For example, a satellite in sun-synchronous orbit might ascend across the equator twelve times a day each time at approximately 15: 00 mean local time.

For the rest of the two spacecrafts ' pass over the near side of the Moon, Mattingly prepared to shift Casper to a circular orbit while Young and Duke prepared Orion for the descent to the lunar surface.

For example, NASA's workhorse space shuttle used cryogenic hydrogen / oxygen propellant as its primary means of getting into orbit, and all of the rockets built for the Soviet space program by Sergei Korolev used liquid oxygen as their oxidiser.

For a satellite in orbit around a planet, the centripetal force is supplied by gravity.

For non-circular orbits or trajectories, only the component of gravitational force directed orthogonal to the path ( toward the center of the osculating circle ) is termed centripetal ; the remaining component acts to speed up or slow down the satellite in its orbit.

For example, the Ruelle – Takens scenario describes how a periodic orbit bifurcates into a torus and the torus into a strange attractor.

For example, if there is a triple star system in which two stars orbit each other closely while a third star is in a more distant orbit, the two closely orbiting stars would be considered a component with two subcomponents.

For example, the planets that orbit the pulsar PSR 1257 are often referred to with capital rather than lowercase letters.

For example, a detector with the mass of Jupiter and 100 % efficiency, placed in close orbit around a neutron star, would only be expected to observe one graviton every 10 years, even under the most favorable conditions.

For many years economical interplanetary travel meant using the Hohmann transfer orbit.

For instance it is the most common way to transfer satellites into geostationary orbit, after first being " parked " in low earth orbit.

For instance, the motion of a spacecraft, regarding its orbit and attitude ( rotation ), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.

For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.

For any specific combination of height above the center of gravity and mass of the planet, there is one specific firing velocity ( unaffected by the mass of the ball, which is assumed to be very small relative to the Earth's mass ) that produces a circular orbit, as shown in ( C ).

# For a given orbit, the ratio of the cube of its semi-major axis to the square of its period is constant.

For example, the 3 numbers which describe the body's initial position, and the 3 values which describe its velocity will describe a unique orbit that can be calculated forwards ( or backwards ).

For example, the orbit of the Moon cannot be accurately described without allowing for the action of the Sun's gravity as well as the Earth's.

For precession of the lunar orbit see lunar precession.

For rocket-powered SSTO, the main challenge is achieving a high enough mass-ratio to carry sufficient propellant to achieve orbit, plus a meaningful payload weight.

For air-breathing SSTO, the main challenge is system complexity and associated research and development costs, material science, and construction techniques necessary for surviving sustained high-speed flight within the atmosphere, and achieving a high enough mass-ratio to carry sufficient propellant to achieve orbit, plus a meaningful payload weight.

For pure rocket approaches Tsiolkovsky's rocket equation shows that dead weight will prevent reaching orbit unless the ratio of propellant to structural mass ( called mass ratio ) is very high — between about 10 and 25 ( i. e. 24 parts propellant weight to 1 part structural weight ; depending on propellant choice ).

For example, no new evidence will demonstrate that the Earth does not orbit around the sun ( heliocentric theory ), or that living things are not made of cells ( cell theory ), that matter is not composed of atoms, or that the surface of the Earth is not divided into solid plates that have moved over geological timescales ( the theory of plate tectonics )... One of the most useful properties of scientific theories is that they can be used to make predictions about natural events or phenomena that have not yet been observed.

For missions beyond low Earth orbit NASA is building the Space Launch System and the Orion spacecraft.

For example, the earth is subject to local torque induced precession due to the gravity of the sun and moon acting upon the earth ’ s axis, but at the same time the solar system is moving around the galactic center.

For accurate astronomical work on land, it was usual to observe sidereal time rather than solar time to measure mean solar time, because the observations of ' fixed ' stars could be measured and reduced more accurately than observations of the Sun ( in spite of the need to make various small compensations, for refraction, aberration, precession, nutation and proper motion ).

For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it is conventional to chart the positions of the stars in the sky according to right ascension and declination, which are based on a frame that follows the Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well.

For that it is assumed that the precession rate is proportional to the projection of the angular velocity of Earth onto the normal direction to Earth, which implies that the plane of oscillation will undergo parallel transport.

For example, it was known in 1859 that the observed perihelion precession of Mercury violated Newtonian mechanics, but the theory remained the best explanation available until relativity was supported by sufficient evidence.

For example, a magnon in a ferromagnet can be considered in one of two perfectly equivalent ways: ( a ) as a mobile defect ( a misdirected spin ) in a perfect alignment of magnetic moments or ( b ) as a quantum of a collective spin wave that involves the precession of many spins.

For the RHSs equal to zero there are non-trivial solutions: torque-free precession.

For such shells, it causes a slow precession of a standing wave about this axis with an angular rate which differs from input one.

" For the same reason, the helical rising ( or zenith ) of Sirius does not slip through the calendar ( at the precession rate of about one day per 71. 6 years ), as other stars do.

( For an alternative approach to calibrating precession, see Alternative Approach to Calibrating Precession in New, alternative, and fringe theories section below ).

For example, the flattening of the Earth causes precession, which causes the axial tilt to change, which affects the long-term movements of all planets.

For example, they provide quantitative predictions of the anomalous precession of the planets in the Solar System, and of the deflection of light by gravity.

For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital.

For example, the orbital 1s < sup > 2 </ sup > ( pronounced " one ess two ") has two electrons and is the lowest energy level ( n

For many of the satellites, it is assumed that the rotation rate is equal to the mean orbital period.

For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the " Linear combination of atomic orbitals molecular orbital method " ansatz.

For a bonding MO with σ-symmetry, the orbital can be labeled σ < sub > g </ sub >, and for an antibonding MO with σ-symmetry the orbital can be labeled σ < sub > u </ sub >, because inversion through the center of symmetry for Figure 4 ( b ) would produce a sign change.

For a bonding MO with π-symmetry the orbital can be labeled π < sub > u </ sub > because inversion through the center of symmetry for Figure 5 ( c ) would produce a sign change.

For example, in internal conversion decay, the energy from an excited nucleus may be used to eject one of the inner orbital electrons from the atom, in a process which produces high speed electrons, but is not beta decay, and ( unlike beta decay ) does not transmute one element to another.

For example, asteroids of the Alinda family are in or close to the 3: 1 resonance, with their orbital eccentricity steadily increased by interactions with Jupiter until they eventually have a close encounter with an inner planet that ejects them from the resonance.

For example, Jupiter's moons Ganymede, Europa and Io are in a 1: 2: 4 orbital resonance.

For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods.

For every element and core ( atomic orbital ) there will be a different binding energy.

For example NASA's space shuttle fires its engines for around 8. 5 minutes, consuming 1, 000 tonnes of solid propellant ( containing 16 % aluminium ) and an additional 2, 000, 000 litres of liquid propellant ( 106, 261 kg of liquid hydrogen fuel ) to lift the 100, 000 kg vehicle ( including the 25, 000 kg payload ) to an altitude of 111 km and an orbital velocity of 30, 000 km / h.

For hardware with the performance used in orbital launch vehicles, expenses of $ 2000 –$ 10, 000 + per kilogram of dry weight are common, primarily from engineering, fabrication, and testing ; raw materials amount to typically around 2 % of total expense.

For very large objects, with very well known orbital elements ( namely, Pluto and Charon ), diameters can be precisely measured by occultation of stars.

For orbital spaceflights, spacecraft enter closed orbits around the Earth or around other celestial bodies.

For example, for ground stations at latitudes of φ = ± 45 ° on the same meridian as the satellite, the time taken for a signal to pass from Earth to the satellite and back again can be computed using the cosine rule, given the geostationary orbital radius r ( derived below ), the Earth's radius R and the speed of light c, as

For example, there are very few asteroids with semimajor axis near 2. 50 AU, period 3. 95 years, which would make three orbits for each orbit of Jupiter ( hence, called the 3: 1 orbital resonance ).

For example, Jupiter's moon Himalia, Saturn's moon Phoebe, and Neptune's moon Nereid have rotation periods in the range of ten hours, while their orbital periods are hundreds of days.

For the bond in the molecule to be stable, the covalent bonding electrons occupy the lower energy bonding orbital, which may be signified by such symbols as σ or π depending on the situation.

For Z > Z < sub > cr </ sub >, if the innermost orbital ( 1s ) is not filled, the electric field of the nucleus will pull an electron out of the vacuum, resulting in the spontaneous emission of a positron ; however, this does not happen if the innermost orbital is filled, so that Z

For example, in the molecular-orbital-linear-combination-of-atomic-orbitals ( LCAO-MO ) approximation, is a molecular orbital ( MO ) given as a linear expansion of atomic orbitals ( AOs ).

For example, suppose that the Earth's orbital position is marked at the summer solstice, when the Earth's axial tilt is pointing directly towards the Sun.