Seismic constraints on rotation of Sun-like starand mass of exoplanetLaurent Gizona,b, Jérome Ballotc,d, Eric Michele, Thorsten Stahna,b, Gérard Vauclairc,d, Hans Bruntte,Pierre-Olivier Quirionf, Othman Benomarg,h, Sylvie Vauclairc,d, Thierry Appourchauxh, Michel Auvergnee, Annie Bagline,Caroline Barbane, Fréderic Baudinh, Michaël Bazoti, Tiago Campantei,j,k, Claude Catalae, William Chaplink,Orlagh Creeveyl,m,n, Sébastien Deheuvelsc,d, Noël Dolezc,d, Yvonne Elsworthk, Rafael Garcíao, Patrick Gaulmep,Stéphane Mathiso, Savita Mathurq, Benoît Mossere, Clara Régulol,m, Ian Roxburghr, David Salabertn, Réza Samadie,Kumiko Satoo, Graham Vernerk,r, Shravan Hanasogea,s, and Katepalli R. Sreenivasant,1

aMax-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany; bInstitut für Astrophysik, Georg-August-Universität Göttingen, 37077Göttingen, Germany; cInstitut de Recherche en Astrophysique et Planétologie, Centre National de la Recherche Scientifique, 31400 Toulouse, France;dUniversité de Toulouse, Université Paul Sabatier/Observatoire Midi-Pyrénées, 31400 Toulouse, France; eLaboratoire d’Études Spatiales et d’Instrumentationen Astrophysique, Observatoire de Paris, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8109, Université Pierre et Marie Curie,Université Denis Diderot, 92195 Meudon, France; fAgence Spatiale Canadienne, Saint-Hubert, Québec, Canada J3Y 8Y9; gSydney Institute for Astronomy,School of Physics, University of Sydney, Sydney, NSW 2006, Australia; hInstitut d’Astrophysique Spatiale, Université Paris Sud–Centre National de la RechercheScientifique (Unité Mixte de Recherche 8617), 91405 Orsay Cedex, France; iCentro de Astrofísica da Universidade do Porto, 4150-762 Porto, Portugal; jDanishAsteroSeismology Centre, Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark; kSchool of Physics and Astronomy, Universityof Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom; lDepartamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife,Spain; mInstituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain; nLaboratoire Lagrange, Unité Mixte de Recherche 7293, Université de NiceSophia-Antipolis, Centre National de la Recherche Scientifique, Observatoire de la Côte d’Azur, 06300 Nice, France; oLaboratoire Astrophysique,Instrumentation, et Modélisation, Institut de Recherche sur les Lois Fondamentales de l’Univers/Service d’Astrophysique–Commissariat à l’Energie Atomique/Direction des Sciences de la Matière–Centre National de la Recherche Scientifique–Université Paris Diderot, 91191 Gif-sur-Yvette Cedex, France; pDepartmentof Astronomy, New Mexico State University, Las Cruces, NM 88003-8001; qHigh Altitude Observatory, National Center for Atmospheric Research, Boulder, CO80307; rAstronomy Unit, School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom; sDepartment of Geosciences,Princeton University, Princeton, NJ 08544; and tPhysics Department and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012

Contributed by Katepalli R. Sreenivasan, February 27, 2013 (sent for review September 26, 2012)

Rotation is thought to drive cyclic magnetic activity in the Sun andSun-like stars. Stellar dynamos, however, are poorly understoodowing to the scarcity of observations of rotation and magneticfields in stars. Here, inferences are drawn on the internal rotationof a distant Sun-like star by studying its global modes of oscillation.We report asteroseismic constraints imposed on the rotation rate andthe inclination of the spin axis of the Sun-like star HD52265, a principaltarget observed by the CoRoT satellite that is known to host aplanetary companion. These seismic inferences are remarkably consis-tent with an independent spectroscopic observation (rotational linebroadening) and with the observed rotation period of star spots.Furthermore, asteroseismology constrains the mass of exoplanet HD52265b. Under the standard assumption that the stellar spin axis andthe axis of the planetary orbit coincide, the minimum spectro-scopic mass of the planet can be converted into a true mass of1:85+0:52

−0:42MJupiter, which implies that it is a planet, not a brown dwarf.

extrasolar planets | stellar oscillations | stellar rotation

Space photometry has made possible high-precision seismol-ogy of Sun-like stars (1–5). Precise measurements of the

frequencies of the global modes of acoustic oscillations placetight constraints on the internal structure of these stars (6). Forexample, improved stellar parameters are used to refine thephysics of stellar interiors and find many applications in astro-physics. Accurate determinations of the radii, masses, and agesof planet-host stars are essential for the characterization ofexoplanets detected in transits (7–9).In this paper, we present an unambiguous measurement of

mean internal rotation (rotation averaged over the entire stellarinterior) and inclination angle of a Sun-like star by means ofasteroseismology. Internal rotation is a fundamental physicalproperty of stars: it affects stellar evolution through increasedmixing of chemicals and mass loss, and is responsible for mag-netic activity (10). Our study extends earlier studies of the seis-mic signature of rotation in α Centauri A (11, 12) and in redgiant stars (13, 14).The star HD 52265 was observed continuously for 117 d be-

tween November 2008 and March 2009 in the asteroseismic field

of the space telescope “convection, rotation, and planetarytransits” (CoRoT) (15). This relatively bright star (visual mag-nitude, 6.3) was selected as a primary target because it hostsa planetary companion, which was detected through the wob-bling of the star via the radial velocity method (16–18). With aneffective temperature (4) of 6;100± 60 K and an absolute lu-minosity (4) of 2:09± 0:24  LSun, HD 52265 is a main-sequenceG0V star. Combining these two values, the stellar radius is de-duced to be 1:30± 0:08  RSun. Isochrone fits (19, 20) give a stellarmass near 1.2 MSun with a typical error of 0.05 MSun and a stellarage between 2.1 and 2.7 Gy. The planetary companion, HD52265b, orbits the star with a period of 119 d, a semimajor axisof 0.5 astronomical unit (AU), and a minimum mass Mp sin ip =1:09± 0:11 MJupiter, where Mp is the true mass of the planet andip is the inclination of the orbital axis to the line of sight (18).HD 52265 is overmetallic with respect to the Sun ð½M=H�=0:19± 0:05Þ, a property that has been associated with the for-mation of hot Jupiters (21). See Table 1 for a summary ofbasic properties.The power spectrum of the HD 52265 CoRoT data exhibits

a series of peaks near 2 mHz caused by global acoustic oscil-lations (Fig. 1). As in the Sun and other stars with outer con-vection zones, these oscillations are continuously excited by near-surface convection (2). The star oscillates in high-overtonemodes whose horizontal spatial patterns are given by sphericalharmonics Ym

l , where l is the harmonic degree and m the azi-muthal order with −l≤m≤ l. The comb-like structure of thepower spectrum is due to a repeating sequence of pulsationsobservable in quadrupole ðl= 2Þ, radial ðl= 0Þ, and dipole ðl= 1Þmodes. The l= 2 and l= 0 modes are remarkably well resolved infrequency space and enable unambiguous identification of modes.

Author contributions: L.G. and T.S. designed research; L.G., J.B., E.M., T.S., G. Vauclair,H.B., P.-O.Q., O.B., S.V., T.A., M.A., A.B., C.B., F.B., M.B., T.C., C.C., W.C., O.C., S.D., N.D., Y.E.,R.G., P.G., S. Mathis, S. Mathur, B.M., C.R., I.R., D.S., R.S., K.S., and G. Verner performedresearch; and L.G., J.B., E.M., T.S., S.H., and K.R.S. wrote the paper.

The authors declare no conflict of interest.1To whom correspondence should be addressed. E-mail: krs3@nyu.edu.

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To first order (22), the spectrum of the mode frequencies isspecified by two characteristic frequencies (Fig. 1, Inset): the“large-frequency separation,” Δν, and the “small-frequency sepa-ration,” δν. The large-frequency separation between consecutivel= 0 modes is the inverse of the sound travel time across a stellardiameter. The small-frequency separation between adjacent l= 2and l= 0 modes is sensitive to the radial gradient of sound speedin the nuclear-burning core, and thus to helium content and theage of the star (23).Fig. 2A shows the power spectrum in échelle format (24) of

HD 52265 using a folding frequency of 98.5 μHz. Modes havemeasurable power over 10 consecutive oscillation overtones(radial orders), 16≤ n≤ 25. For comparison, Fig. 2B shows theéchelle spectrum of the Sun computed using a folding frequencyof 135.3 μHz and 117 d of observations from the VIRGO (25)instrument onboard the Solar and Heliospheric Observatory(SoHO). Although photon noise is higher for HD 52265, thesimilarity between the two power spectra is striking. HD 52265is an object that pulsates like the Sun, although there aremeasurable differences.

ResultsGlobal Fit of the Power Spectrum. We estimate the parameters ofthe individual modes of oscillation by fitting a global parametricmodel to the power spectrum using a maximum-likelihoodtechnique (26), by considering that the probability density function

of the power at any given frequency is an exponential distri-bution. All modes with l≤ 2 are fitted together in the range of1:6− 2:6 mHz. The expectation value of the power spectrumof each individual mode is modeled by a Lorentzian, whoseheight and width are allowed to vary with frequency. To improvethe robustness of the fit, the large- and small-frequency separationsare taken to be smooth (polynomial) functions of the radial order.The noise background is modeled as the sum of a convectivecomponent and a white-noise component. As for the Sun, theconvective component is well approximated by the sum of twoLorentzians, representing the two dominant timescales of con-vection, granulation and supergranulation (2).We include the effects of stellar rotation in the model. First,

rotation removes the frequency degeneracy of the ð2l+ 1Þ azi-muthal components. Assuming a slowly rotating star, the fre-quency of mode ðn; l;mÞ may be approximated by the following:

νnlm = νnl +mΩ=2π; [1]

where Ω is a suitable radial average of the angular velocity overthe star (27). Second, mode visibility depends on the angle ibetween the rotation axis and the line of sight. Assuming (asfor the Sun) energy equipartition in a multiplet ðl; nÞ betweenazimuthal components, mode power is proportional to thefollowing:

Eml ðiÞ=

ðl− jmjÞ!ðl+ jmjÞ!

�Pml ðcos iÞ

�2; [2]

where the Pml are associated Legendre functions (28). For exam-

ple, for dipole modes, E01ðiÞ= cos2 i and E± 1

1 ðiÞ= 1=2 sin2 i. Thus,the ratios in mode power between azimuthal components tell usabout i, whereas the splitting between mode frequencies tells usabout Ω.The fitted multiplets are shown in Fig. 3. The values of Ω and

sin i are inferred at the same time as the mode frequenciesand other mode parameters. The random errors associated withthe estimated mode parameters are deduced from Monte Carlosimulations.

Seismic Stellar Model. In the frequency range of 1.85–2.30 mHzwhere the mode power is the largest, we measure an average

Table 1. Parameters of star HD 52265

Parameter Value Method

Distance 28.95 ± 0.34 pc Astrometry (43)Luminosity 2.09 ± 0.24 LSun Astrometry (4)Effective temperature 6,100 ± 60 K Spectroscopy (4)Metallicity, [M/H] 0.19 ± 0.05 Spectroscopy (4)Main-sequence lifetime ∼ 6 × 109 y Mass–luminosity relation

1pc= 3:086× 1016 m; LSun = 3:8× 1026 W.

Fig. 1. Power spectrum of global acoustic oscillations of HD 52265. The pmodes have measurable power in the range 1.6–2.6 mHz. At low frequen-cies, the power is due to stellar convection and magnetic activity; at highfrequencies it is dominated by photon noise. Inset shows the power spec-trum in the interval 1.97–2.17 mHz, where acoustic modes are labeled withtheir spherical harmonic degrees, l≤ 2. Indicated are the large-frequencyseparation between consecutive radial modes, Δν (sensitive to mean den-sity), and the small-frequency separation between adjacent radial andquadrupole modes, δν (sensitive to age). Mode identification is unambiguousby virtue of the analogy with the solar spectrum.

A B

Fig. 2. Échelle spectrum and comparison with the Sun. (A) Échelle spectrumof HD 52265 using a folding frequency of 98.5 μHz. The power spectrum iscut into frequency segments, which are stacked in the vertical direction.Integers along the right axis indicate the number of frequency segments,starting from zero frequency, i.e., the radial order of the l= 0 modes. Thenearly vertical ridges of power (labeled according to spherical harmonicdegree l) indicate that the folding frequency is close to the large separationΔν. (B) For comparison and mode identification, we show the échelle spec-trum of the Sun using 117 d of SoHO/VIRGO photometry (25) (green chan-nel) and a folding frequency of 135.3 μHz.

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large-frequency separation of Δν= 98:56± 0:13 μHz and an av-erage small-frequency separation of δν= 8:08± 0:16  μHz. Thelarge-frequency separation is proportional to the square root ofthe mean stellar density, implying that HD 52265 is less dense thanthe Sun by a factor of 0:5338± 0:0014. This seismic constraint onthe mean stellar density is 60 times more precise than the spec-troscopic constraint.

We have estimated the fundamental stellar properties of HD52265 by finding the best-fit stellar model among an extended gridof stellar models computed with the Aarhus Stellar EvolutionCode. Using the average large- and small-frequency separationsgiven above together with the observed effective temperature ofthe star and its metallicity (Table 1), the SEEK optimizationprocedure (29) returns a best-fit stellar model with a seismic radiusR= 1:34± 0:02  RSun and a seismic mass M = 1:27± 0:03 MSun,where formal error bars are severalfold smaller than the classicalones (Table 2). The seismic age is 2:37± 0:29 Gy, where we quotethe formal error. By comparison, stellar ages deduced from iso-chrone fits lead to typical errors (30) of 30–50%, which are sig-nificantly worse. Detailed asteroseismic modeling of HD 52265not only places tight constraints on the mass, radius, and age of thestar but also on its initial chemical composition (31).

Internal Stellar Rotation. The global fit of the power spectrumreturns a rotational splitting frequency Ω=2π = 0:98+0:19−0:29 μHz andthe inclination sin i= 0:59+0:18−0:14. The inferred rotational splitting ofHD 52265 is about 2.3 times larger than that of the Sun (Table 2).To further test our methodology, we average the power

spectrum over multiplets with the same l value to smooth outrandom variations of power with frequency due to the realizationnoise (Fig. 3). This average is computed over nine consecutiveradial orders ð16≤ n≤ 24Þ, after shifting multiplets by theircentral frequencies νnl using Fourier interpolation. A similaraveraging procedure was used in the early days of helio-seismology (32) to measure the small frequency separation δν.The average spectra of HD 52265 for l= 0, l= 1, and l= 2 are

shown in Fig. 4. The widths at half-maximum of the profiles forl= 1 and l= 2 modes are larger than that of the l= 0 singlet by20% and 90%, respectively. Thus, the nonradial multiplets arebroadened by rotation, confirming that stellar rotation (Table 2)has a measurable effect, as inferred rigorously from the maxi-mum-likelihood model fit. However, the individual m compo-nents are not resolved due to the intrinsic line width of the modes,which (near the maximum power) is about twice as large as therotational splitting—a situation comparable to that of the Sun.Our seismic estimates of Ω and i are remarkably consistent

with independent measurements from spectroscopy and star spotrotation, as shown in Fig. 5. The observed (4) spectroscopic ro-tational velocity v sin i= 3:6+0:3−1:0 km·s−1 is fully consistent with theseismic value R Ω sin i= 3:4± 0:8 km·s−1 (surface and bulk ro-tation rates of solar-type stars are expected to be similar, as inthe Sun). In addition, the photometric time series of HD 52265 ismodulated by the rotation of star spots at two prominent periodsof 10.8 and 12.7 d, corresponding to the cyclic frequenciesΩspot=2π = 0:91 and 1.07 μHz, values that are consistent withseismology. The two periods may be associated with star spots atdifferent latitudes, thus providing some indication of latitudinaldifferential rotation. Star spot modeling of the CoRoT time series

Fig. 3. Power spectra of the radial (l= 0, Left), dipole (l= 1, Middle), andquadrupole modes (l= 2, Right) of HD 52265 (gray curves). Nine consecutiveradial orders 16≤n≤ 24 are shown, with n decreasing from Top to Bottom.In each panel, the frequency axis is shifted by the central frequency of themultiplet, νnl , obtained from the global fit. The global fit (red curves) is anestimate of the expectation value of the power spectrum and includes theeffects of rotation on oscillations. Each azimuthal component ðn; l;mÞ ina multiplet is modeled by a Lorentzian line profile, describing dampedharmonic oscillation.

Table 2. Asteroseismic vs. classical constraints on properties and rotation of HD 52265

Stellar property Asteroseismology Classical methods

Radius 1.34 ± 0.02 RSun 1.30 ± 0.08 RSun [spectroscopy (4)]Mass 1.27 ± 0.03 MSun 1.21 ± 0.05 MSun [isochrone fits (20)]Age 2.37 ± 0.39 × 109 y 2:7+0:7−1:5   × 109 y [isochrone fits (20)]Bulk rotation, Ω=ΩSun 2:31+0:45−0:69Star spot rotation, Ωspot=ΩSun 2.15 and 2.52 [photometry (4)]Inclination of stellar rotation axis, sin i 0:59+0:18−0:14 0:50+0:15−0:16   [star spot modeling (4, 33)]Sky-projected rotational velocity 3:4 ± 0:8 km·s−1* 3:6+0:3−1:0   km·s−1 [spectroscopy (4)]†

Solar reference values: RSun = 6:96×108 m; MSun = 1:99× 1030 kg; ΩSun=2π = 0:424  μHz.*R Ω sin i, where R and Ω sin i are seismic estimates.†v sin i from spectroscopic rotational broadening. The value 4.7 ± 0.5 km·s−1 quoted in ref. 20 is probably anoverestimate due to the macroturbulence model used.

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including differential rotation (4, 33) returns a rotational fre-quency at the equator Ωeq=2π = 0:99+0:03−0:04 μHz and sin i= 0:50+0:15−0:16(which again is consistent) (Table 2). The general agreement be-tween all these independent measurements strongly supports ourseismic determination of mean internal rotation and inclinationangle of HD 52265.

DiscussionThe seismic radius and mass of HD 52265 have been inferredwith a formal error of 2% and the stellar age with a formal errorof 5% of the main-sequence lifetime. This level of precision onfundamental stellar properties, required to characterize planetsin transit around Sun-like stars (6, 7, 34), is a significant im-provement over classical estimates (Table 2). Although theplanetary companion orbiting HD 52265 does not transit its host,the seismic determination of the direction of the spin axis of thestar provides useful information to further characterize the massof the exoplanet.

Mass of Exoplanet HD 52265b. Under the assumption that the ro-tation axis of the star and the normal to the planetary orbit

coincide, i.e., ip = i, the knowledge of the minimum mass of HD52265b from Doppler spectroscopy ðMpsinipÞ can be used to-gether with the inclination of the stellar spin axis from seismologyto constrain the true mass, Mp. The 1-σ seismic bound sin i> 0:45(irrespective of the value of Ω) implies that Mp < 2:4 MJupiter.Such a mass is well under the lower limit of brown dwarfs,MBD = 13MJupiter. Deuterium burning cannot be sustained belowthis mass threshold. Thus, HD 52265b is likely to be a planet andnot a brown dwarf. [Note that the values sinip = 0:026 andMp = 41 MJupiter, obtained from Hipparcos intermediate astrometry(35), have low significance due to insufficient angular resolution ofthe Hipparcos data (36).] The best seismic fit (Fig. 5, black cross)implies 1:85+0:52−0:42MJupiter. Together, the seismic, spectroscopic, andstar spot constraints on i give Mp = 1:85+0:39−0:40MJupiter. Some relevantcharacteristics of the exoplanet are listed in Table 3.

Formation of Planetary Systems. The formation of Jupiter-massplanets in close orbits (hot Jupiters), like HD 52265b, remains

Fig. 4. Influence of stellar rotation on oscillations. Power spectra are shownfor the radial (Top), dipole (Middle), and quadrupole modes (Bottom), afteraveraging over the nine consecutive radial orders from Fig. 3. The gray curveis the average power spectral density and the red is the average of the fits.For clarity, the frequency resolution is reduced by a factor of 3. Although therotational splitting is too small to separate the azimuthal components,a rotational broadening of the average line profiles of l= 1 and l= 2 is clearlyvisible. The dashed, dotted, and solid blue lines show the azimuthal com-ponentsm= 0,m= ± 1, andm= ± 2, which contribute to the average power.The 2l+ 1 frequencies of the azimuthal components, split by rotationðΩ=2π = 0:98 μHzÞ, are marked by arrows at the bottom of each panel andlabeled by the azimuthal order m. The visibility amplitudes of the azimuthalcomponents are computed for the best-fit inclination angle of i= 368.

Fig. 5. Constraints on stellar rotation and planet mass. The dark-red andlight-red regions are the 1-σ and 2-σ seismic constraints on stellar rota-tion in the plane ðΩ=ΩSunÞ− ðsin iÞ, where Ω is the bulk angular velocity,ΩSun=2π = 0:424 μHz is the solar (Carrington) rotational frequency, and i isthe inclination of the stellar rotation axis to the line of sight. The black di-amond with error bars gives the best-fit seismic values, Ω=ΩSun = 2:31+0:45−0:69and sin i= 0:59+0:19−0:14. For comparison, the two horizontal green lines mark theangular velocity of stellar activity (star spots) deduced from two prominentpeaks in the low-frequency part of the power spectrum. The filled greenellipse represents the 1-σ bound of the equatorial rotation and inclinationangle obtained from star spot modeling of the photometric time series(4, 33). The spectroscopic constraints are given by the dashed (observations)and the solid (1-σ errors) blue curves, as expressed through the sky-projectedangular velocity Ω sin i= ðv sin iÞ=R, where v sin i=3:6+0:3−1:0 km·s−1 is the ob-served spectroscopic rotational broadening and R= 1:34  RSun is the seismicstellar radius. The minimum mass of the planet from radial velocity meas-urements (18) is Mp sin ip = ð1:09± 0:11ÞMJupiter, where ip is the inclination ofthe normal of the planetary orbit to the line of sight. Assuming ip = i, theseismic constraint on sin i can be converted into a constraint (top axis andgray region “HD 52265b”) on the true mass of the planet, Mp, which is wellbelow the brown dwarf limit of 13MJupiter.

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a mystery. In one theory, hot Jupiters are formed in the outerregions of protoplanetary disks and migrate toward the innerregions via friction (37). This scenario favors systems with i= ip.However, a study based on the Rossiter–McLaughlin effect (38)revealed that 80% of a sample of transiting planets show a sky-projected spin-orbit misalignment, λ, greater than 20°. Alter-native formation scenarios like Kozai cycles (39) and planetscattering (40, 41) are required to explain large spin-orbit mis-alignments. The misalignment of the HD 52265 system is notexcluded, as the alignment timescale through tidal interaction(42) is much greater than the age of the star. For other planetsdiscovered with the transit method, ip is known and theknowledge of i (through asteroseismology and/or spot mod-eling) and λ would give the true angle between the stellar

rotation axis and the planet orbital axis. Asteroseismology hasmuch to contribute to the study of the evolutionary history ofexoplanetary systems.

ACKNOWLEDGMENTS. The CoRoT space mission has been developed and isoperated by the Centre National d’Études Spatiales, with the contribution ofAustria, Belgium, Brazil, the European Space Agency (Research and ScientificSupport Department and Science Programme), Germany, and Spain. L.G. andT.S. acknowledge support from Deutsche Forschungsgemeinschaft Sonder-forschungsbereich 963 “Astrophysical Flow Instabilities and Turbulence”(Project A18). J.B. acknowledges support from Agence Nationale de laRecherche through project SiROCO. I.R. acknowledges support from theLeverhulme foundation under Grant 2012-035/4. The National Center forAtmospheric Research is supported by the National Science Foundation.SoHO is a mission of international cooperation between the European SpaceAgency and the National Aeronautics and Space Administration.

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Table 3. Characteristics of exoplanet HD 52265b

Characteristic Value Method

Minimum planet mass, Mp sin ip 1:09± 0:11 MJupiter Radial velocity (18)Semimajor axis of planetary orbit 0:504±0:029 AU Radial velocity (18)Planet mass, Mp 1:85+0:52−0:42MJupiter sin i=sin ip Asteroseismology

MJupiter = 1:899× 1027 kg; 1 AU= 1:496× 1011 m.

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