Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

( Thus Aristotle first suggested a reciprocal or circular causality-as a relation of mutual dependence, action, or influence of cause and effect.

Thus, it results in a circular chain.

Thus to move from one circular orbit to another, at least two brief applications of thrust are needed.

Thus, the circular keyspace is split into contiguous segments whose endpoints are the node identifiers.

Thus if a cone emitted with an initially circular ( or spherical ) cross-section becomes distorted into an ellipse ( ellipsoid ), it is possible for the volume distortion to vanish if the distortions along the principal axes counteract one another.

Thus, Uechi Ryū is also heavily influenced by the circular motions which belong to the kung fu from Fujian province.

Thus, a particle injected into a dipole magnet will travel on a circular or helical trajectory.

Thus the 3-sphere is realized as a disjoint union of these circular fibers.

Thus the total surface area of a right circular cone is:

Thus if cubic units is the volume of the right circular cylinder, by Riemann sums,

Thus both arms have a field argent, both use a chief, which is filled with three circular or near circular devices-bezants and escallops.

Thus, whereas KSHV genome is circular in the nucleus of latently infected cells, it is packaged into infectious viruses as a linear molecule.

Thus, the cross-section of a metal pipe is usually circular.

Thus, when the Russians sent up their first sputnik, American chagrin was human enough, and American determination to put American satellites into orbit was perfectly understandable.

Thus the term asteroid has come increasingly to refer specifically to the small bodies of the inner Solar System out to the orbit of Jupiter, which are usually rocky or metallic.

Thus, reasoned Oort, a comet could not have formed while in its current orbit, and must have been held in an outer reservoir for almost all of its existence.

Thus a single-stage rocket is at a disadvantage because it must carry its entire vehicle mass to orbit, which in turn reduces payload capacity.

Thus it completes one orbit around the Sun for every 4. 02 annual orbits of the Earth.

Thus, when meteoroids meet the Earth's atmosphere head-on ( which would only occur if the meteors were in a retrograde orbit ), the combined speed may reach about 44 miles per second ( 71 kilometers per second ).

Thus, there must be some way to accelerate the spacecraft when it reaches that outer planet if it is to enter orbit about it.

Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the 30 km / s speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane — tasks that are impossible with current spacecraft propulsion systems alone, making gravity assist maneuvers essential.

Thus for the geostationary transfer orbit 7. 73-3. 07 = 4. 66 km / s, the same as, in the absence of gravity, the deceleration would cost.

Thus, 17 hours in each orbit remained for scientific observation.

Thus, Gold's gravity is insufficient to hold its atmosphere, which is pulled loose into an independent orbit around Voy.

Thus, a tuft is either orbiting too slowly ( the " in " tuft ) or too quickly ( the " out " tuft ), compared to the atmosphere, which is in orbit at all points.

Thus if a sky hook has been created, it can effectively convert waste asteroid or lunar material thrown to it, into high grade rocket fuel ( that is by replacing the fuel spent to maintain its own orbit ), by virtue of their kinetic energy.

Thus for example the delta-v for a Hohmann transfer from Earth's orbital radius to Mars ' orbital radius ( to overcome the Sun's gravity ) is many kilometres per second, but the incremental burn from LEO over and above the burn to overcome the Earth's gravity is far less if the burn is done close to the Earth than if the burn to reach a Mars transfer orbit is performed at Earth's orbit, but far away from Earth.

Thus viewing this crater in detail must be done from orbit.

Thus for a more detailed view, the crater must be viewed from orbit.

Thus this crater can not be viewed from Earth, and has only been seen from orbit.

Thus, its iteration orbit, or flow, under suitable provisions ( e. g., f '( 0 ) ≠ 1 ), amounts to the conjugate of the orbit of the monomial, Ψ < sup >− 1 </ sup >( f '( 0 )< sup > n </ sup > Ψ ( x )), where n in this expression serves as a plain exponent.

Thus, so far it appears that an Earth-like planet could easily orbit the star without any complications caused by a gravitationally perturbing body.

Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.

Thus Faulkner reminds us, and wisely, that the `` new '' South has gradually evolved out of the Old South, and consequently its agrarian roots persist.

Thus the image of man has suffered complete fragmentation in personal and spiritual qualities, and complete objectification in sub-human and quasi-mechanistic powers.

Thus earth has fallen to the center of the universe.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the government simultaneously undertook the vast burden of social security which had traditionally been privately discharged, and created a national scarcity which has engendered calamitous problems of social security.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus F satisfies Af if and only if F has the form Af.

Thus in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.

Thus to has light stress both in that was the conclusion that I came to and in that was the conclusion I came to.

Thus, the public-limit price is raised further by a given wage increase the longer it has been since the previous price increase.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus, a well-planned adobe wall of the appropriate thickness is very effective at controlling inside temperature through the wide daily fluctuations typical of desert climates, a factor which has contributed to its longevity as a building material.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus, at pH between 2. 2 and 9. 4, the predominant form adopted by α-amino acids contains a negative carboxylate and a positive α-ammonium group, as shown in structure ( 2 ) on the right, so has net zero charge.

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

Thus, study of this Barnum / Forer effect has been mostly focused on the level of acceptance of fake horoscopes and fake astrological personality profiles.

Thus, it has a year 0, the years before that are designated with negative numbers and the years after that are designated with positive numbers.

Thus the " Aegean Area " has now come to mean the Archipelago with Crete and Cyprus, the Hellenic peninsula with the Ionian islands, and Western Anatolia.

Thus, most recipes that use bay leaves will recommend their removal after the cooking process has finished.

Thus he has him murdered.