What is Period: Definition and 1000 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. H

    Jupiter's Equatorial Rotation Period

    How would I find Jupiter's equatorial rotation period when it begins to tear the planet apart? Is it true that if the centrifugal force is greater than the gravitational force the material can be torn apart? If this is right, can I just set up an inequality for the centrifugal force >...
  2. D

    Solving for Moon B's Orbital Period: A Homework Challenge

    Homework Statement Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 5r. Moon A takes 50 days to complete one orbit. How long does it take moon B to complete and orbit? Homework Equations Kepler's Third Law The...
  3. D

    Proving Periodicity for a Function with Two Elements and a Constant Period

    Homework Statement The elements of f(t) are 1+kt and t here are 0<t<1 the other element is 1 and t here are 1<t<2. f(t+2)=f(t) prove if k is not equal to zero, the period f is 2. i know the graph of element 1 but how should I graph the other element with k. Based from the graph...
  4. D

    What is the Fundamental Period of sin(5t + π) on the Interval (-∞, +∞)?

    Homework Statement The function is defined on (-infinity, +infinity) Find the fundamental period of sin(5t+\pi) Homework Equations The Attempt at a Solution f(x)=sin(5t+\pi) f(x)=f(x+2p) f(x+2p)=sin(5t+\pi+2p) f(x+2\pi/5)=sin(5t+\pi+2\pi/5) The period i got was...
  5. X

    Period of orbiting satellites - Mastering Physics 13.20

    Homework Statement Three satellites orbit a planet of radius R, as shown in the figure. Satellites S_1 and S_3 have mass m. Satellite S_2 has mass 2 m. Satellite S_1 orbits in 250 minutes and the force on S_1 is 10,000 N. See attached figure (knight_Figure_12_26.jpg). a. What is the...
  6. K

    Period of Oscillation of a Meter Stick

    Homework Statement Measure the period of oscillation of a meter stick suspended at one end for small amplitudes. Does T = 2*sqrt(2I/mgL) when I is the rotational inertia about one end? Derive this relation. Homework Equations I = rotational inertia m = mass g = gravitational...
  7. R

    What is the change in period of a pendulum with a temperature-dependent length?

    Homework Statement A simple pendulum uses a steel wire as the string. The length of this wire is 1.1m at room temperature. If the temperature is increased by 10.8 degrees Celsius, the length of the wire increases by 1.58 mm. What is the change in period of the pendulum? Homework...
  8. A

    Calculating period of a function

    Hi I've been given this question for cooursework and am really struggling, help needed! heres the question: What is the period of the function? f(t) = 3t 0≤t≤π, where f(t)=f(t+1) Homework Equations The Attempt at a Solution
  9. F

    Finding Period from Mass and Time: Homework Help

    Homework Statement Hey guys I am not sure how to find the period when I am given the mass and the time, for example mass= .10 k and Time for vibrations= 8.86s Find the Period Homework Equations Im not sure maybe f = 1/t The Attempt at a Solution No idea how to incorporate mass in...
  10. J

    Comet with eccentricity of 0.7 and 200 year period

    Homework Statement A comet of the star Sol has an eccentricity of .7. It takes 200 yrs to complete on orbit 1)find the average distance of the comet from Sol. 2) Find the perihelion and aphelion distances from Sol 3)find the velocity of the comet at perihelion Homework Equations...
  11. U

    Understanding Standing Waves at 60 Hz and 0.4 m Wavelength

    Homework Statement Draw a sketch of of a standing wave created by a string fixed at two ends, the frequency is 60 Hz, the wavelength is 0.4 m. Draw a profile with times t=0, T/4, T/2, 3T/2 Homework Equations period= 1/frequency, The Attempt at a Solution i know that at t/4, you...
  12. M

    Period of Aquila (Latin: 'eagle') constellation

    Ref: http://www.bbc.co.uk/dna/h2g2/A29019332 Does this constellation appears moving from the Earth's reference? I have just read that it travels the 12 zodiacal constellations with a speed of about 67 years per degree. Any thoughts about it? Just found that it is the star Altair...
  13. S

    Do Adults and Children Swing at the Same Frequency?

    URGENT//Period and frequency question Homework Statement 1) An adult and a child are sitting on adjacent identical swings. Once they get moving, the adult, by comparison to the child, will necessarily swing with a) a much greater period b) a much greater frequency c) the same...
  14. M

    How Do You Derive the Torsional Pendulum Period Formula?

    Homework Statement I have to show the formula derivation of this: T=2*pi*\sqrt{\frac{2IL}{pi*r^{4}*G}} based on the fact that I know this: \tau=I\alpha=\frac{pi*G*r^{4}}{2L}\theta Homework Equations See above The Attempt at a Solution Well, I know T=2pi/\omega and...
  15. S

    Finding Density of a Planet Using Period of Orbit

    Homework Statement A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 1.78 hours. What is density (mass/volume) of the planet? Assume that the planet has a uniform density.Homework Equations T^{2}=4*PI^2*r^3/G*M Density =...
  16. D

    Mathematical pendulum - Arbitrary-amplitude period

    Homework Statement Hi! I have a problem with mathematical pendulum. I had to prove that the right expression for the period of the mathematical pendulum is: T=\sqrt{\frac{8l}{g}}\int_0^{\theta_0}\frac{d\theta}{\sqrt{\cos \theta- \cos \theta_0}} I did that via energy, but now I have to...
  17. B

    Find mass of mars given period of moon orbit and radius of orbit

    Homework Statement Given data: A moon of Mars orbits with a period of 459 minutes. The radius of the moon's orbit is 9.4x10^6 m. What is the mass of mars? Homework Equations The Attempt at a Solution The only relevant equation I could find was Fmars on moon= (G*m1*m2)/(r2)...
  18. L

    Orbital Period and Velocity Question

    Homework Statement The space shuttle is in a 310 mile high orbit. What are the shuttle's orbital period, in minutes, and its speed? Homework Equations Period = 2(pi)r/v The Attempt at a Solution I can't figure out how to find the period without already having the velocity.
  19. G

    Computing semimajor axis from ecentricity and period

    Homework Statement Compute the semimajor axes "a" of Halley's Comet. Given: orbital eccentricity e = 0.9673 period P =76 days (2.39674E9 seconds) Gravitational Constant G = 6.67428E-11 solar mass M = 1.9891E30 Kg. Also used in equations are: L = angular momentum of center of mass...
  20. K

    How Long and Fast Did Apollo 11 Orbit the Moon?

    Homework Statement On July 19, 1969, Apollo 11's orbit around the moon was adjusted to an avearge orbit of 111km. The radius of the moon is 1785km, and the mass of the moon is 7.3 * 10^22kg. a. How many minutes did Apollo 11 take to orbit the moon? b. At what velocity did it orbit the moon...
  21. S

    Find the distance from the sun to the planet known the orbital period problem

    Homework Statement the problem asks to find the distance from the sun to a planet. the only information the question gives the the orbital period of 27 years and asks for the answer in km. Homework Equations c= (2)(pi)(r) The Attempt at a Solution assuming the planet revolves...
  22. M

    Fundamental period of a signal

    Hi all, First post here for me. 1. Problem Statement Find the fundamental period of: 3cos(1.3PiN) - 4sin(0.5piN +0.5Pi) 2. Relevant equations: T = 2PI / w 3. My attempt: Not sure how to proceed. By themselves the fundamentals period would be: 3cos(1.3PiN) w = 1.3Pi...
  23. P

    Pendulum Experiment - time period and length of string

    Homework Statement Hi, in class we done the classic pendulum experiment to investigate the relationship between time period and the length of the string. Here are my averages for time period and the length: Length (m)----Average time (T1+T2/2) 0.2 11.3 0.4...
  24. J

    Period of spring -> magnetic field

    http://img142.imageshack.us/img142/7485/physicsb.jpg Hi, sorry that I only mention a first strategy for solution for the following problem, but I can not think of a better one. For the question you will need to look at the image in the appendix: 1. You will see a frame, consisting of...
  25. J

    How do you determine a f(x) is periodic and fundamental period

    OKay so here are two examples: let say 1) f(x) = cos 2x + cos x how do you determine whether this function is periodic? I know I have to find period for each cosine. The first one is pi and second is 2pi. Then what do you do? And eventually, how do you determine the fundamental period...
  26. G

    Question on finding the Fundamental Period of a periodic FM signal

    Homework Statement s(t)=13*cos(2000*pi*t + 100*sin(8*pi*t)) Determine the fundamental period of this signal, i.e., the shortest period. Homework Equations x(t)=A*cos(2*pi*f(c)*t + a*sin(2*pi*f(m) + phi)) A=13; f(c)=1000; a=100; f(m)=4; phi=0 Inverse Euler's - A*cos(omega*t + phi) =...
  27. J

    Find the period of oscillation of a bead on a cycloid string

    Homework Statement Find the period of oscillation of a bead on a cycloid string. If it matters, the original equations of the cycloid were x=a(\theta-sin\theta) and y=a(1+cos\theta) Homework Equations This is a small part of a larger problem... I found the equation of motion of a bead on a...
  28. K

    How did scientists compose the equation for period?

    T=2pi√(l/g) Is it in radian*seconds?
  29. A

    Deriving Orbital Period with Kepler's & Taylor Expansions

    Homework Statement Use Kepler's Third Law and a Taylor expansion to derive the following approximation for the orbital period of a satellite in low Earth orbit with a constant height h above the surface of the Earth. h << R_earth : P \approx P_{0}(1+3h/2R_{e}) Homework Equations Kepler's...
  30. S

    Determine the amplitude of a mechanical wave given only it's velocity and period

    Homework Statement A transverse sinusiodal wave on a string has a period T= 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t=0, an element of the string at x=0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s. Homework...
  31. S

    Shortest period of a simple pendulum

    A uniform disk of radius 0.2m and 5.6 kg mass has a small hole distance d from the disk's center that can serve as a pivot point. What should be the distance d so that this physical pendulum will have the shortest possible period? What will be the period at this distance? So, I know that the...
  32. B

    Mass of a planet given it's satellites orbital radius & period

    Ah, please, someone help me. I've been working on this problem for half an hour, it's the last question on my review before my test, which i want to write right now (correspondence). Homework Statement If a satellite requires 2.5 h to orbit a planet with an orbital radius of 2.6 x 10^5 m...
  33. J

    Period of oscillations of a cone

    Homework Statement A particle of mass m moves on the inside surface of a smooth cone whose axis is vertical and whose half-angle is alpha . Find the period of small oscillations about a horizontal circular orbit a distance h above the vertex.Homework Equations Not sure. Lagrangian maybe F = ma...
  34. G

    Find frequency and period of oscillation

    Homework Statement Consider the pulley to be ideal. If the system disturbed from its equilibrium position by pulling the right hand mass down a slight amount and then released, determine the frequency and period of the oscillation. Radius of pulley is r=2m and I bar of the pulley is 10kg/m2...
  35. P

    Circular path-) finding period

    Circular path---) finding period Homework Statement A 50-g weight tied to a string is twirled in uniform circular motion. If the circumference of the circular path is 207.3 cm and the weight completes 67.1 revolutions per minute, what is the period of the motion, in seconds? Homework...
  36. D

    Calculating the period of a pendulum

    Let the moment of inertia of a pendulum be I and the distance from pivot to the center of gravity of the pendulum, D. Use the conversation of energy principle to show that the period of this pendulum is 2 * pi * sqrt(I / [M*g*D]). My attempt is as follows, I, displace the pendulum by small...
  37. B

    Medical Birth control pills i missed my period

    apparently the green pills are placebo pills I was going to start taking them when my period started it hasnt started yet & my friend said it hasn't started yet because I haven't started taking the green pills I've just been taking the pink pills obviously, I don't want to take the placebo...
  38. K

    Two sinusoidal waves of the same period

    Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by y(x,t)=(2.5 mm)sin(26.0x -4.0 s-1 * t+0.400 rad), with x in meters and t in seconds. 1.) What is the wavelength of the two waves (m)? [I...
  39. A

    What is the period of a bobbing cork?

    Homework Statement A cork floats in water. The cork is a cylinder with radius 1 cm and height 3.4 cm. The density of the cork is 0.55 g/cc. Calculate the period of oscillation if the cork is pushed down a little and released. Homework Equations I think I need help with the restoring...
  40. R

    Kinematics - Minimization of a period

    Homework Statement A mass is released from rest atop an incline angled at Θ relative to the horizon, from a certain distance up the incline (Not height), x_0. This point up the incline is denoted P. The mass then travels along a horizontal path of length S. The mass then goes up an incline...
  41. O

    Differential equations: period of a mass on a hanging spring

    Hey guys. This was a homework problem (I could never figure it out) and I asked my instructor for help as well as researching on the Internet, but still no dice. It seems basic enough but it bothers me that I still don't know how to solve it. Homework Statement Show that the period of the...
  42. S

    Find period of circular disk physical pendulum

    Homework Statement A uniform circular disk whose radius R is 40.0 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period of oscillation? (b) At what radial distance r < R is there a point of suspension that gives the same period? R = .40 m g = 9.81...
  43. L

    Perturbation approximation of the period of a pendulum

    Homework Statement Find the perturbation approximation of the following in terms of powers of θ0. T=\sqrt{\frac{8L}{g}}\int^{\theta_0}_{0} \frac{d\theta}{\sqrt{cos\theta - cos\theta_0}} It is helpful to first perform the change of variable u = θ/θ0 in the integral Homework Equations...
  44. C

    Calculating & Plotting Period of Vibration for Slender Rod AB

    Homework Statement The slender rod AB of weight W_{AB} is attached to two identical collars, each of weight W. The system lies in a horizontal plane and is in equilibrium in the position shown when the collar A is given a small displacement and released. Calculate and plot the period of...
  45. F

    Orbital period variation in binary system

    Homework Statement Using the conservation of angular momentum and Kelper's third law, show that the relative change in orbital period produced by mass transfer is given by 1/P * dP/dt = 3 dM1/dt * (M1 - M2)/(M1M2) Homework Equations L = mu * sqrt(GMa) P^2 = (4*PI^2)/(G(M1+M2)) * a^3...
  46. R

    What is the period of function g(t)?

    How do I find the period of this function? g(t) = cos (4t) + sin (t)
  47. I

    Gravitational force, Speed, and period of a Satellite.

    Homework Statement A satellite that has a mass of 300 kg moves in a circular orbit 5.00 X 107 m above Earth's surface. (a) What is the gravitational force on the satellite? (b) What is the speed of the satellite? (c) What is the period of the satellite? Homework Equations Fg=...
  48. I

    Orbital Period of Apollo Mission

    Homework Statement On each of the apollo missions the command module was placed in a very low aprox circular orbit above the moon. Assum the avrg hieght was 60km above surface of moon and moons radius is 7738km. (Mass of moon=7.34x10^22kg) What was the command modules orbital period...
  49. O

    Does Elevator Acceleration Affect the Oscillation Period of a Spring?

    Homework Statement A mass attached by a light spring to the ceiling of an elevator oscillates vertically while the elevator ascends with constant acceleration. Is the period greater than, less than, or the same as when the elevator is at rest Homework Equations T=2pi * sqrt(m/k) The...
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