Determination of the masses of Jupiter and Saturn from the motion of Trojans

1974 ◽  
Vol 22 ◽  
pp. 93-96
Author(s):  
H. Scholl
Keyword(s):  
Minor Planets ◽  
Planetary Mass ◽  
Orbital Periods ◽  
The Masses ◽  
Two Bodies

The mass of a planet can be determined by the motion of its satellites or by perturbational effects on nearby bodies, such as comets, planets, minor planets. It is well known, for instance, that a body on a nearby orbit which is in close resonance with a planet is suitable for the determination of the planetary mass. In this case the orbital periods of the two bodies are equal or nearly equal to the ratio of small integers (i.e. 1: 1, 2: 1, 3:2).

scholarly journals Mass determination of the 1:3:5 near-resonant planets transiting GJ 9827 (K2-135)

2018 ◽  
Vol 618 ◽  
pp. A116 ◽  
Author(s):  
J. Prieto-Arranz ◽  
E. Palle ◽  
D. Gandolfi ◽  
O. Barragán ◽  
E. W. Guenther ◽  
...  
Keyword(s):  
Planetary System ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Space Mission ◽  
Mass Determination ◽  
Velocity Measurements ◽  
Orbital Periods ◽  
The Masses ◽  
Better Than

Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of Mb = 3.69−0.46+0.48 M⊕ and a radius of Rb = 1.58−0.13+0.14 R⊕, yielding a mean density of ρb = 5.11−1.27+1.74 g cm−3. GJ 9827 c has a mass of Mc = 1.45−0.57+0.58 M⊕, radius of Rc = 1.24−0.11+0.11 R⊕, and a mean density of ρc = 4.13−1.77+2.31 g cm−3. For GJ 9827 d, we derive Md = 1.45−0.57+0.58 M⊕, Rd = 1.24−0.11+0.11 R⊕, and ρd = 1.51−0.53+0.71 g cm−3. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.

scholarly journals The Planetary Masses and the Orbits of the First Four Minor Planets

1971 ◽  
Vol 9 ◽  
pp. 246-249
Author(s):  
J. Schubart
Keyword(s):  
Minor Planets ◽  
Numerical Tests ◽  
The Masses

AbstractNumerical tests are the basis of a study about the effects caused in the orbits of the planets (l)-(4) by possible errors in the system of planetary masses. The masses of five major and three minor planets are considered. Especially, the effects caused by (1) Ceres in the orbit of (2) Pallas since the time of discovery are found to be large enough for a determination of the mass of Ceres. A first result for this mass is (6.7 ±0.4) x 10-10 solar masses.

scholarly journals Two bodies with high eccentricity around the cataclysmic variable QS Vir

2010 ◽  
Vol 6 (S276) ◽  
pp. 495-496 ◽  
Author(s):  
Leonardo A. Almeida ◽  
Francisco Jablonski
Keyword(s):  
Orbital Period ◽  
Giant Planet ◽  
Cataclysmic Variable ◽  
Brown Dwarf ◽  
Period Variations ◽  
Angular Momentum Loss ◽  
Best Fitting ◽  
Orbital Periods ◽  
The Masses ◽  
Two Bodies

AbstractQS Vir is an eclipsing cataclysmic variable with 3.618 hrs orbital period. This system has the interesting characteristics that it does not show mass transfer between the components through the L1 Lagrangian point and shows a complex orbital period variation history. Qian et al. (2010) associated the orbital period variations to the presence of a giant planet in the system plus angular momentum loss via magnetic braking. Parsons et al. (2010) obtained new eclipse timings and observed that the orbital period variations associated to a hypothetical giant planet disagree with their measurements and concluded that the decrease in orbital period is part of a cyclic variation with period ~16 yrs. In this work, we present 28 new eclipse timings of QS Vir and suggest that the orbital period variations can be explained by a model with two circumbinary bodies. The best fitting gives the lower limit to the masses M1 sin(i) ~ 0.0086 M⊙ and M2 sin(i) ~ 0.054 M⊙; orbital periods P1 ~ 14.4 yrs and P2 ~ 16.99 yrs, and eccentricities e1 ~ 0.62 and e2~0.92 for the two external bodies. Under the assumption of coplanarity among the two external bodies and the inner binary, we obtain a giant planet with ~0.009 M⊙ and a brown dwarf with ~ 0.056 M⊙ around the eclipsing binary QS Vir.

scholarly journals A Determination of the Masses of the Five Outer Planets

1971 ◽  
Vol 9 ◽  
pp. 224-232
Author(s):  
R. L. Duncombe ◽  
W. J. Klepczynski ◽  
P. K. Seidelmann
Keyword(s):  
Minor Planets ◽  
Outer Planets ◽  
Extensive Analysis ◽  
The Masses

AbstractPlanetary masses are determined from an extensive analysis of observations of the five outer planets and of seven selected minor planets.

scholarly journals Asteroid Masses and Densities

1971 ◽  
Vol 12 ◽  
pp. 33-39 ◽  
Author(s):  
Joachim Schubart
Keyword(s):  
Total Mass ◽  
Direct Determination ◽  
Absolute Magnitude ◽  
Strong Increase ◽  
Minor Planets ◽  
Solar Mass ◽  
A Value ◽  
The Mean ◽  
The Masses

Before 1966, when Hertz (1966) published his first direct determination of the mass of Vesta, all our knowledge on asteroid masses was based on estimates. The masses of the first four minor planets resulted from the measured diameters by Barnard (1900) (see the paper by Dollfus in this volume) and from estimated mean densities. The diameters of the smaller objects were derived from their brightness and an estimate of their reflectivity (usually the reflectivity of the Moon was adopted). In 1901, Bauschinger and Neugebauer (1901) derived a value for the total mass of the first 458 asteroids. All the diameters were computed from the brightness with an assumed value for the reflectivity. The diameter of Ceres found in this way is very close to Barnard’s (1900) value. The mean density of the 458 asteroids was put equal to that of Earth, and their total mass resulted as 3 X 10-9 solar mass. Stracke (1942) used the same method with an increased material, but the addition of more than 1000 faint asteroids did not bring a significant change in the estimate of the total mass. The report on the McDonald asteroid survey (Kuiper et al., 1958) does not contain another estimate of the total mass of the asteroid ring, but it points to the possibility of a very rapid increase in the number of asteroids with decreasing absolute brightness. If this increase is strong enough, each interval of 1 mag in absolute magnitude can contribute the same amount to the total mass. In the range of magnitudes covered by the Palomar-Leiden survey (PLS) (van Houten et al., 1970), there are no indications for such a strong increase.

scholarly journals Semi-analytical theory of motion for the PSR B1257+12 planetary system

2000 ◽  
Vol 177 ◽  
pp. 77-80
Author(s):  
Maciej Konacki ◽  
Andrzej J. Maciejewski ◽  
Alex Wolszczan
Keyword(s):  
Numerical Simulations ◽  
Planetary System ◽  
Analytical Theory ◽  
Precise Description ◽  
Theory Of Motion ◽  
Dynamical Properties ◽  
Orbital Periods ◽  
The Masses

A planetary system around the pulsar B1257+12 has three planets A, B and C with the orbital periods of 25, 66 and 98 days, respectively (Wolszczan 1994). Dynamical properties of the system have been thoroughly studied by Rasioet al. (1993) and Malhotra (1993). They demonstrated that the gravitational interactions between planets B and C are significant enough to be detected. In such case, the motion of the system is no longer Keplerian and it is necessary to use a more precise description of motion in order to model the data properly. In this paper we derive a semi-analytical theory of motion assuming that the relative inclination of the orbits is small. We perform numerical simulations to show that our theory sucessfully predicts times of arrival of pulsar pulses and allows a determination of orbital inclinations and hence the masses of planets B and C.

scholarly journals X-Ray Determination of the Black-Hole Mass in Cygnus X-1

1998 ◽  
Vol 188 ◽  
pp. 388-389
Author(s):  
A. Kubota ◽  
K. Makishima ◽  
T. Dotani ◽  
H. Inoue ◽  
K. Mitsuda ◽  
...  
Keyword(s):  
Black Hole ◽  
Compact Object ◽  
Optical Observations ◽  
Black Hole Mass ◽  
X Ray ◽  
Upper Limit ◽  
Supergiant Star ◽  
X Ray Binaries ◽  
Two Bodies

About 10 X-ray binaries in our Galaxy and LMC/SMC are considered to contain black hole candidates (BHCs). Among these objects, Cyg X-1 was identified as the first BHC, and it has led BHCs for more than 25 years(Oda 1977, Liang and Nolan 1984). It is a binary system composed of normal blue supergiant star and the X-ray emitting compact object. The orbital kinematics derived from optical observations indicates that the compact object is heavier than ~ 4.8 M⊙ (Herrero 1995), which well exceeds the upper limit mass for a neutron star(Kalogora 1996), where we assume the system consists of only two bodies. This has been the basis for BHC of Cyg X-1.

A NUCLEAR MANY-BODY THEORY AT FINITE TEMPERATURE APPLIED TO A PROTONEUTRON STAR

2002 ◽  
Vol 11 (02) ◽  
pp. 83-104 ◽  
Author(s):  
GUILHERME F. MARRANGHELLO ◽  
CESAR A. Z. VASCONCELLOS ◽  
MANFRED DILLIG ◽  
J. A. DE FREITAS PACHECO
Keyword(s):  
Phase Transition ◽  
Nuclear Matter ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Many Body ◽  
Many Body Theory ◽  
The Masses ◽  
Protoneutron Stars ◽  
Protoneutron Star

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars

scholarly journals Thermal impedance at the interface of contacting bodies: 1-D examples solved by semi-derivatives

2012 ◽  
Vol 16 (2) ◽  
pp. 623-627 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Half Time ◽  
Thermal Impedance ◽  
Entire Domain ◽  
Transient Thermal ◽  
Two Bodies

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface ( x = 0 ) at t = 0 . The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions.

scholarly journals A tale of two periods: determination of the orbital ephemeris of the super-Eddington pulsar NGC 7793 P13

2018 ◽  
Vol 616 ◽  
pp. A186 ◽  
Author(s):  
F. Fürst ◽  
D. J. Walton ◽  
M. Heida ◽  
F. A. Harrison ◽  
D. Barret ◽  
...  
Keyword(s):  
Accretion Disk ◽  
Orbital Period ◽  
Timing Analysis ◽  
X Ray ◽  
System Parameters ◽  
Orbital Resonance ◽  
Photometric Period ◽  
Orbital Periods ◽  
Analyze Data

We present a timing analysis of multiple XMM-Newton and NuSTAR observations of the ultra-luminous pulsar NGC 7793 P13 spread over its 65 d variability period. We use the measured pulse periods to determine the orbital ephemeris, confirm a long orbital period with Porb = 63.9+0.5−0.6 d, and find an eccentricity of e ≤ 0.15. The orbital signature is imprinted on top of a secular spin-up, which seems to get faster as the source becomes brighter. We also analyze data from dense monitoring of the source with Swift and find an optical photometric period of 63.9 ± 0.5 d and an X-ray flux period of 66.8 ± 0.4 d. The optical period is consistent with the orbital period, while the X-ray flux period is significantly longer. We discuss possible reasons for this discrepancy, which could be due to a super-orbital period caused by a precessing accretion disk or an orbital resonance. We put the orbital period of P13 into context with the orbital periods implied for two other ultra-luminous pulsars, M82 X-2 and NGC 5907 ULX, and discuss possible implications for the system parameters.

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