What is Orbital period: Definition and 86 Discussions

The orbital period (also revolution period) is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.
For celestial objects in general the sidereal orbital period (sidereal year) is referred to by the orbital period, determined by a 360° revolution of one celestial body around another, e.g. the Earth orbiting the Sun, relative to the fixed stars projected in the sky. Orbital periods can be defined in several ways. The tropical period is more particular about the position of the parent star. It is the basis for the solar year, and respectively the calendar year.
The synodic period incorporates not only the orbital relation to the parent star, but also to other celestial objects, making it not a mere 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 phenomena or location, such as when any planet returns between its consecutive observed conjunctions with or oppositions 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.
Periods in astronomy are conveniently expressed in various units of time, often in hours, days, or years. They 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 the centre of gravity between two astronomical bodies (barycenter), perturbations by other planets or bodies, orbital resonance, general relativity, etc. Most are investigated by detailed complex astronomical theories using celestial mechanics using precise positional observations of celestial objects via astrometry.

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  1. alexriemann

    A Photon speed for an observer at the photon sphere

    I am asked to compute the orbital period of a photon, in the Scwarzschild spacetime, at the photon sphere for an observer at the same radius, ##r^\star=3M##. I have computed the result, ##\Delta T=6\pi M## where ##c=G=1## ,comparing with the proper time of an observer at infinity. However, as...
  2. S

    Calculation of the orbital period for a binary star system

    Hello guys, Would it be possible to get some help on how to approach this problem? I don't really understand it. do I need to look at the orbital motion of the center of mass here or? If so how should I start? Thanks in advance.
  3. E

    I Circular Orbit in Schwarzschild: Orbital Period

    Schutz finds that the orbital period for a circular orbit in Schwarzschild is $$ P = 2 \pi \sqrt {\frac { r^3} {M} }$$ He gets this from $$ \frac {dt} {d\phi} = \frac {dt / d\tau} {d\phi/d\tau} $$ Where previously he had ## \frac {d\phi}{d\tau} = \tilde L / r^2## and ## \frac {dt}{d\tau} =...
  4. DANIELWR1998

    How do I find way of comparing the density of the Earth and the Moon?

    Surface acceleration is proportional to density and radius of planet (as 2 powers of R cancel with the volume) g(moon)/g(earth) = density(moon)*radius(moon)/density (earth)*radius(earth) = (1/4)*density(moon)/density(earth)
  5. N

    I How to calculate an unknown planet's orbital period?

    In 1846 three astronomers and mathematicians discovered Neptune because Uranus wasn't quite moving as Newton's law of gravity explains. So they did calculations and point the telescope at a specific part of the sky. They discovered Neptune. What formulas did they use? How did they calculate this...
  6. EEristavi

    Universal Gravitation - calculating orbital period of satellite

    I didn't use Kepler's 3rd law and this may be the reason I have a wrong answer. However, I want to know: where I make the mistake. ## ma = \frac {G M m} {R^2}## ## R = (\frac {G M} a)^{1/2}## ##a = \frac {v^2} R## ##V^2 = a R = a (\frac {G M} a)^{1/2} = (G a M)^{1/2}## ##V = (G a M)^{1/4}##...
  7. Johnnyallen

    I Planet mass vs. orbital period

    I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in. Question: Is the mass of the planet also a factor? In other words, does a...
  8. Alexanddros81

    Determine the orbital period of Phobos

    Homework Statement 14.101 The orbit of Phobos, a Martian moon, has an eccentricity of 0.018 and a major semiaxis of length 9380 km. Determine the orbital period of Phobos Homework EquationsThe Attempt at a Solution Can you check my solution?
  9. Y

    Gravitational problem, spacecraft orbital period

    Homework Statement I need help getting started with this problem At what altitude above the surface of the Moon must a lunar module orbit in order to complete each orbit in 1 h 49 min 39 s? Homework Equations g= Gm/r^2 ? The Attempt at a Solution Not quite sure how to start or anything , any...
  10. M

    Orbital Period of the Earth where the Sun's Mass Changes

    Hey, this is going to be my first post here so I'm not sure how it all works, so just tell me if I do something out of order please. Anyway I have been given this homework assignment and part of it was the question stated below...
  11. A

    B Telescope and Stopwatch for the Mass of a Planet

    I was wondering if it is possible to use only a stopwatch and a telescope to find the mass of a planet, such as Saturn. I've experimented with a couple of things but I keep running into problems. I previously asked this question in the homework section, but it does not involve numbers, is not...
  12. A

    How Can You Calculate Saturn's Mass Using a Telescope and Stopwatch?

    Homework Statement Using only a telescope and a stopwatch, find the mass of Saturn.[/B] (This question may or may not make any sense at all, it was a theoretical lab that my professor said without giving us a chance to copy it down and I am trying to recall the question from memory) If it is...
  13. TheBigDig

    What is the orbital period of an asteroid between Earth and Jupiter?

    Homework Statement The orbit of an asteroid extends from the Earth’s orbit to Jupiter’s orbit, just touching both. Assume that the planetary orbits are circular and co-planar and that Newton’s constant G, the mass of the sun Ms, the mass of the asteroid ma and the radii of the Earth’s and...
  14. T

    Finding Orbital Period of Unknown Planet

    Homework Statement A satellite is in circular orbit at an altitude of 800 km above the surface of a nonrotating planet with an orbital speed of 3.7 km/s. The minimum speed needed to escape from the surface of the planet is 9.8 km/s, and G = 6.67 × 10-11 N · m2/kg2. The orbital period of the...
  15. P

    Orbital Period Calculation for Binary Star Systems

    Homework Statement Homework Equations (In picture)[/B]The Attempt at a Solution (In picture) [/B]
  16. AwesomeTrains

    Derivation of orbital period - Hydrogen

    Hey everyone! 1. Homework Statement I've been giving the equation for a gaussian wave packet and from that I have to derive this formula: T_{Kepler}=2\pi \bar n ^3 by doing a first order taylor series approximation at \bar n of the phase: f(x)=f(\bar n)+\frac{df}{dx}|_{\bar n}(x-\bar...
  17. Drakkith

    Exoplanet Eccentricity vs Orbital Period

    I have a question concerning the eccentricity vs orbital period of observed exoplanets. Going to this link let's you plot different exoplanet properties on each axis of a graph. Plugging in Orbital Period for the X-axis and Eccentricity for the Y-axis shows that a trend towards decreasing...
  18. G

    Exploring Positronium's Orbital Period in the Far Future

    In the far future(10^85 years) an “element” called positronium will develop with a diameter of the current observable universe of 93 billion light years. (Remember that light travels at 3 × 10^8 m/s). This element consists of an electron and a positron, both of which have a mass 9.11 × 10^−31...
  19. C

    Day length and orbital period + apparent luminosity

    Homework Statement I am actually an MD student, but I have been working on writing a novel. I wanted to create exoplanets that were suitable for human habitation, and I had a guy help me over the summer come up with plausible numbers for a variety of variables. Where I am having trouble now is...
  20. K

    Orbital period around Schwarzschild radius

    Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...
  21. L

    Given the Mass & Orbital Period, Find the Gravitational Force

    Homework Statement A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? M_E = 6.0x10^{24} kg m_s = 8410 kg T_s = 927 min = 55,620 s G =...
  22. avito009

    Calculation the orbital period of Moon.

    Newton showed that if gravity at a distance R was proportional to 1/R2, then indeed the acceleration g measured at the Earth's surface would correctly predict the orbital period T of the Moon. (Remember Earths gravity causes the moon to orbit the Earth.) We can find the answer using MKS system...
  23. M

    Orbital period of two moons in the same orbit

    1. Homework Statement Two identical moons of mass m maintain opposite positions in the same circular orbit of radius R around a planet of mass M. Find T2 the square of the orbital period. 2. Homework Equations T2=(4*pi2*R3)/ ( G*M ) [b]3. The Attempt at a Solution Hi...
  24. S

    What Is the Orbital Period of a Satellite at 1000 km Altitude?

    Homework Statement If a satellite is to orbit Earth at an altitude of 1.00x10^3 Km, what would be its orbital period? rs = 1.00x10^3 km, Mearth = 5.97x10^24 kg, Gravitational Constant = 6.67x10^-11 Homework Equations T= 2∏√r^3/GM The Attempt at a Solution rs = 0.815484549m...
  25. W

    Calculating Orbital Period of 3 Planets with Similar Mass

    Homework Statement The three planets (v1, v2 and v3) in the diagram all have similar mass and are in a line equally spaced so that v1 and v3 are orbiting around v2 synchronously. If the mass of each of the planets are M and the radius of the orbit is R, what is the orbital period...
  26. S

    Orbital period of eclipsing binaries

    based on the data in the table I want to calculate the orbital period of the eclipsing binary but I want to state my answer in equation form so that any observer can predict the times of future eclipses. Does anyone have an idea on how I go about doing that with the given data. I tried to find a...
  27. J

    Orbital period of a star in the Milky Way?

    So here's a question I'm struggling with: The rotation speed of the sun around the Milky Way center is 220 km/s and it takes the sun around 200 million years to orbit once around center of the galaxy. Given that the rotation curve is relatively flat (i.e. the rotation speed stays the same as...
  28. B

    Determine Orbital Period Of Satellite

    Homework Statement An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 6.32 m/s^2. Determine the orbital period of the satellite [in minutes].Homework Equations g= G \frac{M_E}{r^2} Solving for r, and G is a constant T^2=K_sr^3...
  29. C

    Orbital period - Where does M1+M2 come from?

    I must say that I have not studied celestial mechanics other than the crumbs I learned at high school. Now, what discomforts me is the orbital period formula I saw on Wikipedia: T=2\pi\sqrt{\frac{a^3}{G(M_1+M_2)}} I do not understand where does this M1+M2 can possibly come from. My thinking is...
  30. C

    Orbital Period of satellite in terms of v and r

    Homework Statement "A satellite orbits the Earth in a circular orbit of radius r. If the orbital speed of the satellite is v, what is the orbital period T of the satellite in terms of v and r? You must explain how you derive the expression for the period."Homework Equations Speed =...
  31. P

    Determining Orbital Period of a Planet

    Using the equation P2 = (4 * pi2 * a3)/(G(M+m)) to find the orbital period of Earth where: P = orbital period a = semi-major axis = 1.50e11 m G = 6.67e-11 m3 kg-1 s-2 M = mass of sun (in this case) = 1.989e30 kg m = mass of Earth = 5.972e24 kg I have been trying to find the orbital...
  32. D

    Universal gravitation 2- determine the planet's orbital period

    Homework Statement A planet's mean distance from the sun is 2.00x10^11 m. Determine the planet's orbital period. Use information found in textbook. Homework Equations So I use the following equations: R=h+Rs T=2∏√(R3/GxMs) From the textbook I got the following values...
  33. M

    Orbital period of satellite about a nonrotating body

    Homework Statement A satellite is in circular orbit at an altitude of 1000 km above the surface of a nonrotating planet with n orbital speed of 5.3 km/s. The escape velocity for the planet is 11.3 km/s. In this situation the orbital period of the satellite, in minutes, is...? Homework...
  34. C

    Deriving an equation for orbital period

    Hi guys, I derived an equation for determining orbital period, given an altitude, speed, and mass of the primary and the object orbiting it. I think it makes sense, but I'd welcome anyone who is willing to check it for conceptual error or nonsensical math. Here is the equation: P = \frac{2 \pi...
  35. P

    Find Aphelion of an elliptical orbit given Perihelion and Orbital Period

    Homework Statement Comet Halley approaches the Sun to within 0.570 AU, and its orbital period is 75.6 years. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean Earth‐Sun distance.) How far from the Sun will Halleyʹs comet travel before it starts its return...
  36. F

    How Does the Bohr Model Calculate Electron Orbital Periods and Number of Orbits?

    1)Use the bohr model, calculate the orbital period in eachlevel(n=1,2,3) 2) the average lifetime of the first excited level of a hydrogen atom is 1.0 10^-8 s. In the bohr model, how many orbits does an electron in the n=2 level complete before returning to the ground level? Homework...
  37. J

    Uncertainty of planetary orbital period

    I've been searching all over the place, and I cannot find any data showing the error bars of orbital periods of planets. Once source estimates the uncertainty of Jupiter to be "1 arcsec per 250 years" but I cannot find anything to back this up. Does anybody have any hints as to where I should...
  38. B

    Show that the satellite's orbital period P at large distances (r a) is given by

    Homework Statement Assuming that the satellite's orbit is circular, show that its orbital period P at large distances (r>>a) is given by the expression: P=[(4pi/GM)^(1/2)] r^(3/2) (1-(3/4)((a^2)/(4r^2)) J(subscript2)) Comment on the behavious of P in the limits as r approaches infinity...
  39. X

    How Far Should a Satellite Be from Earth to Match the Moon's Orbital Period?

    Homework Statement A satellite is placed between the Earth and the Moon, along a straight line that connects their centers of mass. The satellite has an orbital period around the Earth that is the same as that of the Moon, 27.3 days. How far away from the Earth should this satellite be placed...
  40. T

    Discovering mass of a star and orbital period of one of two planets

    Homework Statement Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 41.7 km/s and 55.5 km/s. The slower planet's orbital period is 8.04 years. (a) What is the mass of the star? (b)...
  41. O

    How Do You Calculate the Orbital Period of a Satellite?

    Homework Statement An Earth satellite is observed to have a height of perigee of 100 n mi and a height of apogee of 600 n mi. Find the period of the orbit. Homework Equations (1) Period = (2*pi/sqrt(mu)) * A^(2/3) (2) rp+ra = 2A Where: Mu is the Standard Gravitational Parameter...
  42. M

    How Is the Orbital Period of a Satellite Determined?

    Homework Statement by using Newtons law of universal gravitaion and the relationship for the centripetal force, show that the orbital period T for a satellite circling a planet of mass M in orbit of radius r is given by : T= 2pi sqrt r^3/GM Homework Equations none given The...
  43. B

    How Do You Calculate Orbital Period with Limited Data?

    Homework Statement An Earth station receives data transmitted back in time from a future intergalactic expedition. The table summarizes the data for the moons of a planet that will be discovered in a distant galaxy. Moon 1: only has orbital radius = 5E7 meters Just only this...
  44. C

    Astrophysics: nuclear reactions orbital period spectral class equivalence principl

    Homework Statement 1. Suppose you are told that a star has been observed with a UBV color index of B-V=1.6 and that interstellar reddening is negligible. In addition, its apparent visual magnitude is 9.8. Detailed spectroscopy also reveals that the star has all the characteristics of a main...
  45. S

    Astrophysics - calculating orbital period

    Homework Statement Show that a satellite in low-Earth orbit is approximately P = C(1 + 3h/2R_E) where h is the height of the satellite, C is a constant, and R_E is the radius of the earth) Homework Equations Unsure The Attempt at a Solution I have no idea how to approach this.
  46. H

    Calculating Orbital Period of Asteroid Between Mars & Jupiter

    Homework Statement An asteroid is located between Mars and Jupiter. It is thought that a planet once orbited here but was somehow destroyed and broken up into small chunks(perhaps by getting hit by a comet or asteroid). If an asteroid in this belt has an average distance from the sun of 500 *...
  47. P

    Determining Mass from Orbital Period and Radius

    Homework Statement What is the mass of a planet (in kg and in percent of the mass of the sun), if: its period is 3.09 days, the radius of the circular orbit is 6.43E9 m, and the orbital velocity is 151 km/s.Homework Equations I'm unsure what formulas to use, though these seem relevant. F=...
  48. P

    Finding the Masses of a binary star using the distance, angle and orbital period

    Homework Statement Two stars are in a circular visual binary system. The orbital period of the binary is 30 years. The distance to the binary is 20 parsecs. The angular radius of the orbit of each star is 1". What are the masses of the two stars? Homework Equations I am assuming that...
  49. X

    Problem: Orbital Period - eclipse time - Illumination time ?

    Problem: Orbital Period - eclipse time - Illumination time ?? Homework Statement An educational institute has decided to launch a small satellite having mass and volume of CubeSat specifications i.e. mass of 1.33kg and volume of 10 cm cube. Due to some launch constraints, there are three...
  50. B

    Calculating Orbital Period of Satellites

    How do you calculate the orbital period of an object, eg. a satellite, if the only known values are the radius of the orbit and the mass of the central object?