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. 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...
  2. ItsTheSebbe

    Prove that the period of a SHM is 2pi*sqrt(m/k)

    Homework Statement When I was in high school I was thaught that the period of a simple harmonic oscillation (mass on spring, ball on pendulum, etc) was equal to ##T=2\pi \sqrt \frac m k## though they have never explained to me why. That's what I wanted to find out. So for example, let's take a...
  3. M

    Show existence of arc-length parameterized period p'....

    Homework Statement Let γ : R → Rn be a regular (smooth) closed curve with period p. Show that there exist an orientation preserving diffeomorphism ϕ: R → R, a number p' ∈ R such that ϕ(s + p') = ϕ(s) + p and γ' = γ ◦ ϕ is an arclength parametrized closed curve with period p' Homework...
  4. StrangelyQuarky

    How Do You Derive the Period of a Pendulum with Arbitrary Amplitude?

    Homework Statement A pendulum obeys the equation \ddot{\theta} = -\sin(\theta) and has amplitude \theta_0 . I have to show that the period is T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{\sqrt{1-\alpha \sin^2(\phi)}} where \alpha = \sin^2(\frac{\theta_0}{2}) 2. The attempt at a solution...
  5. F

    Need for Lorentz transformation in pre-relativity period

    What was the need for Lorentz transformation in pre-relativity period? Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...
  6. G

    A Period matrix of the Jacobian variety of a curve

    Consider an algebraic variety, X which is a smooth algebraic manifold specified as the zero set of a known polynomial. I would appreciate resource recommendations preferably or an outline of approaches as to how one can compute the period matrix of X, or more precisely, of the Jacobian variety...
  7. M

    Finding the effect of air resistance on period of oscilation

    Homework Statement I'm currently working on the "cavendish" experiment and wish to use/develop a method separate from the casus we've been provided. Now I've nicely calculated and derived everything I need to know, including all the corrections that have to be made for the mass of the rod, the...
  8. TheSodesa

    The period, angular frequency of a piecewise function

    Homework Statement The function ##f## is defined as follows: \begin{equation*} f(t) = \begin{cases} 1, \text{ when } 2k < t < (2k+1),\\ 0, \text{ when } t = k,\\ 2, \text{ when } (2k-1) < t < 2k, & k \in \mathbb{Z}\\ \end{cases} \end{equation*} What is the period ##T## of the function ##f##...
  9. X

    Scaling The Solar System By A Factor ##\alpha##

    I am given the solution to the first part of the problem, however not the second part - would appreciate for someone to double check my work! Cheers. 1. Homework Statement If a scale model of the solar system is made using materials of the same respective average density as the sun and...
  10. Vitani11

    Finding the period of rotation of this system....

    Homework Statement Three identical stars, each with mass m, form the verticies of an equilateral triangle with side length d and rotate in a circular orbit due to their mutual gravitation. What is the period τ of their rotation? I set up the FBD for each star and am now trying to figure out...
  11. S

    Measuring the period of SHM using sound

    Hello! First time posting here. I'm studying the IB and need to complete my required experimental write-up. I am looking to replicate the well-known experiment that finds the value of g by investigating the relationship between period and length of string for a simple pendulum. 1. Homework...
  12. Vanessa Avila

    Finding the astronaut's weight on a planet's surface

    Homework Statement A landing craft with mass 1.22×10^4 kg is in a circular orbit a distance 5.50×10^5 m above the surface of a planet. The period of the orbit is 5100 s . The astronauts in the lander measure the diameter of the planet to be 9.50×10^6 m . The lander sets down at the north pole...
  13. lahanadar

    Period of a complex exponential signal

    I have a simple complex exponential signal of the form x(t)=ejωt. To find period of the signal I tested if x(t)=x(t+nT) for all n: ejωt=ejω(t+nT) ⇒ ejωnT=1=ej2πk where n and k are integers. Then I find a general period expression as T=2πk/ωn Period T means it is the least time a signal...
  14. K

    Simple Harmonic Motion - Determine the period of oscillation

    Homework Statement A very light, rigid rod with a length of 0.620m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. (a)Determine the period of oscillation. (b)By what percentage does this differ from...
  15. R

    Period of pendulum moved to Jupiter's moon Io

    Homework Statement you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s Homework Equations T=2*π√l/g[/B]The Attempt at a Solution T1/T2=√(g2/g1)
  16. 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...
  17. T

    A Importance of optical period in coherent radiation

    I am reading a text on coherent radiation and not quite understanding a particular statement. To provide some background, the authors state that coherent radiation can arise from light-matter interactions even when considering lengths, ##L##, much smaller than the wavelength (i.e. ##V \sim L^3...
  18. Cocoleia

    Period and velocity at perihelion/aphelion

    Homework Statement I need to find first of all the period of Halley's comet given that: eccentricity: 0.967 perihelion: 8.8x10^7 km and AU = 1.496x10^8km Homework Equations Kepler's laws The Attempt at a Solution I think that the Perihelion = a(1-e) where a is the semi major axis. So I...
  19. G

    Finding the period of small vertical oscillations

    Homework Statement I need to find the period of small vertical oscillations about equilibrium position of a string whose motion can be described by the following equation: d2x/dt2 = (-g/h)*x Answer: 2π√(h/g) Homework Equations I know that the time period is given by the formula T = 2πω where...
  20. tony873004

    Determining the period of a pendulum with an accelerometer

    I've got an accelerometer swinging back and forth on a string collecting data. But because of the tolerance of the accelerometer, the data is not quite clean enough to simply determine when positive turns to negative, or passes through equilibrium. Here's the data. (arbitrary reading vs. time...
  21. MalachiK

    Time period of system with constant restoring force

    Homework Statement Two smooth planes are joined at one end so that they form a V shape. The join is such that a mass placed on one of the planes will slide smoothly down one side of the V and then move up the other side. Find the period of the motion (T) of such a mass in terms of x0 (the...
  22. G

    Finding the time period using the potential

    Homework Statement A particle of unit mass moves in one dimension with potential V(x) = ½μ2x2 + εx4 (ε>0). Discuss the motion of the particle. If the particle released from rest at x=a (a>0) express the time period T for the particle to return to a in the form of an integral and show that when...
  23. Vitani11

    In which case is the period larger? ( Above earth or below?)

    Homework Statement A pendulum clock is adjusted so that it keeps excellent time on the ground. The clock is brought to a mine of depth h below the ground and then raised a height h above the ground to see the differences. In which case is the error larger? Homework Equations T = 2π √(L/g) L =...
  24. S

    Calculating the Year Length of a Gak Planet

    Question: A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 6.18 kg and notes that it takes 0.928 s to fall a distance of 8.37 m. The Gak’s planet orbits its sun...
  25. CassiopeiaA

    A Take FFT to find time period for eclipsing binaries

    I am trying to use Kepler Data for Eclipsing Binaries to estimate time period, and then other parameters such as mass, eccentricity, semi-major axis, distance, etc. of the binary systems. I want to write code in MATLAB which will use FFT to find the time period. The available data has the...
  26. kubaanglin

    Period of motion of an object dropped through the Earth

    Homework Statement An object of mass ##m## moves in a smooth, straight tunnel dug between two points on the Earth’s surface. Show that the object moves with simple harmonic motion, ##a = - ω^2 x##. Find the period of this motion. You can assume that the Earth’s density is uniform. Homework...
  27. F

    The reciprocal relationship between frequency and period

    I was asked by a friend to explain why the frequency, ##f## and period, ##T## of a wave. The initial explanation I gave to them was as follows: Heuristically, the period of a wave is defined as ##T=\frac{\text{number of units time}}{\text{cycle}}##, and its frequency as ##f=\frac{\text{number...
  28. S

    I How to Fold Data Points to a Period

    Hello! I need to fold some data points to a period, but I am not sure what does that mean. Some help please.
  29. moenste

    Body on a spring: expression for the period T

    Homework Statement (a) A body of mass m is suspended from a vertical, light, helical spring of force constant k, as in Fig. 1. Write down an expression for the period T of vertical oscillations of m. (b) Two such identical springs are now joined as in Fig. 2 and support the same mass m. In...
  30. Pao44445

    Time Period of SHM | 500kg Car w/ 196,000 N/m

    Homework Statement a man sits in a car that makes the center gravity of the car is pulled down by 0.3 cm. After he gets out of the car, find the time period of the car while it is moving in SHM Mass of the car = 500kg Spring constant = 196,000 N/m Homework Equations ? The Attempt at a...
  31. Deebu R

    How Does the Time Period Change with Orbit Radius in Satellite Motion?

    Homework Statement If the time period of a satellite in the orbit of radius r around a planet is T, then the time period of a satellite in the orbit of radius 4r is T'= ? 2. The attempt at a solution To be honest I have no idea how to solve this. First I thought Keplers third law may be the...
  32. cnnn

    I Moon revolution period 27.32, but got 27.53 from equation?

    Hello, I'm trying to calculate Moon revolution period but always got 27.53 instead of 27.32. G = 6.674e-11 (m^3 kg^-1 s^-2) M = 5.9724e24 (kg) from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html R = 384400000 (m) Earth Moon distance From 4π^2 * R^3 = GM*T^2, got moon revolution...
  33. Muthumanimaran

    Find the Time period using First Integral

    Recently I lend the Classical mechanics book written by Goldstein from the library, In the last page, someone scribbled this problem without any solution, I am just curious and want to give a try the problem mentioned below. I just want to know whether my approach and my solution is correct or...
  34. R

    Using Kepler's 3rd Law to find Period of Venus

    Homework Statement Deduce, from the equations employed in Q4 and Q5, the exponent n in the equation: T = k rn where k is a constant and T is the period of a satellite which orbits at a radius r from a massive object in space. Hence, how long is the “year” on Venus if its distance from the Sun...
  35. P

    A Frequency analysis of signal with unknown period

    I was reading up on (discrete) Fourier transform when my mind started to think of an what-if scenario: Assumed I'm sampling a signal of the form a1*sin(b1+c1) + a2*sin(b2+c2) + a3*sin(b3+c3) + ... + aN*sin(bN+cN) + some noise where the a's represents magnitudes, b's represents frequencies and...
  36. P

    Harmonic Motion with External Force: Impact on Period?

    Homework Statement A particle with mass m is undergoing with harmonic motion with a period T, we introduce an external force F proportional to velocity v so that F= -bv with b a constant and we assume that the particle continues to oscillate how does the period change? Homework Equations F= m...
  37. D

    Time of oscillation of a pendulum

    Homework Statement A rigib poll of length 2L is made into a V shape so that each leg has length L. What is the period of oscillation for small angle. The angle between the legs is 120 degrees Homework Equations 3. The Attempt at a Solution [/B] I tried to calculate the period by imagining a...
  38. C

    Period of Motion: Find Mass 0.85kg Piston's Period of Motion

    The movement of a particular piston of mass 0.85kg may be modeled with a simple harmonic. Given that its acceleration is 8m/s when 10cm from the mid position. Find the period of the motion?? I found velocity to = 1.26m/s, but I am not even sure if i need to calculate the velocity.
  39. Just144Ice

    Find Density Given 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 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density. Homework Equations T^2=(4pi^2r^3)/GM V=4/3piR^3 Density= Mass/...
  40. awholenumber

    B In trigonometry, what is the period of a wave?

    what does the period of a wave , in trigonometry ... depend on ? does it depend on the ratio of the length of the sides of the right angled triangle like this ? does it depend on the angle ?? what are all the values you need to plot a graph like this ? ??
  41. JulienB

    Deriving the Time Period of a Pendulum with Small Angle Approximation

    Hi everybody! I have a quick question about a pendulum. The first question of a problem asked me to find an integral expression for the time period of a pendulum without the small angle approximation, which I did and I got that: ##T(\varphi) = 4\sqrt{\frac{l}{g}} \int_{0}^{\pi/2}...
  42. James Ray

    Pendulum pulse vertical flick period

    Homework Statement Homework Equations T= 2pi*sqrt(L/g) The Attempt at a Solution T= 2pi*sqrt(0.325/9.8)=1.14 s That seems like a reasonable answer. [/B]
  43. D

    Interpreting the Wording of a Wave Problem: Understanding Speed and Period

    Hello. A problem I have given my physics class states, "The distance between two crests in a wave is 1.5 m, and two crests pass a pole each second. What is the speed and period of the wave?" I believe the proper solution should be v = 3 m/s, and T = 0.5 s. In order for two crests to pass a given...
  44. S

    Graph of stationary wave after moving for half period

    Homework Statement A stationary wave travels along a stretched string. Part of this wave at a particular instant is shown...
  45. R

    Pendulum Length and Period Calculations

    Homework Statement Homework Equations T=2pi√(L/g) The Attempt at a Solution I am just making sure I am doing these right. For the first one, I used the equation to determine the length it would be on Earth. The length I got was g/pi^2 = 0.993 m. I thought that it would have to stay the same...
  46. H

    Rotational period for constant mass but different volume

    Homework Statement The Earth's radius is 6371 km. If the Earth's radius were to increase by 30 m (0.03 km), but no change in mass, by what percentage would the Earth's rotational period increase? (Model the Earth as a uniform sphere) Homework Equations ∑Torque = Iα v = rω a = rα KE = (1/2)Iω^2...
  47. ing_it

    Physical Pendulum - Rod - Period and Distance From Center of Mass

    Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...
  48. V

    Radius and period of charge in B field

    Homework Statement A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.460 T magnetic field? Note: I hope this question is meant in advanced...
  49. L

    Time period in harmonic oscillation.

    Homework Statement Homework Equations Find Time Period. Find the error in my solution. The Attempt at a Solution Where i am wrong ?
  50. H

    I Why must the oscillatory period of a stable orbit be constant at all distances

    Consider a stable circular orbit (with a central force) subjected to small perturbations. The orbit equation is given by (3.45). The text argues that the ##\beta## in (3.46) must be a constant over the domain of ##r_0##: "Otherwise, since ##\beta## can take on only discrete rational values (for...
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