Theorbital period (alsorevolution period) is the amount of time a givenastronomical object takes to complete oneorbit around another object. Inastronomy, it usually applies toplanets orasteroids orbiting theSun,moons orbiting planets,exoplanets orbiting otherstars, orbinary stars. It may also refer to the time it takes asatellite orbiting a planet or moon to complete one orbit.
For celestial objects in general, the orbital period is determined by a 360° revolution ofone body around itsprimary,e.g. Earth around the Sun.
Periods in astronomy are expressed inunits of time, usually hours, days, or years.Its reciprocal is theorbital frequency, a kind ofrevolution frequency, in units ofhertz.
For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity.
Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period T:
For instance, for completing an orbit every 24 hours around a mass of 100 kg, a small body has to orbit at a distance of 1.08 meters from the central body'scenter of mass.
In the special case of perfectly circular orbits, the semimajor axis a is equal to the radius of the orbit, and the orbital velocity is constant and equal to
where:
r is the circular orbit's radius in meters,
This corresponds to1⁄√2 times (≈ 0.707 times) theescape velocity.
For a perfect sphere of uniformdensity, it is possible to rewrite the first equation without measuring the mass as:
where:
r is the sphere's radius
a is the orbit's semi-major axis,
G is the gravitational constant,
ρ is the density of the sphere.
For instance, a small body in circular orbit 10.5cm above the surface of a sphere oftungsten half a metre in radius would travel at slightly more than 1mm/s, completing an orbit every hour. If the same sphere were made oflead the small body would need to orbit just 6.7mm above the surface for sustaining the same orbital period.
When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean densityρ (in kg/m3), the above equation simplifies to
(sincer now nearly equalsa). Thus the orbital period in low orbit depends only on the density of the central body, regardless of its size.
So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5,515 kg/m3,[2] e.g.Mercury with 5,427 kg/m3 andVenus with 5,243 kg/m3) we get:
T = 1.41 hours
and for a body made of water (ρ ≈ 1,000 kg/m3),[3] or bodies with a similar density, e.g. Saturn's moonsIapetus with 1,088 kg/m3 andTethys with 984 kg/m3 we get:
T = 3.30 hours
Thus, as an alternative for using a very small number likeG, the strength of universal gravity can be described using some reference material, such as water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal"unit of time if we have a unit of density.[citation needed][original research?]
Log-log plot of periodT vs semi-major axisa (average of aphelion and perihelion) of some Solar System orbits (crosses denoting Kepler's values) showing thata³/T² is constant (green line)
Incelestial mechanics, when both orbiting bodies' masses have to be taken into account, the orbital periodT can be calculated as follows:[4]
where:
a is the sum of thesemi-major axes of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular orbits),
M1 +M2 is the sum of the masses of the two bodies,
Orbital periods can be defined in several ways. Thetropical period is more particularly about the position of the parent star. It is the basis for thesolar year, and respectively thecalendar year.
Thesynodic period refers not to the orbital relation to the parent star, but to othercelestial objects, making it not a merely different approach to the orbit of an object around its parent, but a period of orbital relations with other objects, normally Earth, and their orbits around the Sun. It applies to the elapsed time where planets return to the same kind of phenomenon or location, such as when any planet returns between its consecutive observedconjunctions with oroppositions to the Sun. For example,Jupiter has asynodic period of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months.
There are manyperiods related to the orbits of objects, each of which are often used in the various fields ofastronomy andastrophysics, particularly they must not be confused with other revolving periods likerotational periods. Examples of some of the common orbital ones include the following:
Thesynodic period is the amount of time that it takes for an object to reappear at the same point in relation to two or more other objects. In common usage, these two objects are typically Earth and the Sun. The time between two successiveoppositions or two successiveconjunctions is also equal to the synodic period. For celestial bodies in theSolar System, the synodic period (with respect to Earth and the Sun) differs from the tropical period owing to Earth's motion around the Sun. For example, the synodic period of theMoon's orbit as seen fromEarth, relative to theSun, is 29.5 mean solar days, since the Moon's phase and position relative to the Sun and Earth repeats after this period. This is longer than the sidereal period of its orbit around Earth, which is 27.3 mean solar days, owing to the motion of Earth around the Sun.
Thedraconitic period (alsodraconic period ornodal period), is the time that elapses between two passages of the object through itsascending node, the point of its orbit where it crosses theecliptic from the southern to the northern hemisphere. This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, theline of nodes, also precesses with respect to the fixed stars. Although the plane of the ecliptic is often held fixed at the position it occupied at a specificepoch, the orbital plane of the object still precesses, causing the draconitic period to differ from the sidereal period.[5]
Theanomalistic period is the time that elapses between two passages of an object at itsperiapsis (in the case of the planets in theSolar System, called theperihelion), the point of its closest approach to the attracting body. It differs from the sidereal period because the object'ssemi-major axis typically advances slowly.
Also, thetropical period of Earth (atropical year) is the interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at aright ascension of0 hr. One Earthyear is slightly shorter than the period for the Sun to complete one circuit along theecliptic (asidereal year) because theinclined axis andequatorial plane slowlyprecess (rotate with respect toreference stars), realigning with the Sun before the orbit completes. This cycle of axial precession for Earth, known asprecession of the equinoxes, recurs roughly every 25,772 years.[6]
Periods can be also defined under different specific astronomical definitions that are mostly caused by the small complex external gravitational influences of other celestial objects. Such variations also include the true placement of thecentre of gravity between twoastronomical bodies (barycenter),perturbations by other planets or bodies,orbital resonance,general relativity, etc. Most are investigated by detailed complex astronomical theories usingcelestial mechanics using precise positional observations of celestial objects viaastrometry.
One of the observable characteristics of two bodies which orbit a third body in different orbits, and thus have different orbital periods, is theirsynodic period, which is the time betweenconjunctions.
An example of this related period description is the repeated cycles for celestial bodies as observed from the Earth's surface, thesynodic period, applying to the elapsed time where planets return to the same kind of phenomenon orlocation—for example, when any planet returns between its consecutive observedconjunctions with oroppositions to the Sun. For example,Jupiter has a synodic period of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months.
If the orbital periods of the two bodies around the third are calledT1 andT2, so thatT1 < T2, their synodic period is given by:[7]
In the case of a planet'smoon, the synodic period usually means the Sun-synodic period, namely, the time it takes the moon to complete its illumination phases, completing the solar phases for an astronomer on the planet's surface. The Earth's motion does not determine this value for other planets because an Earth observer is not orbited by the moons in question. For example,Deimos's synodic period is 1.2648 days, 0.18% longer than Deimos's sidereal period of 1.2624 d.[citation needed]
The concept of synodic period applies not just to the Earth, but also to other planets as well;[citation needed] the computation of synodic periods applies the same formula as above.[citation needed] The following table lists the synodic periods of some planets relative to each theSun and each other:[original research?][citation needed]
