DYNAMICS AROUND AN ASTEROID MODELED AS A MASS TRIPOLE

The orbital dynamics of a spacecraft orbiting around irregular small celestial bodies is a challenging problem. Diffculties to model the gravity field of these bodies arise from the poor knowledge of the exact shape as observed from the Earth. In order to understand the complex dynamical environment in the vicinity of irregular asteroids, several studies have been conducted using simplified models. In this work, we investigate the qualitative dynamics in the vicinity of an asteroid with an arched shape using a tripole model based on the existence of three mass points linked to each other by rods with given lengths and negligible masses. We applied our results to some real systems, namely, asteroids 8567, 243 Ida and 433 Eros and also Phobos, one of the natural satellites of Mars.

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Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube

Mathematical Problems in Engineering ◽

10.1155/2015/493903 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 4

Author(s):

Flaviane C. F. Venditti ◽

Antonio F. B. A. Prado

Keyword(s):

Gravitational Field ◽

Three Dimensional ◽

Orbital Dynamics ◽

Keplerian Orbits ◽

The Earth ◽

Celestial Bodies ◽

Good Potential ◽

Exact Shape ◽

Nonspherical Shape ◽

Irregular Body

The orbital dynamics around irregular shaped bodies is an actual topic in astrodynamics, because celestial bodies are not perfect spheres. When it comes to small celestial bodies, like asteroids and comets, it is even more import to consider the nonspherical shape. The gravitational field around them may generate trajectories that are different from Keplerian orbits. Modeling an irregular body can be a hard task, especially because it is difficult to know the exact shape when observing it from the Earth, due to their small sizes and long distances. Some asteroids have been observed, but it is still a small amount compared to all existing asteroids in the Solar System. An approximation of their shape can be made as a sum of several known geometric shapes. Some three-dimensional figures have closed equations for the potential and, in this work, the formulation of a cube is considered. The results give the mappings showing the orbits that are less perturbed and then have a good potential to be used by spacecrafts that need to minimize station-keeping maneuvers. Points in the orbit that minimizes the perturbations are found and they can be used for constellations of nanosatellites.

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The cometary impactor flux at the Earth

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307003559 ◽

2006 ◽

Vol 2 (S236) ◽

pp. 441-450 ◽

Cited By ~ 7

Author(s):

Paul R. Weissman

Keyword(s):

Size Distribution ◽

Poor Knowledge ◽

Cometary Nuclei ◽

Long Period ◽

The Poor ◽

The Earth ◽

The Mean ◽

Impact Energies ◽

Near Earth Asteroids ◽

Perihelion Passage

AbstractComets account for a small but very significant fraction of impactors on the Earth. Although the total number of Earth-crossing comets is modest as compared with asteroids, the more eccentric and inclined orbits of the comets result in much higher encounter velocities with the planet. Additionally, some Earth-crossing comets are significantly larger than any current near-Earth asteroids (NEAs); comets 1P/Halley and C/1995 O1 Hale-Bopp are good examples of this. Thus, the most energetic impacts on the Earth likely result from comets and not NEAs. The mean impact probability for long-period comets is 2.4× 10−9per comet per perihelion passage, assuming the perihelion distribution of Everhart (1967), with a most probable encounter velocity of 53.5 km sec−1. There are 21 known Earth-crossing Jupiter-family comets with a mean impact probability of 1.6× 10−9per comet per year and a most probable encounter velocity of 17.0 km sec−1. For the 16 known Earth-crossing Halley-type comets the mean impact probability is 1.2× 10−10per year with a most probable encounter velocity of 51.3 km sec−1. The poor knowledge of the size distribution of cometary nuclei makes it difficult to estimate actual impact energies at this time, though that situation is slowly improving, in particular for the Jupiter-family comets.

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III. On the nature and construction of the sun and fixed stars

Philosophical Transactions of the Royal Society of London ◽

10.1098/rstl.1795.0005 ◽

1795 ◽

Vol 85 ◽

pp. 46-72 ◽

Cited By ~ 13

Keyword(s):

Central Body ◽

Planetary System ◽

Considerable Progress ◽

The Sun ◽

Great Satisfaction ◽

The Earth ◽

The World ◽

Celestial Bodies ◽

The Universe ◽

Made In

Among the celestial bodies the sun is certainly the first which should attract our notice. It is a fountain of light that illuminates the world! it is the cause of that heat which maintains the productive power of nature, and makes the earth a fit habitation for man! it is the central body of the planetary system; and what renders a knowledge of its nature still more interesting to us is, that the numberless stars which compose the universe, appear, by the strictest analogy, to be similar bodies. Their innate light is so intense, that it reaches the eye of the observer from the remotest regions of space, and forcibly claims his notice. Now, if we are convinced that an inquiry into the nature and properties of the sun is highly worthy of our notice, we may also with great satisfaction reflect on the considerable progress that has already been made in our knowledge of this eminent body. It would require a long detail to enumerate all the various discoveries which have been made on this subject; I shall, therefore, content myself with giving only the most capital of them.

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Allowing the Poor to Share the Earth

Journal of Moral Philosophy ◽

10.1163/174552411x588982 ◽

2011 ◽

Vol 8 (3) ◽

pp. 335-352 ◽

Cited By ~ 15

Author(s):

Thomas Pogge

Keyword(s):

Environmental Degradation ◽

Natural Resource ◽

Global Fund ◽

Resource Depletion ◽

The Poor ◽

The Earth ◽

Urgent Task ◽

Institutional Mechanism ◽

Natural Resource Depletion

AbstractTwo of the greatest challenges facing humanity are environmental degradation and the persistence of poverty. Both can be met by instituting a Global Resources Dividend (GRD) that would slow pollution and natural-resource depletion while collecting funds to avert poverty worldwide. Unlike Hillel Steiner's Global Fund, which is presented as a fully just regime governing the use of planetary resources, the GRD is meant as merely a modest but widely acceptable and therefore realistic step toward justice. Paula Casal has set forth various ways in which this step might be improved upon. Solid counter-arguments can be given to her criticisms and suggestions. But to specify the best (effective and realizable) design of an appropriate global institutional mechanism with some confidence, economists, political scientists, jurists, environmental scientists, and activists would need to be drawn in to help think through the immense empirical and political complexities posed by this urgent task.

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Aesthetization of the christian ethical ideal in o. wilde's fairy tale «The Happy Prince»

Vìsnik Marìupolʹsʹkogo deržavnogo unìversitetu. Serìâ: Fìlologìâ ◽

10.34079/2226-3055-2020-13-22-11-16 ◽

2020 ◽

Vol 13 (22) ◽

pp. 11-16

Author(s):

Vitaliia Aleksenko ◽

Keyword(s):

Fairy Tale ◽

Ancient Philosophy ◽

Christian Doctrine ◽

Dead Bird ◽

The Poor ◽

The Earth ◽

Christian Love ◽

The Aesthetic ◽

The Relationship ◽

Precious Stones

The paper explores the problem of the relationship between the ideas of aesthetics and the Christian doctrine of active love in the famous tale written by O. Wilde. The research which emphasizes the Christian basis of the author's outlook became the methodological basis of the present study on the background of a detailed analysis of various assessments of the writer's position, interpreted as an immoral aesthete and as a supporter of socialist ideas or a recipient of ideas of ancient philosophy of spiritual beauty. The study proves this in detail, analyzing the plot and figurative solutions of the fairy tale «Happy Prince», taking into account the traditional Christian symbols. Thus, the image of the Prince-Statue, decorated with gold and precious stones, is interpreted as a symbol of Christ, who gives his splendor and power to save the poor. It is also reminiscent of the words of Christ, who tells a young rich man who seeks perfection to sell his wealth and give money to the poor. The very values of the earthly world, gold and precious stones, luxurious things made of them, are transparently interpreted in an ironically reduced tone. The confirmation of the fact that the aestheticization of being yields to the hidden spiritual greatness of Christian love and self-sacrifice is also that that the values of the earthly world, gold and precious stones are transparently interpreted in an ironic tone in the fairy tale. The swallow, being the ancient symbol of the Renaissance, this bird was lured by the perishable beauty of idols and tombs of Egypt, the biblical symbol of captivity. The swallow finds its purpose in the service of the Prince, scattering his precious clothes to the poor. And here the ethical criterion turns out to be higher than the aesthetic one. They are not rewarded on the Earth: the bird dies of the cold, and the remains of an unpresentable statue of the prince are demolished, the decisive word to belong to the professor of aesthetics. However, the angel of God brings the most precious things he has found in this city to the heavenly palaces of the Lord: the tin heart of the Prince, torn by grief, and a dead bird. By analyzing the writer's ideological system with implicit implications, Wilde's position is quite obvious: despite his apparent admiration for the aesthetics of beauty, the writer rejects ultimately the doctrine of aesthetics and exalts Christian values, setting out his concept in the style of a parable.

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Husbanding the Earth and Hedging out the Poor

Land and Freedom ◽

10.4324/9781003063162-2 ◽

2020 ◽

pp. 5-18

Author(s):

Laura Brace

Keyword(s):

The Poor ◽

The Earth

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Dating of Polar Ice By 32Si

Journal of Glaciology ◽

10.3189/s0022143000031828 ◽

1973 ◽

Vol 12 (66) ◽

pp. 411-416 ◽

Cited By ~ 2

Author(s):

Henrik B. Clausen

Keyword(s):

Half Life ◽

Specific Activity ◽

Greenland Ice Sheet ◽

Cosmic Ray ◽

Polar Ice ◽

Poor Knowledge ◽

The Poor ◽

Glacier Ice ◽

Cosmic Ray Flux

32Si dating of glacier ice has hitherto been complicated by the poor knowledge of the half life. Furthermore, fall-out of bomb-produced 32Si impedes the determination of the specific activity of cosmic-ray produced 32Si in recent precipitation. Measurements on well-dated pre-bomb samples from the Greenland ice sheet establish a calibration for 32Si dating of up to 1 000 year old polar ice samples of the magnitude of 1 metric ton. If the technique is used on temperate glaciers, samples of pre-bomb deposits (or from after 1970) must be collected for comparison with samples of old ice, using an apparent half life of 295±25 years. Due to secular cosmic-ray flux variations, the true half life of 32Si is estimated at the slightly higher value of 330±40 years.

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All Plain Sailing

Journal of Navigation ◽

10.1017/s0373463300047020 ◽

1956 ◽

Vol 9 (2) ◽

pp. 230-232 ◽

Cited By ~ 1

Author(s):

E. G. R. Taylor

Keyword(s):

Teaching Practice ◽

Mean Value ◽

Mathematical School ◽

Initial Decision ◽

The Earth ◽

Cylindrical Projection ◽

Extended Plane ◽

History Of ◽

Exact Shape ◽

John Wilson

‘The Earth is an ellipsoid’, says the Admiralty Navigation Manual firmly, although in a later volume the expression is softened to ‘approximately ellipsoidal’, For in fact, as was implied by Captain Topley, the exact shape of the Earth is not yet known. Nevertheless, for nautical purposes it appears sound teaching practice to consider it a perfect sphere and then explain the departures of the nautical mile or minute of arc from its mean value. Nor need one quarrel with the Manual's statement that ‘to regard certain small triangles as plane is not to disregard the initial decision to regard the Earth as a sphere’. But the writer next indulges in an historical aside which cannot be allowed to pass. ‘This assumption (he says) gives rise to the expression plane sailing, which is popularly referred to as if plane were spelt plain and the sailing were free from difficulty’. But this is to put the cart before the horse. ‘Plain sailing’ was the original term, and it was only sophisticated into ‘plane sailing’ during the eighteenth century by teachers of navigation among whom John Robertson was the chief. Robertson was master at the Mathematical School of Christ's Hospital towards the middle of the century, and afterwards taught at the Portsmouth Naval College, finally becoming Librarian to the Royal Society. His Elements of Navigation was considered authoritative and ran into many editions, a later master at the Hospital, James Wilson, prefixing to it a Dissertation on the history of navigation which was also accepted as definitive. It is in this volume that we read: ‘Plane sailing is the art of navigating a ship upon principles deduced from the notion of the Earth's being an extended Plane. On this supposition the meridians are esteemed as parallel right lines…’, and the author goes on to what he terms the Plane Chart, with its equally-spaced meridians. There is little doubt that his passage is the source of the theory taught to modern sailors that ‘Plain Chart’ is a corruption of ‘Plane Chart’, while the latter was drawn by people who believed the Earth was flat. Actually we have only to go back a generation from Robertson to find an almost identical description of the chart—actually an equal-spaced conventional cylindrical projection of the sphere—but with the addition of the words ‘The rectangle formed by these meridians and parallels they (i.e. mariners) call the Plain Chart’. This was said in 1714 by John Wilson, a teacher in Edinburgh.

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