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Physics 312 Introduction to Astrophysics Lecture 14 James Buckley [email protected] Lecture 14: Extrasolar Planets Kepler Circular acceleration (wikipedia!) • 1.4m mirror, 95 Mpixel camera Named after Johannes Kepler, launched March 7 2009. Monitors brightnes of 145,000 • As of January 2015, Kepler has found >1000 (confirmed) exoplanets and more stars. than 400 stellar systems. ∆⃗v ⃗a = • ∆tEarth-sized planets in the Based on Kepler data could be as many as 40 billion habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy. The nearest such planet could be 12 light years away! Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Results ofacceleration Extrasolar Planet Searches Circular • ⃗a = ∆⃗v ∆t • (Almost) habitable exoplanets Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Potentially Habitable Planets Circular acceleration • ⃗a = ∆⃗v ∆t • Update - habitable planets! Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Brightness, B (W/m2) Transits acceleration Circular • ⃗a = ∆⃗v ∆t f ⇥B B Time, t (days) Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Transits acceleration Circular Fraction of light blocked by planet = cross sectional area of planet cross sectional area of star f= R⇤ ⇡Rp2 ⇡R⇤2 For a jupiter sized planet passing in front of a sun-sized star: R⇤ ⇡ 10 ⇥ Rp • R p ⃗a = ∆⃗vf ∆t ⇡ 1 = 1% 100 Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Kepler Data Circular acceleration • ⃗a = ∆⃗v ∆t Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Brightness, B (W/m2) Transit time jitter Circular acceleration • ⃗a = ∆⃗v ∆t Jitter in transit time indicates gravitational effect of other planets Time, t (days) Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Orbital Velocity and Doppler Shift Circular acceleration • We’d like to get the planet’s velocity from the Doppler shift, but it is important to note that the star is MUCH brighter than the planet; we can only measure the Doppler shift of the star light not the planet light. How do we relate the velocity of the planet (that we get from Kepler’s law) to the velocity of the star? vp • Since momentum is conserved throughout the orbit, the star and planet must always have equal and opposite momenta mp r ⃗a = ∆⃗v mp vp = ms vs ∆t vs ms Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Doppler Shift Circular acceleration • ⃗a = = ∆⃗ vv ∆t c As an example, let’s calculate the redshift of a Jupiter mass planet in a mercury like orbit around a star with the same mass as our sun Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Putting it all together Circularm acceleration p If the mass of the planet is comparable to the mass of the star, we need to use a slightly modified version of Kepler’s third law vp a P2 = r 4⇡ 2 a3 G(mp + ms ) But for many cases, the mass of the star is much larger than that of the planet and we can use the approximation vs ms • ∆⃗v ms mp ✓ 2 ◆ 4⇡ 2 P ⇡ a3 Gms We can measure the period (transits or Doppler ⃗ shifts) a = and can determine the mass of the star from its spectral properties. This gives the orbital radius a, ∆t which can be used to dermine the velocity vp ⇡ distance circumference 2⇡a = = time period P mp vp = ms vs And if we also have a Doppler shift measurement of the star’s velocity, we can determine the mass of the planet and, with the transit data giving radius, determine density - terrestrial vs. Jovian Physics 125, J. Buckley Physics 312 - Lecture 1 = 4⇡ d2 No-Greenhouse Temperature Circular acceleration Incident Flux, F = L/A = L 4⇡d2 A re a, A Absorptivity averaged over solar spectrum: R ↵⌫ F⌫ d⌫ ↵visible = R F⌫ d⌫ L albedo ⌘ reflectivity of visible light Z avis = exp ↵vis ds d Absorbed Flux, Fabs = Pabs = Fabs · ⇡R2 = • ⃗a = ∆⃗v Emitted Power Pem = ( ∆t ✓ L ⇡ ◆1/4 (1 a) d2 1/4 L(1 avis ) 4⇡d2 L(1 avis )R2 4d2 T 4 ) · 4⇡R2 avis )R2 = 4⇡ T 4 R2 4d2 1/4 (1 a) For our sun : T = 280 K d2 In equilibrium Pabs = Pem 1 T = 2 – p. 25/27 L(1 Physics 312, J. Buckley Physics 312 - Lecture 1 – p. 25/27 How good is the approximation? Circular acceleration • Earth: - Earth’s albedo (optical reflectivity) is a=0.3 - Earth is at a distance of 1 a.u= 1.5 x 1011 m - No-greenhouse temperature is T=256K. Actually, the average temperature of the Earth’s surface is 288K, so there is some greenhouse effect • Venus: - •Venus’ albedo a=0.8 (less visible light is absorbed) ∆⃗v ∆t ⃗a the = Earth). - d=0.723 a.u (not too different from - No Greenhouse temperature is T=220K, but the temperature of Venus is 730K!!! More greenhouse gases! - Early on, water was vaporized - runaway greenhouse effect more CO2 released from rocks, high density CO2 atmosphere Physics 312, J. Buckley Physics 312 - Lecture 1 – p. 25/27 The Greenhouse Effect Circular acceleration • ⃗a = ∆⃗v ∆t Source: OSTP Physics 312, J. Buckley Physics 312 - Lecture 1 – p. 25/27 ses interact Greenhouse gases? Circular acceleration • A greenhouse gas is defined as a gas that efficiently absorbs (and re- emits) Why IR radiation. do certain gases interact Molecules with more than two with radiation? Molecules more twomuch lessatoms a gas can than absorb efficiently • Suchwith tend at tooptical absorbwavelengths, radiation more radiation impinges on a atomswithout tend toWhen absorb radiation more violating Kirchoff’s laweffectively since this only demands of than diatomicequality molecules molecule, it can excite the molecule, effectively than diatomic molecules absorption and emission at a given wavelength. such as N2 and O2. This is because such as N2 and O2. by This is because either vibrating (vibrational of the net balance of their electron of the net balance of their electron(rotational energy) or rotating What makes a greenhouse gas aconfiguration. good IR absober? Typicallydiatomic these are • configuration.energy) That is it. whyMolecules diatomic of a particular That is whyCH molecules withare vibrational and rotational energy levels that are 4separated nitrogen and nitrogen and oxygen not CH4 oxygen are not kind of gas have a different shape by energies wavelengths gases. - need a dipole moment so greenhouse gases.corresponding to IRgreenhouse frommolecules molecules of another type of • symmetric are not as good. gas, and so are excited by radiation ∆⃗v ⃗a2 = in different ways. N2, O N2, O2 H2O H2O ∆t nges on a ite the molecule, vibrational rotational es of a particular different shape nother type of ited by radiation CO2 CH CH 4 4 CO2 CO2 N2, O2 H 2O CO Physics 312, J. Buckley 2 Physics 312 - Lecture 1 – p. 25/27 Solar Constant Circular acceleration H2O • L⊙ = 3.826 × 1033 erg s−1 • Earth is at a distance d = 1 AU = 1.496 × 1013 cm • Radiant flux incident on earth is F = L⊙ = 1.360 × 106 erg s−1 cm−2 2 4πd • Converting to more familiar units: • F ∆⃗v−2 = 1.360 × 106 erg⃗as−1 = cm × ∆t = 1.36 kW m -2 −1 ! 100 cm 1m "2 × 1 joule 107 erg Physics 125, J. Buckley PhysicsPhysics 312 - Lecture 1 – p.525/27 312 - Lecture – p.12/16 CH4 The Magnitude Scale Circular acceleration M=1 M=2 M=3 M=4 M=5 M=6 • Hipparchus (followed by Ptolemy) created a catalog of about 1000 stars that were grouped into six Magnitude groups. Ptolemy called the brightest stars first magnitude or M = 1, the second • brightest stars second magnitude M = 2 and so on. ∆⃗v • In the early 19th century, William Herschel devised a method to ⃗a = ∆t make quantitative measurements of magnitude. Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Physics 312 - Lecture 5 – p.3/16 Friedrich Wilhelm Herschel Friedrich Wilhelm Herschel Circular acceleration • Born in•Hanover Germany, 1738.Germany Unsuited for Army life, 15, left Germany Born in Hanover, November 1738 for England in 1757 and took up music then transitioned to astronomy. • Built a 48” reflector telescope with a 4000 pound grant from King George III. Eventually, used a•20” refractorteacher, (picturedcomposer, above) for many of his observations. • Music bandmaster • Discovered Uranus, moons reflector of planets, telescope binary⃗ and orbits. nebulae (his son • Built astars = with 48-inch 4000Catalogued pound grant from ∆t continued work in the southern hemisphere). Believed nebulae were clusters of stars he called King George ``island nebulae’’ - close toIII the modern concept of galaxies. • 20-foot refractor (above) forWilliam, most observations Sister, Caroline Lucretia Herschel workedused with Sir discovered a number of comets, was inducted into the Royal Astronomical Society, and was awarded thePhysics Prussian Gold of 312 - Lecture 5 – Medal p.5/16 Science shortly before her death at 97. Physics 312, J. Buckley • Unsuited for army life, left Germany for England in 1757 ∆⃗v • Physics 312 - Lecture 1 – p. 25/27 Herschel’s Method Circular acceleration Star 1 To find the relative brightness of a bright star (star 1) to a dim star (star 2), you can stop down the aperture of one telescope until the two stars appear to be equally bright. Star 2 Stars appear equally bright if F 1 · A1 = F 2 · A2 A2 A1 F1 A2 = F2 A1 • ∆⃗v ∆t was able to determine that Herschel ⃗a = two stars di↵ering in magnitude m = 1 had relative brightness of F1 /F2 = 2.5 Physics 312, J. Buckley Physics 312 - Lecture 1 – p. 25/27 Magnitude Scale Circular acceleration • In modern times, we define magnitude so that a difference of 5 magnitudes corresponds exactly to a factor of 100 in brightness • i.e., a difference in magnitude of ∆m = 1 corresponds to 1001/5 = 2.512 • Or we can write: F2 = 100(m1 −m2 )/5 = 2.512m1 −m2 F1 • ⃗a = ∆⃗v ∆t Physics 125, J. Buckley Physics 312 - Lecture 5 – p.7/16 Physics 312 - Lecture 1 – p. 25/27 Absolute magnitude Circular acceleration F10 F (1/10pc)2 = 1/d2 ! "2 d = 10 pc 100(m−M )/5 = d = 10(m−M +5)/5 pc • m−M ∆⃗v =⃗a =5 log ∆t 10 ! d 1pc " −5 Physics 125, J. Buckley 312 - Lecture PhysicsPhysics 312 - Lecture 1 – p. 525/27– p.8/16 Absolute magnitude of the Sun Circular acceleration • The apparent magnitude of the sun is msun = −26.81 and is at a distance of d = 1 AU = 4.848 × 10−6 pc • Calculate the absolute magnitude of the sun: Msun = msun − 5 log10 (4.848 × 10−6 ) + 5 = 4.76 • ⃗a = ∆⃗v ∆t Physics 125, J. Buckley 312 - 1Lecture 5 – p.9/16 Physics Physics 312 - Lecture – p. 25/27 1.2 Host star Radius (r) 0.52 −0.04 R 1.3 Orbit Temperature (T) 3748 (± 112) K 2 Habitability Metallicity +0.06 [Fe/H] 0.16 (± 0.14) +0.8 Age 3 Discovery and follow-up studies 4.4 −0.7[3] Gyr Physical characteristics 4 See also Mass (m) 1.3 −0.7 M⊕ 5 References Radius (r) 1.12 (± 0.16) R⊕ +2.6 6 External links Stellar flux Kepler-438b - Wikipedia 18h Coordinates: Kepler-438b 46m 35.000s, +41° 57ʹ 03.93ʺ (F⊙) +0.67 1.40 −0.77 ⊕ From Wikipedia, the free encyclopedia Kepler-438b (also known by its Kepler Object of Interest designation KOI-3284.01) is a confirmed near-Earth-sized exoplanet, likely rocky, orbiting on the inner edge of the habitable zone of the red dwarf as it receives 1.4 times our Kepler-438b[1][2][3] Exoplanet List of exoplanets or nearly 4.5 × 1015 km) from Earth in the constellation Lyra.[1][2] The planet was discovered by NASA's Kepler spacecraft using the transit method, in which the dimming effect that a planet causes as it crosses in front of its star is measured. NASA announced the confirmation of the exoplanet on 6 January 2015.[1] Although it is not habitable, as of June 2015, it has the highest index on the Earth Similarity Index, with a rating of 0.88.[6] Kepler-438b is approximately 470 light years from Earth, so travelling there is presently impossible within a human lifetime. The German-designed Helios probes, notable for having set the current speed record among spacecraft at 252,792 km/h, would take some two million years to travel to Kepler-438b.[7] (mV) 14.467 Mass 1.2 Host star 1.3 Orbit +0.06 0.544 −0.04 M Radius (r) 0.52 −0.04 R Temperature (T) 3748 (± 112) K +0.06 [Fe/H] 0.16 (± 0.14) +0.8 4.4 −0.7[3] Gyr Physical characteristics Mass (m) Radius (r) Stellar flux (T) 1.12 (± 0.16) R⊕ 276 K (3 °C; 37 °F) Mass, radius and temperature Semi-major axis (a) 0.16600 AU Kepler-438b is an Earth-sized planet, an exoplanet that has a mass and radius close to that of Earth. It has a radius of 1.12 R⊕, and a mass of 1.3 M⊕. It has an equilibrium temperature Kepler-442b - Wikipedia of 276 K (3 °C; 37 °F), close to that of Earth. Eccentricity (e) +0.01 0.03 −0.03[3] Orbital (P) 35.23319 d physics and chemistry, with 1.00studies being the most similar, Distance ly ww.openexoplanetca 1120 Kepler-438+b) 3 Discovery and follow-up Kepler-438b has an index of 0.88, the highest known to date, talogue.com) (342[3] pc) making currently the most Earth-like planet in terms of 4 Seeitalso 6 External links old,[3] 200 or million than (342only parsecs, nearlyyears 1.0553younger × 1016 km) Sun.[8] [1][7] The planet andinthe has a surface of Earth theSun constellation Lyra.temperature the from 5778 was K.[9]discovered by NASA's Kepler spacecraft using the transit method, in which the dimming effect that a planet causes as crosses in frontmagnitude, of its star is or measured. NASA announced The itstar's apparent how bright it appears from [7] the perspective, confirmation of exoplanet on 6 January 2015. Earth's is the 14.467. Therefore, it is too dim to be seen with the naked eye. Contents Orbit Characteristics Kepler-442b is a super-Earth, an exoplanet with a mass and radius bigger than that of Earth, but smaller than that of the ice giants Uranus and Neptune. It has an equilibrium m 27.98s, +39° 16ʹ 48.30ʺ (i) 19h 0189.860° Discovery information The planet orbits a (M-type) red dwarf star named Kepler[1][2][7] known its Kepler Object of 438.Kepler-442b The star has a mass(also of 0.54 M by and a radius of 0.52 Interest designation KOI-4742.01) is a confirmed near-EarthR , sized both exoplanet, lower thanlikely thoserocky, of the Sun bywithin almost It has a orbiting thehalf. habitable surface 3748 K and isstar estimated to be about about [8] Kepler-442, zonetemperature of the K-typeofmain-sequence 2015[4] temperature of 233 K (−40 °C; −40 °F).[5] It has a radius of 1.34 R⊕. Because of its radius, it is likely to be a rocky planet with a solid surface. The mass of the exoplanet is Transit List of exoplanets Discovery status star.[10] KOI-3284.01; Kepler-438 b; KOI-3284 b; 1.2 Host star 1.3 Orbit Habitability Host star has a mass of 0.61 M and a radius of 0.60 R . It has a temperature of 4402 K and is around 2.9 billion years old, with some uncertainty. In comparison, the Sun is 4.6 billion somewhat metal-poor, with a metallicity (Fe/H) of −0.37, or Database references 42% of the solar amount.[2] Its luminosity (L ) is 11% that Extrasolar Planets data of(http://exoplanet.eu/plan of the Sun. Approximate size comparison a hypothetical Encyclopaedia et.php?p1=Kepler-438&p2=b superhabitable planet with Earth. The star's apparent magnitude, or how bright it appears from ) Parent star Habitability The planet 2was announced as orbiting within the habitable zone of Kepler-438, a region where liquid 3 Discovery and follow-up studieswater could exist on the surface of the planet. In the Earth Similarity Index (ESI), which measures 4 See also how similar are planets to Earth as to physics and chemistry, with 1.00 being the most similar, 5 References Kepler-438b has an index of 0.88, the highest known to date, making it currently the most Earth-like planet in terms of 6 External links radius and stellar flux.[1][2] However it has been found that Apparent https://en.wikipedia.org/wiki/Kepler-438b Mass, radius and temperature pac.caltech.edu/cgi-bin/Displ 112.3 days and an orbital radius of about 0.4 times that of (δ) +39° 16ʹ 48.30ʺ ayOverview/nph-DisplayOve Earth's (a little larger than the distance of Mercury from the (mV) 14.976[2] rview?objname=Kepler-438+ Sun, which is about 0.38 AU).[1][7] It receives about 70% of b) the sunlight that Earth receives from the Sun. magnitude Distance 1120 ly Open Exoplanet (342[3] data )(http://www.openexopla pc Catalogue (http://w netcatalogue.com/search/?id= Spectral type K?V[4] ww.openexoplanetca Kepler-438+b) Mass The planet was announced as being located within the talogue.com) (m) 0.61 (± 0.03)[2] M Radius Metallicity (r) 0.60 (± 0.02)[2] R (T) 4402 (± 100)[2] K habitable zone of its star, a region where liquid water could exist on the surface of the planet. It was described as being one of the most Earth-like planets, in terms of size and temperature, yet found.[1][7] It is outside of the zone (around 0.02 AU) where tidal forces from its host star would be [Fe/H] −0.37 (± 0.10)[2] 2.9+8.1[2] Gyr Age enough to tidally lock it.[9] −0.2 Physical characteristics Kepler-442b is a super-Earth, an exoplanet with a mass and radius bigger than that of Earth, but smaller than that of the ice giants Uranus and Neptune. It has an equilibrium temperature of 233 K (−40 °C; −40 °F).[5] It has a radius of 1.34 R⊕. Because of its radius, it is likely to be a rocky planet with a solid surface. The mass of the exoplanet is (r) 0.60 (± 0.02)[2] R Temperature (T) 4402 (± 100)[2] K Metallicity [Fe/H] −0.37 (± 0.10)[2] 2.9+8.1[2] Gyr Age −0.2 Mass (m) Radius (r) Mass (m) Radius (r) 2.3+5.9[5] M⊕ −1.3 1.34+0.11[2] R⊕ https://en.wikipedia.org/wiki/Kepler-442b −0.18 Stellar flux (F⊙) 0.73 (± 0.11)[6] ⊕ estimated to be 2.34 M⊕.[9] The surface gravity on Kepler442b would be 30% stronger than that of Earth, assuming a Temperature (T) 233 K (−40 °C; −40 °F) rocky composition similar to that of Earth.[10] Semi-major axis (a) 0.409+0.209[2] AU Host star Eccentricity (e) 0.04+0.08[2] The planet orbits a (K-type) star named Kepler-442. The star has a mass of 0.61 M and a radius of 0.60 R . It has a temperature of 4402 K and is around 2.9 billion years old, Orbital period (P) 112.3053+0.024 (i) 89.94+0.06[2]° −0.12 Orbital elements Inclination −0.060 −0.04 −0.0028 [2] d 2.3+5.9[5] M⊕ −1.3 1.34+0.11[2] R⊕ −0.18 10/19/16, 11:17 AM Stellar flux (F⊙) 0.73 (± 0.11)[6] ⊕ (T) 233 K (−40 °C; −40 °F) Orbital elements (a) 0.409+0.209[2] AU Eccentricity (e) 0.04+0.08[2] −0.04 Orbital period (P) 112.3053+0.024 (i) 89.94+0.06[2]° −0.12 Inclination −0.060 −0.0028 [2] d Discovery information Discovery date 6 January 2015[2][3] Discoverer(s) Kepler spacecraft Discovery method Transit Discovery status Published referred article Other designations KOI-4742.01; Kepler-442 b; KOI-4742 b; K04742.01; WISE J190127.98+391648.2 b; KIC 4138008 b; 2MASS J19012797+3916482 b Database references Extrasolar Planets Encyclopaedia data (http://exoplanet.eu/plan et.php?p1=Kepler-442&p2=b ) SIMBAD data (http://simbad.u-strasbg.f r/simbad/sim-id?Ident=Keple r-442+b) Exoplanet Archive data (http://exoplanetarchive.i pac.caltech.edu/cgi-bin/Displ ayOverview/nph-DisplayOve rview?objname=Kepler-442+ b) Habitability Temperature Characteristics data (http://simbad.u-strasbg.f seen with the naked eye. Kepler-442 (KOI-4742) r/simbad/sim-id?Ident=Keple Lyra[1] Orbit r-438+b) Right (α) 19h 01m 27.98s Exoplanet Archive data (http://exoplanetarchive.i ascension Kepler-442b orbits its host star with an orbital period of Declination 0.61 (± 0.03)[2] M Radius Semi-major axis K03284.01; WISE J184634.98+415704.0 b; KIC years old[11] and has a temperature of 5778 K.[12] The star is 6497146 b; 2MASS J18463499+4157039 b Constellation (m) rocky composition similar to that of Earth.[10] Earth's perspective, is 14.97. Therefore, it is too dim to be 1 Characteristics Kepler-438b orbits its parent star once every 35.2 days.[1][2] It is likely tidally1.1 locked to its distance to its Mass,due radius andclose temperature K?V[4] Mass Temperature Published refereed article The planet orbits a (K-type) star named Kepler-442. The star Other designations SIMBAD Star Spectral type estimated to be 2.34 M⊕.[9] The surface gravity on Kepler442b would be 30% stronger than that of Earth, assuming a Discoverer(s) Kepler-442b Kepler spacecraft Discovery method Exoplanet data (http://simbad.u-strasbg.f r/simbad/sim-id?Ident=Keple Kepler-442 r-438+b) (KOI-4742) Physical characteristics period Discovery date SIMBAD Constellation Exoplanet Archive Lyra data[1](http://exoplanetarchive.i h 01m 27.98s Right (α) 19pac.caltech.edu/cgi-bin/Displ ayOverview/nph-DisplayOve ascension rview?objname=Kepler-438+ The planet announced as orbiting within the habitable Declination (δ) +39° 16ʹ 48.30ʺ 1.3was Orbit b) zone of Kepler-438, a region where liquid water could exist Apparent (m ) 14.976[2] on2theHabitability surface of the planet. In the Earth Similarity Index Open Exoplanet V data (http://www.openexopla (ESI), which measures how similar are planets to Earth as to magnitude Catalogue (http://w netcatalogue.com/search/?id= Mass, radius and temperature Orbital elements Inclination Coordinates: Extrasolar Planets data (http://exoplanet.eu/plan Encyclopaedia et.php?p1=Kepler-438&p2=b Approximate size comparison of a hypothetical superhabitable) planet with Earth. 1.1 Mass, radius and temperature (F⊙) Temperature From Wikipedia, the free encyclopedia +0.01 Habitability 1.2 Host star +0.67 Kepler-442b Host star 0.03 −0.03[3] Discovery information radius and stellar flux.[1][2] However it has been found that 5 References +2.6 1.3 −0.7 M⊕ 1.40 −0.77 ⊕ Characteristics 0.16600 AU (e) Eccentricity FromHost Wikipedia, star the free encyclopedia https://en.wikipedia.org/wiki/Kepler-438b 6 External links (a) axis star.[10] M?V Age 5 References Semi-major Kepler-438b orbits its parent star once every 35.2 days.[1][2] Parent star It is tidally locked due to its close distance to its 1 likely Characteristics Star (m) Metallicity 4 See also Orbital elements Kepler-442b Contents 470[2] ly Spectral type 1.1 Mass, radius and temperature 3 Discovery and follow-up studies 276 K (3 °C; 37 °F) Orbital (P) 35.23319 d period Coordinates: 19h 01m 27.98s, +39° 16ʹ 48.30ʺ Inclination (i) 89.860° Orbit (145 pc) 2 Habitability (T) [4] Distance 1 Characteristics Mass, radius and temperature Temperature Discovery date 2015 [1][2][7] The planet orbits(also a (M-type) star named Kepler-442b knownred bydwarf its Kepler ObjectKeplerof Kepler-442b Approximate size comparison of Kepler-438b (right) withInterest 438.designation The star hasKOI-4742.01) a mass of 0.54isMa confirmed and a radius of 0.52 Discoverer(s) Kepler spacecraft near-EarthEarth , both lower than thoseorbiting of the Sun by almost half. It has a Exoplanet sizedRexoplanet, likely rocky, within the habitable List of exoplanets Discovery method Transit temperature of 3748 K and is estimated to be about zone surface of the K-type main-sequence star[8] Kepler-442, about Parent star Discovery status Published refereed article [3] billion years onlyor200 million years×younger than 1,1204.4 light-years (342old, parsecs, nearly 1.0553 1016 km) Star Kepler-438 Other designations [8] and the Sun has a surface Sun. 5778 from the Earth in the constellation Lyra.[1][7]temperature The planet of was KOI-3284.01; Kepler-438 b; KOI-3284 b; Constellation Lyra[2] [9] K. discovered by NASA's Kepler spacecraft using the transit K03284.01; WISE J184634.98+415704.0 b; KIC Right (α) 18h 46m 35.000s method, in which the dimming effect that a planet causes as 6497146 b; 2MASS J18463499+4157039 b The star's apparent or howNASA bright announced it appears from it crosses in front of its magnitude, star is measured. ascension Earth's perspective, is 14.467. Therefore, it is too dim to be Database references the confirmation the exoplanet on 6 January 2015.[7] Declination (δ) +41° 57ʹ 3.93ʺ seen with theofnaked eye. Apparent magnitude Contents Characteristics Kepler-438b is an Earth-sized planet, an exoplanet that has a Kepler-442b mass- Wikipedia and radius close to that of Earth. It has a radius of 1.12 R⊕, and a mass of 1.3 M⊕. It has an equilibrium temperature of 276 K (3 °C; 37 °F), close to that of Earth. solar flex.[5] Kepler-438, about 470 light-years (145 parsecs, 4.4 billion years 1,120 light-years 10/19/16, 11:16 AM Open Exoplanet data (http://www.openexopla Catalogue (http://w netcatalogue.com/search/?id= ww.openexoplanetca Kepler-442+b) talogue.com) Page 1 of 3 Exam Questions Circular acceleration • Consider a planet orbiting a star with twice the mass, and twice the luminosity of the sun. If the orbital period is 2 solar years, what is the surface temperature of the planet? How could one determine the mass of the planet (if you measure the Doppler shift of the star)? • Consider a star with some RA and DEC, viewed at some sidereal time, plot the appearance of the night sky. Draw and label RA and DEC lines • ⃗a = ∆⃗v ∆t Physics 125, J. Buckley Physics 312 - Lecture 1 – p. 25/27