Earth, mass

The inner, or terrestrial, planets, from Mercury to Mars, including the planetoids. These have masses between 0.06 and 1 Earth masses, densities between 3,000 and 5,500 kg/m3, and similar structures ... 

Table 7.1 Planetary data (based on the Earth mass of 5.974 x 1024 kg and diameter 12 756 km)...

Planet Semi-major axis (AU) Sideral period (Earth-year) Mass (Earth-mass) Diameter (Earth- diameter) Density (g cm"3) Diurnal temperature variation (K)... 

These detection techniques have found heavy planets with up to 400 Earth-mass but are unlikely to detect Earth-mass planets because the Doppler shift is too small. The first extrasolar planet to be discovered by the Doppler variation technique was 51-Pegasi, with the results shown in Figure 7.9. Precise radial... 

Note Mass, radius and brightness are given in solar units. For example, Sirius A has 2.3 solar masses, is 2.5 times the size of the Sun and is intrinsically 35 times brighter than the Sun. 1 Solar mass = 2 x 1030 kg = 330000 Earth masses 1 solar radius = 700000 km = 110 Earth radii. 

The dissociation reaction predicted by Umemoto et al. s calculations has important implications for creating good models of planetary formation. At the simplest level, it gives new information about what materials exist inside large planets. The calculations predict, for example, that the center of Uranus or Neptune can contain MgSiC>3, but that the cores of Jupiter or Saturn will not. At a more detailed level, the thermodynamic properties of the materials can be used to model phenomena such as convection inside planets. Umemoto et al. speculated that the dissociation reaction above might severely limit convection inside dense-Satum, a Saturn-like planet that has been discovered outside the solar system with a mass of 67 Earth masses. 

The radioactive products of the Sedan detonation were present in the fireball and mixed into the mass of earth moved by the detonation. As the fireball cooled, condensation occurred, and radioactivity in various forms was scavenged by earth materials entering the cloud. Apparently a large fraction of the residual tritium from the explosive was present in the cloud as tritiated steam. This tritiated water was entrained by the ejecta as it fell onto the surrounding land surface, and the resulting postshot substratum thus contained a most significant and mobile tracer. Other radionuclides scavenged by the ejected earth mass constitute another type of tracer for Sedan ejecta. 

PROBLEM 2.4.7. If a satellite is to reach an orbit 100 km above the surface of the earth, what tangential velocity must it have as it enters the orbit How long will it take to make one revolution around the earth (earth mass = 5.977 x 1024 kg earth radius = 6.371 x 106 m) ... 

Figure 10.4 A simulation of oligarchic growth in the inner region of a proto-planetary disk around a solar-mass star. In the inner disk, embryos grow to 0.1 Earth-masses in <106 years. Growth then slows dramatically. Embryos continue to grow larger beyond the snowline at 2.5 AU. The simulation uses the semi-analytic model of Chambers (2008) with Esom ccl/a.

Safronov (1979) suggested that Mars- to Earth-mass planetary embryos left over from the accretion process could have caused the excitation and depletion of the Asteroid Belt. In this model, these embryos were scattered inwards by Jupiter onto orbits that traveled through the Asteroid Belt. Petit et al. (1999) modeled this scenario in detail and showed that it cannot fully explain the observed mass depletion and dynamical excitation of the Asteroid Belt, especially the orbital inclinations. 

Mercury is an important part of the solar system puzzle, yet we know less about it than any other planet, except Pluto. Mercury is the smallest of the terrestrial planets (0.05 Earth masses) and the closest to the Sun. Its relatively high density (5.4 g cm ) indicates that it has a large metallic core (—3/4 of the planet s radius) compared to its silicate mande and crust. The existence of a magnetic field implies that the metallic core is stiU partly molten. The surface is heavily cratered like the highlands of the Moon, but some areas are smooth and less cratered, possibly like the lunar maria (but not as dark). Its surface composition, as explained in the next section, appears to be low in FeO (only —3 wt.%), which implies that either its crust is anorthositic (Jeanloz et al., 1995) or its mande is similarly low in FeO (Robinson and Taylor, 2001). 

In units of Earth radii, where 1 Earth radius = 6,378 X 10 cm at the equator. In Earth masses, where 1 Earth mass — 5.974 X 10 g. 

Calculated bulk rock trace-element systematics of eclogites have wider implications for mantle recycling models and bulk silicate earth mass balance. The subchondritic Nb/Ta, Nb/La, and Ti/Zr of both continental cmst and depleted mantle require the existence of an additional reservoir with superchondritic ratios to complete the terrestrial mass balance. Rudnick et al. (2000) have shown that rutile-bearing eclogites from cratonic mantle have suitably superchondritic Nb/Ta, Nb/La, and Ti/Zr such that if this component formed 1 -6% by weight of the bulk silicate earth, this would resolve the mass imbalance. This mass fraction far exceeds the likely mass of eclogite in the continental lithosphere and so the material is proposed to reside in the lower mantle, possibly at the core-mantle boundary. 

On Mars (a tenth of Earth mass and 38% of its radius), the present water inventory is much less, enough to cover the planet to a few tens of meters puddle oceans (Carr, 1996). On Venus, which must have been very nearly Earth s twin prior to the giant impact on Earth (0.815 modern Earth mass, 95% of its radius), the atmosphere evolved to its present runaway CO2 greenhouse. There has been much speculation about early Venusian oceans, perhaps some kilometers deep, but possibly only a few meters if Venus formed too close to the Sun to inherit a large water inventory (see Taylor, 2001 for a brief summary of this dispute). 

From Triton s 5.866 day period of revolution around Neptune and its 220,000 mi (354,300 km) mean distance from it, astronomers estimated Neptune s mass to be 17.14 Earth masses, according to Kepler s third law. From Neptune s mean radius of 15,290 mi (24,625 km), a mean density (mass divided by volume) of 1.64 grams/cm was found. These values are similar to the ones found for Uranus. Uranus is slightly larger than Neptune, but Neptune is considerably more massive and denser than Uranus. Thus, Neptune is one of the Jovian planets, which are characterized by large sizes and masses but low mean densities (compared with Earth). The last characteristic implies that Jovian planets have extremely thick atmospheres and are largely or mostly composed of gases. 

The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr s quantization of angular momentum to the revolution of Earth (mass 6.0 X 10 " kg), which moves with a velocity of 3.0 X 10" m s in a circular orbit (radius 1.5 X 10 m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earth-sun system. What would be the effect of an increase in by 1 ... 

Models for the formation of the giant planets suggest that a rocky planetary embryo of about ten Earth masses can form rapidly, within 10s years. Once this embryo is established these massive planetary embryos accumulate two Earth masses of solar nebular gas over 107 yr (Kortenkamp et al., 2001). 

Most analytical balances used today are electronic balances. The mechanical single-pan balance is still used, though, and so we will describe its operation. Both types are based on comparison of one weight against another (the electronic one for calibration) and have in common factors such as zero-point drift and air buoyancy. We really deal with masses rather than weights. The weight of an object is the force exerted on it by the gravitational attraction. This force will differ at different locations on Earth. Mass, on the other hand, is the quantity of matter of which the object is composed and is invariant. 

The distance (d) was calculated from the centers of mass (center of the earth, mass mp center of the apple, mass m2), and the weakening of the force with the square of the distance (1/d ) meant that if the distance doubled, the force was only one-quarter of the original. 

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