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.
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} =...
Hi ...
I have answered this question and I think that F/mg equals 3.
But I've asked it from someone and he told me that F/mg is 4.
Can someone help me find out which one is correct ???
My answer :
For part (a) of this problem,
The solution is,
However why did say show the motion is periodic, but then the solutions don't show it, instead explain how it is periodic?
Is there a way to prove that the motion is periodic other than the solution to part (b)?
Many thanks!
hi ! I'm having a lot of trouble simplifying my expression for one of my homework questions. I know someone asked about this homework problem already, but the answers didn't really help me figure out how to simplify it.. I really have no idea what steps to take, and I've even consulted all my...
The known expression of the wave function is
where A is the amplitude, k the wave number and ω the angular velocity.
The mathematical definition of arc length for a generical function in an interval [a,b] is
where, in our sinusoidal case:
For our purpose (calculation of the length in one...
Hi, I have been thinking about pendulums a bit and discovered that a HO(harmonic Oscillator) will take the same time to complete one period T no matter which amplitude A/length l it has, if stiffness k and mass m are the same.
But moving on to a simple pendulum suddenly the time period for one...
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...
This question is related to Shor's algorithm and its use of modular exponentiation.
In the table below, the period of the sequence in the third column is obviously equal to 4. That is, its value repeats every fourth row.
What I am trying to find out is why it is that when the first value in...
When the platform moves with constant acceleration, the equation of Newton's 2nd law of motion is
Forward force - W sin 30o = m.a
Forward force = m (a + g sin 30o) ⇒ apparent gravity = a + g sin 30o
Final period of pendulum = ##\sqrt{\frac{g}{a+g \sin 30^{0}}} \times 2 = 2.38 s##
Is this...
Hi,
I am having to refresh my oscilloscope knowledge and am confused about one last function generator setting... Burst period.
If I have 1 cycle at say 700 kHz it is 1.43us. If I set number of cycles to 10 then that is 10 * 1.43us = 14.3us time. This is my ON burst.
So what is the burst...
hello, i have some diffuculties with this problem, there's the point where the spring is attached to the rod and according to the equation of time period of physical pendulum , h represent the distance from the COM and the pivot point. here the pivot point is at the COM. and i know that it can't...
Find amplitude, period, PS, VS. graph 2 periods of
$y=3\cos(\pi x-2)+5$
ok I think these are the plug ins we use
$Y=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B $
or
$A\cos\left(\omega x-\phi\right)+B$
A=amplitude B=VS or veritical shift
$T = \dfrac{2\pi}{\omega-\phi}$...
$$y=2 A \cos 2 \pi\left(\frac{\nu_{1}-\nu_{2}}{2}\right) t \sin 2 \pi\left(\frac{\nu_{1}+\nu_{2}}{2}\right) t$$
Can you explain me the significance of the above equation in the context of waves and oscillations? It's something to do with 'beats,'.
Find amplitude, period, PS, VS. then graph.
ok I think these are the plug ins we use
$Y_{cos}=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B
\implies A\cos\left(\omega x-\phi\right)+B
\implies T=\dfrac{2\pi}{\omega}
\implies PS=\dfrac{\phi}{\omega}$
ok I wanted to do...
I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment?
I also need to know the...
for (a) ##T=\frac {2\pi}{\omega}##
$$\omega=\frac {2\pi}{T}$$
$$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$
$$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$
for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...
The owner of an ice cream shop kept records of the average number of sales per month for 2019. Create a sinusoidal equation to model this information of number of sales per month.
I found the maximum, minimum for this, but how can I find the period of from this table.
As I already know formula...
$\tiny{\textbf{7.8.11 Campbell HS}}$
Find (A)mplitude, (P)eriod, PS, VS. graph 2 periods
$y=3\cos(\pi x-2)+5$
by observation we have A=3 and VS=5
ok assume $\omega=\pi$
so if period is $T=\dfrac{2\pi}{\omega}$ then $T=\dfrac{2\pi}{\pi}=2$
This is not homework. I found this question when browsing and there is also solution but I do not understand it. This is part of the solution:
My questions:
1)
From equation (i): ΔT = m.a, I think ΔT refers to W - T (weight of block - tension of string). I got this from free body diagram and...
$\tiny\textbf{7.8.a09 Radford HS}$
Find amplitude, period, PS, VS. then graph.
$y=\cos\left(x+\dfrac{\pi}{2}\right)$
For the graphs of $y=A\sin(\omega x - \phi)$ or $y=A\cos(\omega x - \phi),\omega>0$
Amplitude $=|A|$
Period $T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2}=\pi$
PS...
$\tiny{ACT.trig.01}$
What is the period of the function $f(x)=\csc{4x}$
$a. \pi \quad b, 2\pi \quad c. 4\pi \quad d. \dfrac{\pi}{4} \quad e. \dfrac{\pi}{2}$
well we should know the answer by observation
but I had to graph it
looks like $\dfrac{\pi}{2}$
The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
The following attempt gives the wrong answer, and I would like to know where it goes wrong.
Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through.
Let ##m## be the mass of the ball, ##r## be the radius...
My attempt at solving case B
I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this...
I've already found the potential and force that produce the given orbit. my results were:
##V=-\frac{al^2}{mr^3}##
##\vec{F}=-\frac{-3al^2}{mr^4}\hat{r}##
Now, I've been trying to find the period using the equation
##t=\sqrt{\frac{m}{2}}\int_{r_0}^{r}\frac{dr'}{\sqrt{E-V_{eff}}}##
Using...
Using this stimulation: https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html
It looks like frequency is decreasing as I increase tension but online it says frequency increases as tension does. Also, I am unsure about what happens to the Period
Hello :oldsmile:
I have heard that various organisms in Carboniferous period had gigantic sizes because of relatively high Oxygen level in atmosphere. Today it is equal to 21 %, but at that time it was higher:
https://www.nationalgeographic.com/science/article/carboniferous
So, organisms...
I attempted this assignment, and scored a 5/10. The solutions are not given until a later date. I need to understand this material before I progress to the next section. The following are my attempts at the solution.
The number of cycles in each pulse increases:
The PD is determined by the...
I am currently studying Electrical Engineering and I have this question: An energy band is formed by the overlapping of atomic orbitals of atoms coming close to each other.I suspect that if the energy of the atomic orbital of the valence electrons of a chemical element is less than the energy of...
Hi,
I know there's are 2 normal modes because the system has 2 mass. I did the Newton's law for both mass.
##m\ddot x_1 = -\frac{mgx_1}{l} -k(x_1 - x_2)## (1)
##m\ddot x_2 = -\frac{mgx_2}{l} +k(x_1 - x_2)## (2)
In the pendulum mode ##x_1 = x_2## and in the breathing mode ##x_1 = -x_2##
I get...
We can find that (1+e)/(1-e) = 8 => 1+e = 8 - 8e => 9e=7 => e=7/9. I'm not sure if I need this.
We can also find the time period of Earth ## T=\frac{2 \pi r}{v} = 3.14* 10^7 s##
I think I need more information from somewhere else. What am I missing?
This problem honestly got me in big confusion.
I managed to find the angle ##\theta## at which the rod rests by equalling the components of weight and Lorentz's force... but from this point on I really don't know how to manage the harmonic oscillation part.
Let's say you have a leaking tab, and the probability of a droplet in any given second is 1%, regardless of whether there was a drop previously.
How would you calculate the probability of n drops in a minute?
No drops in a second is 0.99, so no drops over a minute is 0.99^60. Hence one or more...
The equation that governs the period of a pendulum’s swinging. T=2π√L/g
Where T is the period, L is the length of the pendulum and g is a constant, equal to 9.8 m/s2. The symbol g is a measure of the strength of Earth’s gravity, and has a different value on other planets and moons.
On our...
So my doubt is at the beginning of the problems hey are saying that the ball obeys stokes law and on the latter part of the question they are saying that no buoyant force is acting then how does the velocity of the ball change in the end?
Also what is the use of specifying 'the ball never...
https://www.asi.edu.au/wp-content/uploads/2016/10/ASOEsolns2012.pdf
Q11 D) Markers comments: Few students reached part (d) and very few of those who did realized that the amplitude does affect the time taken for each of Mordred’s bounces. i.e. the energy losses results in shorter periods...
Say that we have an instance where something falls down from a certain height with constant acceleration g. We know that the average speed with regards to the time period is less than (u+v)/2 since we spend less time at the higher speeds.
How do we actually calculate the average speed over a...
This is a problem very easy to deal with if we consider the effective spring constant, however, i want to avoid this solution, and see how to justify the period of this motion just by analyse the forces or the energy, what seems a little hard to me.
First of all we would need to find the force...
https://arxiv.org/abs/1905.10074
The paper finds that one can reduce the number of qubits to a constant (just one works) used in the last, modular exponential register of the variants of Shor's algorithm, used to factor integers and find discrete logarithms, by applying a universal hash...
I made and understood the letters a b c, but i don't understand the letter d.
I thought it would be the double of the answer C [], but seems that's not right, since the book says the answer is two times the answer of B [ two times this[ ]
1.
How will the motion of M be? I assume wire S is inelastic so will M move downwards but not in straight line? (I mean M moves downwards but because the left side of pulley is connected to S, it will be static and the right side of pulley can go down along the extension of the spring so its...
Here is the picture on the system.
I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position.
In the thread...
If the bottom disk is free to spin, will it necessarily spin? all the forces in this disk don't produce a torque.
I don't know why we disregard it's inertia moment when it is free to spin (It's intuitively set, but I can't see it mathematically)
:\
For A) I just have to calculate the time taken to travel from the middle to the wall and multiply that number by 4, since it travels the same distance 4 times.
##t=\frac{x_0}{v_0}##
B)The energy is an exponential function
##T(n)=T_0.(1-\frac{2}{100})^n##
So
##v^2={v_0}^2.(1-\frac{2}{100})^n##...