The intersection of the periodic orbit with the Poincaré section is a fixed point of the Poincaré map F. By a translation, the point can be assumed to be at x = 0.

By using the atmosphere of Mars to slow down the spacecraft in its orbit, rather than firing its engine or thrusters, Odyssey was able to save more than of propellant.

By attaching a counterweight at the end ( or by further extending the cable upward for the same purpose ), the center of mass is kept well above the level of geostationary orbit.

By using a counterweight, a cable would be lowered from geostationary orbit to the surface of Earth, while the counterweight was extended from the satellite away from Earth, keeping the cable constantly over the same spot on the surface of the Earth.

* 06: 53 UT The Khabarovsk ground station sends Gagarin the following message via HF radio, " By order of No. 33 ( General Nikolai Kamanin ) the transmitters have been switched on, and we are transmitting this: the flight is proceeding as planned and the orbit is as calculated.

By extension, the term year can mean the orbital period of any planet: for example, a " Martian year " is the time in which Mars completes its own orbit.

By varying the magnetic sail's field strength over the course of its orbit, a magnetic sail can give itself a " perigee kick " raising the altitude of its orbit's apogee.

By leaving the vehicle's power source on the ground and by using ambient atmosphere as reaction mass for much of its ascent, a lightcraft would be capable of delivering a very large percentage of its launch mass to orbit.

By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body ( such as a planet orbiting the Sun even closer than Mercury ) had been fruitless.

By the same formula we can find the geostationary-type orbit of an object in relation to Mars ( this type of orbit above is referred to as an areostationary orbit if it is above Mars ).

By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, and concluded that they must be binary systems ; the first orbit of a binary star, however, was not computed until 1827, when Félix Savary computed the orbit of Xi Ursae Majoris.

By tilting the axis of the Orbital relative to its orbit around a star a convenient day-night cycle can be experienced by the inhabitants.

By definition, the positions of the Tropic of Cancer, Tropic of Capricorn, Arctic Circle and Antarctic Circle all depend on the tilt of the Earth's axis relative to the plane of its orbit around the sun, known technically as the " obliquity of the ecliptic ".

By the year 2200, comet 78P / Gehrels will probably migrate outwards into a centaur-like orbit.

By attaching a counterweight at the end, inertia ensures that the cable remains stretched taut, countering the gravitational pull on the lower sections and thereby allowing the elevator to remain in geostationary orbit.

By comparison, the International Space Station and Space Shuttle typically orbit at 350 – 400 km, within the F-layer of the ionosphere where they encounter enough atmospheric drag to require reboosts every few months.

By analyzing the perturbation of Kugultinov's orbit due to the gravitational pull of Themis, the mass of Themis was determined to be approximately 2. 89 solar masses.

By 1845 astronomers found that the orbit of planet Uranus around the Sun departed from expectations.

By analysing irregularities in the orbit, Karpal discovers that the devastating burst of energy will reach Earth within the next four days.

By leaving the vehicle's power source on the ground and by using ambient atmosphere as reaction mass for much of its ascent, a lightcraft could potentially be capable of delivering a very large percentage of its launch mass to orbit.

By November 1961, the Soviets had launched Yuri Gagarin and Gherman Titov into orbit during the Vostok 1 and Vostok 2 manned orbital flights.

By 1971, 12 percent of the total area of South Vietnam had been sprayed with defoliating chemicals, at an average concentration of 13 times the recommended USDA application rate for domestic use.

By 1971, 12 percent of the total area of South Vietnam had been sprayed with defoliating chemicals, at an average concentration of 13 times the recommended USDA application rate for domestic use.

By the 13 June, the Imperial Field Commander, Prince Louis of Baden, had joined them in Großheppach.

By both chance and providence, Ruth, a destitute, widowed and childless outsider, becomes an ancestress of King David ( Ruth 4: 13 ).

By age 13 Chaplin had fully abandoned education.

By the time he stepped down in 1988 he had completed 13 years at the production helm.

By 13, 000 to 11, 000 BCE, people began collecting wild grains.

By 1910, 13. 5 million immigrants were living in the United States.

By forging Mathieu as an absolute rationalist, analyzing every situation, and functioning entirely on reason, he removed any strands of authentic content from his character and as a result, Mathieu could " recognize no allegiance except to self " ( Sartre 1942: 13 ), though he realized that without " responsibility for my own existence, it would seem utterly absurd to go on existing " ( Sartre 1942: 14 ).

By winning their first 13 games, the Saints also set the record for the longest undefeated season opening ( 13 – 0 ) by an NFC team since the AFL – NFL merger, surpassing the previous record ( 12 – 0 ) held by the 1985 Chicago Bears.

By the time the civil conflict ended and the government of New Granada and the government of the Isthmus had negotiated the Isthmus's reincorporation to the union, Panama's First Republic had been free for 13 months.

By July 2005, Coca-Cola enjoyed a market share of 19. 4 percent, followed by Pepsi with 13 percent.

By 13 March Richard had returned to England, and by 12 May he had set sail for Normandy with some 300 ships, eager to take the war to Philip.

By the time he was 13 years old, his father was also dead, having ended his days in Ballymena dependent on the charity of relatives.

By this time, the Metropolitan Police had grown from its initial 1, 000 officers to about 13, 000 and needed more administrative staff and a bigger headquarters.

By 1750, slavery was a legal institution in all of the 13 American colonies, and the profits of the slave trade and of West Indian plantations amounted to 5 % of the British economy at the time of the Industrial Revolution.

By 1927, there were 13 states, both in the North and South, that considered some form of anti-evolution law.

By this time the denomination operated two colleges, a medical school, a dozen academies, 27 hospitals, and 13 publishing houses.

By November 13, the Taliban had withdrawn from both Kabul and Jalalabad.

By age 13, he had scored over 1, 000 goals.

** Holocaust: By order of the Vichy France government headed by Pierre Laval, French police officers round-up 13, 000 – 20, 000 Jews and imprison them in the Winter Velodrome.

By this time, the group had largely disowned the upbeat pop singles from the Britpop era, and favoured the more arty, experimental work on Blur and 13.

By 2001, the membership had increased to approximately 2, 100 men in 25 provinces, 700 enclosed nuns in 70 monasteries, and 13 affiliated Congregations and Institutes.

By an ordinance of Louis Philippe I of France of 13 August 1830, it was decided that the king's children ( and his sister ) would continue to bear the arms of Orléans, that Louis-Philippe's eldest son, as Prince Royal, would bear the title of duc d ' Orléans, that the younger sons would continue to have their existing titles, and that the sister and daughters of the king would only be styled " princesses d ' Orléans ", which meant the Orléans royalty did not take the name " of France ".