accuracy to a degree) 'olaris’ altitude gi6es the latitude$

De6ices li4e sextants and octants are used to determine the altitude of 'olaris$


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A sextant sighting of 'olaris shows that it is ?*° abo6e the hori:on) so your latitude is

?*° C$ As the sun pee4s abo6e the hori:on) you note the time on your watch" 2"&& am$

hen you left London you set your watch to the cloc4 at the (reenwich 8bser6atory and

you ha6en’t reset it$ -he watch shows the time in London$

9emember that this is the %ernal Euinox .March ,,/) which means the sun should ha6erisen 6ery close to 1"&& am$ But your watch shows 2"&& am$ -he two hour difference between the time the sun tells .local time 1 am/ and what your watch shows

.(reenwich Mean -ime 2 am/ represents your longitude$ A one hour difference would

indicate that you were !° est of the prime meridian$ -wo hours means you are +&°

est) and that is your longitude$

7our position is ?*° C latitude and +&° longitude$

If your watch 4ept time to within one second and you mar4ed the sun’s rising to within

one second) you would be within one mile of your true location in longitude$ ith a good

sextant that is s4illfully used and 4nowing how much 'olaris is shifted from the C#')your latitude position would similarly be about mile in error$

Looking to the hea"ens for clocks###and disco"ering the speed of light$

(alileo disco6ered Jupiter’s moons a century and a half before ;arrison’s in6ention of a

precise sea0going mechanical cloc4$ -he idea that Jupiter and its moons could be used asa cloc4 for marine na6igation) therefore) seemed most attracti6e) and (alileo not only

suggested this) but e6en designed a special telescope that made it easier to sight the

moons at sea$ But astronomers did not yet ha6e good enough ephemerides of Jupiter’s

moons to really ma4e the method wor4$

-he


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#assini had been timing the period of Io around Jupiter mar4ing each orbit by when the

moon left Jupiter’s shadow$ ;is data showed that when Jupiter and earth were close) theobser6ed times of Io’s eclipse agreed with those predicted by the ephemeris$ But when

Jupiter and earth were far apart) the obser6ed eclipse times occurred & to , minutes

later than predicted$

;e originally deduced that this was a result of light ta4ing a finite time to tra6el from

Jupiter to earth$ ;owe6er he changed his mind) belie6ing that light could not ha6e a finite

speed) and thought that something else was responsible for the errant timings$

9oemer) howe6er) agreed with #assini’s first interpretation of the data and used #assini’s

wor4 to determine the speed of light arri6ing at a 6alue that was about *&= of the 6alueof c that we accept today$


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Jupiter’s Moon Io and the Speed of Light

The Lab Activity

STARTING THE PROGRAM

-he Jupiter$s %oons and the Speed o Light program is a standard program under

MS0indows$ -o run it) clic4 on the #LEA icon labeled Jupiter %oons & Speed o Light on you des4top$ Select File Login from the menu bar) and type in your name when

as4ed$ If you then clic4 8>K) you will see the title screen for the Jupiter$s %oons and

the Speed o Light e'ercise) and will be able acti6ate the program from the menu barusing the File %un menu option$

ACCESSING HELP FILESBy selecting the &elp option from the menu bar) you can find general instructions

on using the Jupiter’s Moons program and its features$ -he help files are arranged bytopic) and can be accessed @ust by clic4ing on the desired topic$ -he ;elp menu item also

pro6ides access to the #LEA website and other websites of interest to users of the program$

SUMMARY OF THE LAB ACTIVITY

-he speed of light will be determined using a method de6eloped in the *th #entury by

8le 9oemer using data obtained by (io6anni #assini$

In this acti6ity) you will obser6e Jupiter

using the #LEA simulation Jupiter’sMoons and the Speed of LightK$ .See


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Distances between Jupiter and the earth are found by clic4ing 9ecordK on the bottom

right of the main window$

Alternati6ely) con@unction and opposition dates) as well as distances can be determined from

planetary data found at the 5$S$ Ca6al 8bser6atory .5SC8/ opocentric Configuration of

Ma'or Solar Syste! (odies(

http"aa$usno$na6y$mildatadocsssconf$php

In practice) dates about two months after con@unction and a month prior to opposition pro6ide obser6ing situations that allow Io’s eclipses to be seen more easily$

(io6anni #assini obser6ed the time when Io emerged from Jupiter’s shadow$ In thisacti6ity you will instead obser6e when Io enters the shadow$

OVERVIEW OF THE OBSERVING PROCEDURE

8n the far date) obser6e and time an eclipse of Io$ -hen use the synodic period of Io to predict an eclipse se6eral months later$ 8bser6e and time the predicted eclipse andcompare the predicted time to the obser6ed time$

Since the light from Io ta4es more time to tra6el the distance between Jupiter and earthwhen they are far) and less when they are near) the difference in time . ΔT/ between

predicted and obser6ed time corresponds to the time light had to tra6el the difference in

distance . ΔD/$

>nowing the difference in distances between Jupiter and earth on the two dates and the

difference in time permits a straightforward calculation of the speed of light"

Speed of Light c ΔD ΔT

&

http://aa.usno.navy.mil/data/docs/ssconf.phphttp://aa.usno.navy.mil/data/docs/ssconf.php


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BEFORE YOU BEGIN

◊ Bec!"e #a"i$ia% &ith the CLEA 'i"($ati!)*

Y!( 'h!($+ be ab$e t!,

• Set !ates an! ti'es( Select the File )bser"ation Date Set Date*i!e+

option from the menu bar$

• C+ange t+e %ie/ 'agni&iation( #lic4 the buttons at the bottom of the 6iew

screen to choose &&) ,&&) +&& or ?&& times magnification$


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• Deter'ine /+en on$"ntion an! o--osition o"r( Select File )bser"ation

Date Jupiter 1heno!ena from the Menu Bar$ 7ou will see a window as in


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Jupiter’s Moons and the Speed of Light ?


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PART 0 1 OBSERVING PROCEDURE 1 A WOR2ED E3AMPLE

-he following is an example that determines the speed of light from Jupiter’s satellite Io$or4 this example through using the program before trying your own determination on

another set of dates$

0* Fi)+ t&! +ate' &he) -(4ite% a)+ ea%th a%e #a% a)+ )ea%5 preferably about two tothree months after Jupiter is in con@unction and a about month before Jupiter is at

opposition -hese conditions ensure that Jupiter’s shadow is to the east of the planet so that

eclipses are easily seen.

The Fa% Date a)+ Nea% Date #!% thi' e6a"4$e a%e,

Far Date = March 1, 200 !three "onths after con#unction $%ear Date = Ma& '1, 200 !a(out a "onth (efore opposition$

8n these dates the orbital geometry allows Jupiter to be easily obser6ed from earth$ In

March) the local time for obser6ing Jupiter would be a few hours before dawn$ In Mayobser6ing would be around midnight$

O%er%ie/ o& t+e Te+ni one /+en t+e -lanets are

&ar &ro' ea+ ot+er> an! t+e ot+er /+en t+e are ne,t near000t+e

&ar !ate /ill #e near on$"ntion> an! t+e near !ate a#o"t a'ont+ #e&ore t+e ne-t opposition.

Ste- ?( O#ser%e an! ti'e an eli-se o& Io lose to t+e far !ate. Sine

eli-ses o"r e%er o"-le o& !as 8ro"g+l;> o" $"st /at+

8a!%aning t+e ti'e slo/l;> "ntil Io !isa--ears. Reor! t+e ti'e.

Ste-s @0:( Pre!it t+e -reise ti'e an eli-se o& Io lose to t+e near !ate

#ase! on t+e -erio! o& Io.

Ste- ( O#ser%e an! ti'e t+e eli-se o& Io. It’s i'-ortant to start

o#ser%ing a &e/ +o"rs #e&ore t+e -re!ite! ti'e> so as not to 'iss

t+e e,at ti'e o& t+e eli-se.

Ste-s B0( Cal"late t+e !i&&erene #et/een t+e -re!ite! an! o#ser%e!

ti'e o& t+e near eli-se> an! t+e !i&&erene in !istane #et/eenEart+ an! J"-iter at t+e ti'es o& t+e t/o eli-ses.

Ste-s 0=9( Cal"late t+e s-ee! o& lig+t 8t+e ti'e !i&&erene !i%i!e! #

t+e !i&&erene in !istane; an! o'-are t+is /it+ t+e ae-te!

%al"e o& t+e s-ee! o& lig+t.

!

I"4!%ta)t N!te,7ou may obtain data from the simulation that are close to but not exactly the same as what

appears in the example$ Differences of a few seconds to a minute are to be expected$ -hisis due to the simulation and not necessarily a reflection of your obser6ing techniue$


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In addition) these dates put Jupiter’s shadow on the east side of the planet so that it is

possible to obser6e moons mo6ing into the shadow$

-he relati6e positions of Jupiter) earth and the Sun for these two dates are shown in the

diagram in


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-ime of the


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safe side, let4s start our obser"ations 607 JD, or 809 hours, before the predicted

eclipse ti!e0 In other words, since the predicted eclipse ti!e is Julian Day

899;7


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0*C!"4a%e y!(% va$(e t! c


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PART 7 1 YOUR OBSERVATIONS AND CALCULATIONS

F!% each va$(e y!( #i)+ !% ca$c($ate "a9e '(%e y!( 'h!& the ()it'

1- Fi)+ t&! +ate' &he) -(4ite% a)+ ea%th a%e #a% a)+ )ea%5 prefera(*& a(out a "onth (eforeJupiter is at opposition and a(out t4o to three "onths after Jupiter is in con#unction Theseconditions ensure that Jupiter’s shado4 is to the east of the p*anet so that ec*ipses are easi*& seen-


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/- Fi)+ the +i##e%e)ce bet&ee) the ti"e' !# the 4%e+icte+ ec$i4'e a)+ the !b'e%ve+ ec$i4'e

-ime Difference .T/ QQQQQQQQQQQQQQQQ

- Fi)+ the cha)@e i) +i'ta)ce bet&ee) -(4ite% a)+ ea%th #%!" the Fa% Date t!the Nea% Date

#hange in Distance .D/ QQQQQQQQQQQQQQQQ

- Ca$c($ate the S4ee+ !# Li@ht

Speed of Light QQQQQQQQQQQQQQQQ

#on6ert this 6alue in au minute to the more familiar meters second

Speed of Light QQQQQQQQQQQQQQQQ

10- C!"4a%e y!(% va$(e t! c

'ercent Difference QQQQQQQQQQQQQQQQ

UESTIONS AND DISCUSSION

In this acti6ity you set the 8bser6ation Inter6al to &$&&! hours .2 seconds/$ -his

represents how accurate your cloc4K was it 4ept time to about ,& seconds o6er three or four months$

&ow would your prediction and e"entual deter!ination of the speed of light ha"e

changed if your clock was accurate to se"eral !inutes instead of 86 seconds?

Similarly the 6alues of the distances between Jupiter and earth were gi6en by thesimulation to fi6e decimals places of one astronomical unit$ In other words) the distances

were 4nown to within F+& miles or !&& 4m$

&ow would your deter!ination of the speed of light ha"e been affected if the distances

were known to only a half astrono!ical unit?

,


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Este software de #LEA de las lunas de JRpiter es una simulacin del experiemento

reali:ado + centenares atras para determiner la 6elocidad de la lu:$

- En el vacio

comunicaciones entre elControl Terrestre de Houston y Neil Armstrong, cuando esteseconvirtió en el primer hombre que puso un pie sobre laLuna: después de cada pregunta,

Houston tenía que esperar cerca de 3 s para el regreso de una respuesta aun cuando los

astronautas respondían inmediatamente.

- Velocidad orbital de Jupiter es de 13,0697 km/s principalmente compuesto hidrogeno

Programa Pioneer (1973 y 1974)

Pioneer 10 fue la primera sonda espacial en explorar júpiter, que lo hizo en diciembre de

1973, seguida por laPioneer 11 trece meses después. ; observó su atmósfera y cinturones

de radiación, detectó su campo magnético.

Las misionesVoyager mejoraron la comprensión de los satélites galileanos y contribuyeron

en el descubrimiento de losAnillos de Júpiter, tomaron las primeras imágenes de su

atmósfera y revelaron que la Gran Mancha Roja es unanticiclón

ULYSSES

Galileo(1995-2003) quien hizo 35 orbitas y fue destruida haciendolo entrar a la atmosfera

NEW HORIZONS EL ULTIMO EN EL 2007

- Ío[editar]

Artículo principal: Ío (satélite)

Es el satélite galileano más cercano a Júpiter. Las fuerzas de marea provocadas por la

fuerte atracción gravitatoria de Júpiter son tan marcadas que provocan un vulcanismo muy

activo, cuya consecuencia es la ausencia total de cráteres de impacto. Su superficie está

cubierta deazufre.

Europa[editar]

Artículo principal: Europa (satélite)

Es el más pequeño de los satélites galileanos, sin embargo quizás sea el más interesante.

Está cubierto por una capa dehielo, y tiene muy pocoscráteres, lo que indica una superficie

relativamente joven. Se piensa (y existen bastantes evidencias a favor) que debajo de la

"cáscara" de hielo sólido de su superficie debe existir un océano de agua líquida. Las

,,

https://es.wikipedia.org/w/index.php?title=Control_Terrestre&action=edit&redlink=1https://es.wikipedia.org/wiki/Houstonhttps://es.wikipedia.org/wiki/Houstonhttps://es.wikipedia.org/wiki/Neil_Armstronghttps://es.wikipedia.org/wiki/Neil_Armstronghttps://es.wikipedia.org/wiki/Apollo_XIhttps://es.wikipedia.org/wiki/Lunahttps://es.wikipedia.org/wiki/Lunahttps://es.wikipedia.org/wiki/Anillos_de_J%C3%BApiterhttps://es.wikipedia.org/wiki/Anticicl%C3%B3nhttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=2https://es.wikipedia.org/wiki/%C3%8Do_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Azufrehttps://es.wikipedia.org/wiki/Azufrehttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=3https://es.wikipedia.org/wiki/Europa_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Hielohttps://es.wikipedia.org/wiki/Hielohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/w/index.php?title=Control_Terrestre&action=edit&redlink=1https://es.wikipedia.org/wiki/Houstonhttps://es.wikipedia.org/wiki/Neil_Armstronghttps://es.wikipedia.org/wiki/Apollo_XIhttps://es.wikipedia.org/wiki/Lunahttps://es.wikipedia.org/wiki/Anillos_de_J%C3%BApiterhttps://es.wikipedia.org/wiki/Anticicl%C3%B3nhttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=2https://es.wikipedia.org/wiki/%C3%8Do_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Azufrehttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=3https://es.wikipedia.org/wiki/Europa_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Hielohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impacto


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estimaciones del grosor de la cáscara de hielo van desde 10 a 100km. Además, se cree

que en esta luna, hay existencia de oxígeno.

Ganímedes[editar]

Artículo principal: Ganímedes (satélite)

No sólo es el satélite más grande de Júpiter, sino también el más grande delSistema Solar.

En marzo de 2015 se confirmó que Ganímedes tiene un océano escondido debajo de su

superficie, cubierta de hielos. Este océano tiene una profundidad de unos 100 kilómetros, 10

veces más que los mares de la Tierra."Es un paso más hacia el descubrimiento de un

ambiente habitable".

Ganímedes está compuesto de silicato y hielo, con una corteza de hielos que flota encima

de un fangoso manto.

Calisto[editar]

Artículo principal: Calisto (satélite)

Es el satélite galileano más lejano de Júpiter, y es también el que tiene la superficie más

vieja, ya que está saturada decráteres.

Este ejercicio recrea fielmente la experiencia de Roemer para medir la velocidad de la luz. Teniendo la posibilidad deobservar el Sistema Joviano en cualquier momento, es posible encontrar la ocurrencia exacta de eclipses de Io estandocerca y lejos de la Tierra. ara este !ltimo caso, la diferencia entre el momento en que el eclipse realmente se ve y cuandose deber"a #aber visto, responde al tiempo que demora la luz en viajar una distancia extra.

,+
https://es.wikipedia.org/wiki/Kil%C3%B3metrohttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=4https://es.wikipedia.org/wiki/Gan%C3%ADmedes_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Sistema_Solarhttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=5https://es.wikipedia.org/wiki/Calisto_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impactohttps://es.wikipedia.org/wiki/Kil%C3%B3metrohttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=4https://es.wikipedia.org/wiki/Gan%C3%ADmedes_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Sistema_Solarhttps://es.wikipedia.org/w/index.php?title=Sat%C3%A9lite_galileano&action=edit&section=5https://es.wikipedia.org/wiki/Calisto_(sat%C3%A9lite)https://es.wikipedia.org/wiki/Cr%C3%A1ter_de_impacto

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