16,286 research outputs found
Hamiltonians of Spherically Symmetric, Scale-Free Galaxies in Action-Angle Coordinates
We present a simple formula for the Hamiltonian in terms of the actions for
spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or
logarithmic function of a linear combination of the actions. Our expression
reduces to the well-known results for the familiar cases of the harmonic
oscillator and the Kepler potential. For other power-laws, as well as for the
singular isothermal sphere, it is exact for the radial and circular orbits, and
very accurate for general orbits. Numerical tests show that the errors are
always small, with mean errors across a grid of actions always less than 1 %
and maximum errors less than 2.5 %. Simple first-order corrections can reduce
mean errors to less than 0.6 % and maximum errors to less than 1 %. We use our
new result to show that :[1] the misalignment angle between debris in a stream
and a progenitor is always very nearly zero in spherical scale-free potentials,
demonstrating that streams can be sometimes well approximated by orbits, [2]
the effects of an adiabatic change in the stellar density profile in the inner
regions of a galaxy weaken any existing 1/r density cusp, which is reduced to
. More generally, we derive the full range of adiabatic cusp
transformations and show how to relate the starting cusp index to the final
cusp index. It follows that adiabatic transformations can never erase a dark
matter cusp.Comment: 6 pages, MNRAS, in pres
Future monitoring of charged particle energy deposition into the upper atmosphere and comments on possible relationships between atmospheric phenomena and solar and/or geomagnetic activity
Monitoring of earth's atmosphere was conducted for several years utilizing the ITOS series of low-altitude, polar-orbiting weather satellites. A space environment monitoring package was included in these satellites to perform measurements of a portion of earth's charged particle environment. The charged particle observations proposed for the low-altitude weather satellite TIROS N, are described which will provide the capability of routine monitoring of the instantaneous total energy deposition into the upper atmosphere by the precipitation of charged particles from higher altitudes. Such observations may be of use in future studies of the relationships between geomagnetic activity and atmospheric weather pattern developments. Estimates are given to assess the potential importance of this type of energy deposition. Discussion and examples are presented illustrating the importance of distinguishing between solar and geomagnetic activity as possible causative sources. Such differentiation is necessary because of the widely different spatial and time scales involved in the atmospheric energy input resulting from these various sources of activity
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Asteroids in the Inner Solar System I - Existence
Ensembles of in-plane and inclined orbits in the vicinity of the Lagrange
points of the terrestrial planets are integrated for up to 100 million years.
The integrations incorporate the gravitational effects of Sun and the eight
planets (Pluto is neglected). Mercury is the least likely planet, as it is
unable to retain tadpole orbits over 100 million year timescales. Both Venus
and the Earth are much more promising, as they possess rich families of stable
tadpole and horseshoe orbits. Our survey of Trojans in the orbital plane of
Venus is undertaken for 25 million years. Some 40% of the survivors are on
tadpole orbits. For the Earth, the integrations are pursued for 50 million
years. The stable zones in the orbital plane are larger for the Earth than for
Venus, but fewer of the survivors are tadpoles. Both Venus and the Earth also
have regions in which inclined test particles can endure near the Lagrange
points. For Venus, only test particles close to the orbital plane are stable.
For the Earth, there are two bands of stability, one at low inclinations (i <
16 degrees) and one at moderate inclinations (between 24 degrees and 34
degrees). The inclined test particles that evade close encounters are primarily
moving on tadpole orbits. Our survey of in-plane test particles near the
Martian Lagrange points shows no survivors after 60 million years. Low
inclination test particles do not persist, as their inclinations are quickly
increased until the effects of a secular resonance with Jupiter cause
de-stabilisation. Numerical integrations of inclined test particles for
timespans of 25 million years show stable zones for inclinations between 14 and
40 degrees.Comment: 20 pages, 21 figures, Monthly Notices (in press
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