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.
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...
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.
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} =...
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)
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...
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}##...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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 =...
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...
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...
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...
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...
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...
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...
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...
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...
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 =...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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.
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 *...
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=...
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...
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...
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?