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### How to calculate the orbit and rotation period???

Posted: 30.06.2008, 09:37
Greetings Forum...
If we assume that a certain star has a mass of: M and there is a certain planet orbiting it at X A.U. or km, and has a mass of: m.
How can we calculate it's orbit period (the time the planet need to complete it's circling the parent star) ????
and How can we calculate it's rotation period??? and how to calculate the length of days of this planet, for i had read that rotation period is not same for length of day....

sorry for my bad english... for your all help i give my humble gratitude...

### Re: How to calculate the orbit and rotation period???

Posted: 30.06.2008, 11:22

### Re: How to calculate the orbit and rotation period???

Posted: 03.07.2008, 02:21
thank you mr. selden. i try to read the wikibooks.
hmm... i wonder if there is a program that can calculate the orbital and rotation period of certain planet with a certain mass...

### Re: How to calculate the orbit and rotation period???

Posted: 03.07.2008, 02:26
but i can't fuigure it out...
i not so good at physic...
maybe a simple formula of calculating orbital (revolutional) period and rotation period of planet with X mass orbiting a star with X mass with semimajor axis X km...

### Re: How to calculate the orbit and rotation period???

Posted: 03.07.2008, 10:14
Andirius,

Unfortunately, to be able to calculate orbital parameters you have to understand algebra, and to calculate where planets are in their orbits, you have to understand calculus and, too often, the horror known as elliptical integrals.

You might take a look at the Web page http://www.lepp.cornell.edu/~seb/celest ... eters.html
It might help a little.

### Re: How to calculate the orbit and rotation period???

Posted: 03.07.2008, 11:00
There's no formula for rotation period, as this is set by the planet's formation and evolutionary history. (Tidal forces will eventually synchronise the rotation period so that rotation period = orbital period, but this is only usually relevant for very close-in planets on near-circular orbits)

Orbital period: $$P=\sqrt{\frac{4 \pi^2 r^3}{GM}}$$

Where P is the period, r is the semimajor axis, M is the mass of the star and G is the gravitational constant.

Learn to use Google calculator, which has constants like the mass of the Sun (m_sun) and the gravitational constant (G) built-in, and will handle the units for you.

### Re: How to calculate the orbit and rotation period???

Posted: 05.07.2008, 23:59
Length of solar day = Length of sidereal day * (1 + 1 / ((length of year/length of sidereal day) - 1))

NOTE: Make sure the time units are all the same

### Re: How to calculate the orbit and rotation period???

Posted: 07.07.2008, 18:33
bdm wrote:Length of solar day = Length of sidereal day * (1 + 1 / ((length of year/length of sidereal day) - 1))

NOTE: Make sure the time units are all the same
That works if the planet is prograde...

If the rotation is retrograde the expression becomes

Length of solar day = Length of sidereal day * (1 - 1 / ((length of year/length of sidereal day) + 1))

### Re: How to calculate the orbit and rotation period???

Posted: 09.07.2008, 08:17
thanks

there some more question pop out in my tiny brain...
if we ignoring all the tidal forces is there a way to calculate the rotation period??? or we just make up the number?
and why giant gas planet tend to rotate faster than rocky ones??? is it connected to inertia???
and what make a planet rotate backward (retrograde)??? tidal forces or because a thick atmosphere like Venus???
and maybe someone will answer my question about atmosphere in another post.

I'm asking all this question to make a "realistic" or at least semi realistic solar system settings for my story... it's not as easy as i think before ... need more study...
i hope that i don't make you guys irritated with all my question, I'm just confused because my lack of science...

### Re: How to calculate the orbit and rotation period???

Posted: 09.07.2008, 08:59
Hi i hope the folowing helps

OrbitalRadius (AU) CUBED = OrbitalPeriod (Earth Years) SQUARED / Mass (solar units)

you can re arrange this to calculate the other perameters

this is only true for orbits around Stellar mass objects, for planitary orbits you need to go the whole hog and work out everything

### Re: How to calculate the orbit and rotation period???

Posted: 09.07.2008, 10:29
Andirius wrote:thanks

there some more question pop out in my tiny brain...
if we ignoring all the tidal forces is there a way to calculate the rotation period??? or we just make up the number?
If there are no noticable tidal forces, then the rotation period is determined by the rotational speed of the original protoplanetary nebula as it condensed into the planetary body. We have no way to know the rotational speed of the original nebula.
and why giant gas planet tend to rotate faster than rocky ones??? is it connected to inertia???
Planets that had more material condense into them are likely to rotate faster, like Jupiter and Saturn.
and what make a planet rotate backward (retrograde)???
Probably a collision with another body when the solar system was young.
tidal forces or because a thick atmosphere like Venus???
both of those are very unlikely. The Sun's tidal forces on Venus are relatively small. There's not that much mass in its atmosphere.
and maybe someone will answer my question about atmosphere in another post.

I'm asking all this question to make a "realistic" or at least semi realistic solar system settings for my story... it's not as easy as i think before ... need more study...
i hope that i don't make you guys irritated with all my question, I'm just confused because my lack of science...
The best way to cure the lack of knowledge is to read books about the topics you need to know.

### Re: How to calculate the orbit and rotation period???

Posted: 09.07.2008, 13:05
selden wrote:
Andrius wrote:tidal forces or because a thick atmosphere like Venus???
both of those are very unlikely. The Sun's tidal forces on Venus are relatively small. There's not that much mass in its atmosphere.
Thing is, the oceans on Earth seem to have effects on the tidal evolution of the Earth-Moon system, and they have low mass in comparison to the rest of the planet. In some sense, the Venusian atmosphere is an ocean (if you want to call supercritical carbon dioxide an ocean), and judging from this abstract, dense Venus-style atmospheres CAN have an effect on the rotational evolution of a planet... (according to this article (pdf), the dense atmosphere actually makes the 1:1 spin orbit resonance unstable)

### Re: How to calculate the orbit and rotation period???

Posted: 10.07.2008, 09:17
thanks to mr. selden and mr. ajtribick

well it seems that i really need to read more books... but in my country (Indonesia to more be more specific) there are not so much book about astrophysics, most of them is about "how to become rich fast" books and love novel so i had a shortage on physic books...
i really don't know how to find the material i searching and the search engine is not helping either... wikipedia although informative lack coherency (what do we expect from collective writings from multiple authors???) and sometime confusing (lack of citation)...
where can i find the relevant information i need??? (don't bother wikibooks, i can't understand a single things, believe me i have tried and i totally lost finding the pages [most of them don't had link*red*]...)

best regards...

### Re: How to calculate the orbit and rotation period???

Posted: 15.07.2008, 15:12
Andirius wrote:thanks to mr. selden and mr. ajtribick

well it seems that i really need to read more books... but in my country (Indonesia to more be more specific) there are not so much book about astrophysics, most of them is about "how to become rich fast" books and love novel so i had a shortage on physic books...
i really don't know how to find the material i searching and the search engine is not helping either... wikipedia although informative lack coherency (what do we expect from collective writings from multiple authors???) and sometime confusing (lack of citation)...
where can i find the relevant information i need??? (don't bother wikibooks, i can't understand a single things, believe me i have tried and i totally lost finding the pages [most of them don't had link*red*]...)

best regards...

Maybe you could look at libraries for physics books and look for books to buy online.

### Re: How to calculate the orbit and rotation period???

Posted: 25.11.2008, 11:41
Calculate the orbital period of a spacecraft around the moon
1. During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of 100km. How long did it take to go around the Moon once?

2. T= 2(pi)(r^3/2) / root (GM)
mass of moon = 7.35 X 10^22
radius of moon= 1.74 X 10^6

3. I think that is the correct equation, and I've tried plugging all the values in. I know that the radius will have the 100km (100,000m) added on to it...right?