Period Definition and 1000 Threads

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. 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...
  2. Calpalned

    Using Kepler's third law, determine the period

    Homework Statement If there were a planet three times farther from the sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun? Assume the orbit is a circle. Homework Equations Kepler's 3rd Law ##= (\frac{r_1}{r_2})^3 = (\frac{T_1}{T_2})^2 ## The Attempt...
  3. R

    Finding period of any type of function

    Homework Statement 1. The period of the function f(x) = tanπx + x - [x], where [.] is the greatest integer or floor function is? 2. The period of the function f(x) = sin2πx + x - [x], where [.] is the greatest integer or floor function is? Homework Equations For sin (ax+ b) + c where a,b,c...
  4. Dennydont

    Period of Motion for Masses on Rod w/ Spring Constant 5.4 Nm.rad-1

    Homework Statement A light rod of length 0.5 m has two point masses of mass 1.6 kg attached at either end. The rod is pivoted about its centre and is attached to a spring which exerts a moment on the rod that is proportional to the angle the rod is displaced from the equilibrium position and...
  5. Dennydont

    What is the period of a compound pendulum?

    Homework Statement A compound pendulum consists of a thin rod of length 1.4 m and a disc of radius 0.2 m. The centre of the disc is attached to the end of the rod and the pendulum pivots about the opposite end of the rod. Both the mass of the rod and the mass of the disc are the same, each...
  6. G

    Rotational Period of Large Body

    Homework Statement The Sun rotates on its axis every 25 days. The sun currently has a radius of 7X10^8 m. When it expands into a Red Giant (in about 4 billion years) it will have a radius of 1.5X10^11 m. What will its rotational period be assuming the same mass for both, and they are both...
  7. matqkks

    MHB Why do most mathematics literature use 2L for the period of a function?

    Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?
  8. matqkks

    Why is 2L Used for Function Periods?

    Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?
  9. D

    Superposition of two cosine waves

    Homework Statement Superposition of two cosine waves with different periods and different amplitudes. Homework Equations This is basically: acos(y*t) + bcos(x*t) The Attempt at a Solution I looked at different trig functions but it seems it is not a standard solution. I've found solutions...
  10. 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...
  11. W

    Finding the initial velocity and time period of a projectile

    Homework Statement In the Fig. What should be the initial velocity (magnitude and direction) of the arrow? Also calculate the time of flight. Homework EquationsThe Attempt at a Solution I have formulated 2 equations: v*cos(theta) * t = 20 and 3 = (v * Sin(theta) * t) + (9.81 * t^2)/2 when...
  12. B

    For a circular motion period to length and mass question.

    Homework Statement [/B] We are given a graph, with the information of the period, and the radius of the string. We amassed this data on our own. The graphing of it is quartic, but we have to make it into a linear graph?Homework Equations N/A The Attempt at a Solution [/B] First we tried to...
  13. Philethan

    The period of the spring without ignoring its mass

    Homework Statement A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track. The force constant of the spring is k and the equilibrium length is l. Assume that all portions of the spring oscillate in phase and that the...
  14. R

    Wavelength, period of vibration in seconds

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Okay, I am having trouble with the units. I have the values for the wavenumber and I am trying to find the period. These are the formulas that I am trying. T = 1/f ; f = c/lambda example...
  15. S

    Rotation period of electron orbiting a proton

    Homework Statement An electron is rotating around a proton (at rest) in a perfect circular orbit. If the radius of the orbit is r=10^-10 m, how long is the rotation period [hint: the radial acceleration is entirely due to the electric force] k=9*10^9 q=1.6*10^-19 Homework Equations 1...
  16. R

    Period of Oscillation Homework Statement

    Homework Statement Assume that the potential is symmetric with respect to zero and the system has amplitude ##a##, show that the period is given by : ##T=\sqrt{8m}\int^a_0\frac{dx}{\sqrt{V(a)-V(x)}}.## Homework Equations ##E = \frac12 m(\frac{dx}{dt})^2+V(x)##The Attempt at a Solution For a...
  17. M

    How can the period of oscillation be determined using energy considerations?

    Homework Statement Attached Homework EquationsThe Attempt at a Solution I've managed to do parts i) and ii) with not much bother. But as for iii) then I haven't a clue how to show that the period of oscillation is given by that. I've always been under the impression it is simply given by...
  18. E

    How Do You Calculate the Period of Oscillation in a Harmonic Potential?

    Homework Statement A harmonic potential is parameterised as: V(x)=\frac{k}{2}(x-x_{0})^2An object moves within this potential with a total energy E > 0. (i) Where are the two turning points of the motion xA and xB? (ii) Write down the equation of motion for the object, and use it to find...
  19. P

    Partial derivative of a square root

    Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...
  20. T

    Calculate time (or fraction of orb. period) of sat. in umbra

    Greetings! I would like to know how to calculate the time, or fraction of orbital period, that a satellite spends in umbra? (total solar eclipse for satellite when they aren't affected by Solar radiation pressure and solar panels don't generate power). Information given would be satellite's...
  21. R

    Rotation period of a space station

    Homework Statement To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of If the centrifuge diameter is 13.5m , what should be its rotation...
  22. M

    Why is a gyroscope's precession fastest at 45 degrees?

    I did an experiment in which I varied the starting angle of elevation of a gyroscope. I noticed that at 45 degrees, the precessional period (amount of time to perform one spin) is the lowest, while at 0 degrees and 75 degrees, the precessional period is higher. If I plotted this on a graph, it...
  23. Nathanael

    What is the Time Period of a Pivoted Rod with Attached Springs?

    Homework Statement [/B] A system consisting of a rod of mass M and length L is pivoted at its centre P. Two springs of spring constants k1 and k2 are attached as shown. They are relaxed when the rod is horizontal. What is the time period of the rod if it is given a slight angular displacement...
  24. mark!

    Viruses alive in period of finding host?

    It is known that viruses arent alive. They need a host to replicate. My question is, if they need a host to replicate and stay present in the world, how can be present in the period they don't have a host to begin with? And how long can this period last, forever? It's becoming interesting for me...
  25. P

    Period and Tension of a Pendulum

    Homework Statement A simple pendulum experiment is constructed from a point mass m attached to a pivot by a massless rod of length L in a constant gravitational field. The rod is released from an angle θ0 < π/2 at rest and the period of motion is found to be T0. Ignore air resistance and...
  26. P

    Simple harmonic motion period with velocity defined

    Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...
  27. M

    How Does Standing Up Affect the Swing Period of a Child?

    Homework Statement Question: If a child gets up from sitting position to standing while swinging, how does the period change? Homework Equations Period of a physical pendulum: T = 2π√(I/mgL), where I is the moment of inertia and L is the distance between the pivot and center of mass Period of...
  28. Boe Nancy

    Moon Orbit Period Calc: Equatorial Radius of Earth & Time

    Homework Statement The orbit of the moon is approximately a circle of radius 60 times the equatorial radius of the earth. Calculate the time taken for the Moon to complete one orbit, neglecting the rotation of the earth. Equatorial radius of the Earth = 6.4 *10^6m 1 day = 8.6*10^4s...
  29. J

    Find period from centripetal motion that provides its own gravity

    Homework Statement The cylindrical space station, d = 280m in diameter, rotates in order to provide artificial gravity of g for the occupants. How much time does the station take to complete one rotation? Homework Equations velocity= (2*pi*r)/period acceleration = v^2/r The Attempt at a...
  30. 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...
  31. deusy

    Determining the Period of sin(ax)*cos(bx)

    Homework Statement I'm trying to work out the period of a function of the form sin(ax)*cos(bx), where a =/= b. I'm trying solve how the values for a and b relate to the period. I've graphed a lot of functions, but I'm struggling to notice any patterns. The period always seems somewhat related...
  32. 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...
  33. 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 =...
  34. P

    Quarter period symmetry in Fourier series

    Suppose we have some function f(x) with period L. My book states that if it is even around the point x=L/4, it satisfies f(L/4-x)=-f(x-L/4), whilst if it is odd it satisfies f(L/4-x)=f(x-L/4). Then we define s=x-L/4 so we have for the function to be odd or even about L/4 that f(s)=±f(-s)...
  35. C

    Period of a Proton's Orbit arount magnetic field

    Homework Statement A proton moves perpendicular to a magnetic field of .005 T. What is the period of the proton's circular orbit? Homework Equations 1. T=2pi/v 2. FB=qv x BThe Attempt at a Solution I know I need to solve for velocity first so I can use the period equation, but I don't...
  36. T

    Calculating the Period of a Simple Pendulum

    A simple pendulum is suspended from a ceiling 3.2m high and the bob height from the floor is measured to be 68cm. Calculate the period of small amplitude oscillations of the bob. I converted 68cm to 0.68m. The total length of the pendulum must be 3.2 - 0.68 = 2.52. When working with the...
  37. thephysicist

    Time period of a heavy spring with an attached mass at the end

    I want to know the way to derive the time period equation of a spring mass system accounting for the mass of the spring but not using the energy analysis method but by proceeding in the same way as we do by ignoring the mass of the spring. Please help. I did not find any texts at my level. Any...
  38. 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...
  39. 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...
  40. J

    What is the force of tension in a string connecting two revolving satellites?

    Homework Statement Two satellites connected by a string revolve in concentric circular orbits of radius r and 2r Two satellites of equal masses m revolve around the planet of mass M. The satellites have extremely small mass compared to the planet, m≪M. The radii of the orbits of the...
  41. H

    Find the period of the space shuttle in alternate universe

    Find the period T of the space shuttle Homework Statement (See image of problem statement for nice layout; the questions are stated below) A space shuttle of mass m is in a circular orbit of radius r around a planet of mass M in an alternate universe. In this alternate universe the laws...
  42. S

    What is the relationship between beat period and cosine cycles in a graph?

    Homework Statement please refer to the notes , since we know that a cycle of cosine is as in the photo 1 , why the beat period has 8 complete cycle of cosine? Homework Equations The Attempt at a Solution
  43. J

    Time period of a conical pendulum by D'Alembert's principle

    Homework Statement Finding the time period of a conical pendulum by D'Alembert's principle. The string is of a constant length and all dissipations are to be ignored. Homework Equations The time period of a conical pendulum is 2\pi \sqrt{\frac{r}{g\tan\theta}}. I need to arrive at this result...
  44. A

    Proving period of f/g could be less than period of f and g

    Homework Statement Prove that if f and g are periodic with period p , then f/g is also periodic, but its period could be smaller than p. The Attempt at a Solution So, the first part seems simple enough. ##\frac{f(x+p)}{g(x+p)}=\frac{f}{g}(x + p)=\frac{f}{g}(x)## But how exactly do I...
  45. B

    Simple rotational period problem

    Homework Statement Determine the length of day on a planet. Imagine a planet with an acceleration at the equator of a_{equator} = 10 \,\, m/s^2 (ignoring rotation). Object dropped at equator falls with an acceleration of: a_{obj} = 9.7 \,\, m/s^2 , r = 6.2 \times 10^6 \,\, m ...
  46. T

    Min Period of oscillation of a rod

    Homework Statement An iron rod of length L is hung at a common point with threads of length 'l' which are attached to the two ends of the rod. The rod is displaced a bit in the plane of the threads. What is the length of the threads if the period of the swinging of the rod is the least, and...
  47. Z

    The period for small oscillations of a system

    Homework Statement See picture : Homework Equations ##\sum M_{O}=I_{O}\ddot{\theta }## The Attempt at a Solution Consider the free-body diagram associated with an arbitrary positive angular displacement ##\theta##; The moment about point ##O## is given by ##\sum...
  48. K

    How is Luminosity Converted to Distance in Binary Star Period Calculation?

    The problem is attached, and the official answer is given. The step in the answer does not make a lot of sense to me. How does the luminosity L converted directly into distance d, and why is the solar distance is used? And where does the dm=0.75 come from. It's just not making sense to me...
  49. S

    Oscillations, calculating spring constant, amplitude, period

    Homework Statement A spring stretches 0.150m when a 0.300kg object is hung from it. The spring is then stretched an additional 0.100m from this equilibrium point and released. A) Calculate the spring constant (k) B) Calculate the amplitude, period of motion T, frequency f and angular...
  50. E

    How does period compar- Don't understand solution

    Homework Statement Suppose that you make careful observations of a pendulum on the surface of the Earth. You then move to Mars, where g is about 40% of the value on the surface of the Earth. How does the period of the pendulum on Mars compare with the period of the pendulum on Earth The period...
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