|
|
|
Thread Tools | Display Modes |
#11
|
|||
|
|||
Finding minimum rotation period
On 17 Jun 2006 18:17:43 GMT, Ricky Romaya
wrote: Hi, If given a planet's mass, radius, and density, how can I find out the minimum rotation period, or maximum rotation speed, assuming the planet is rotating around it's own axis and is a perfect sphere? Wikipedia only give a hint that for celestial bodies, the body's tensile strength is the one supplying the centripetal force, and if the angular speed is much greater in respect to it's density, the body will break. I couldn't find any equations which relates the tensile strength or density with centripetal force. Please help TIA Here are some interesting facts, using the earth as an example.. The gravity inside the earth is proportional to the radius, beginning with 0 at the center and increasing linearly to the surface. So g(r) = g0*r/R It's proportional to r. Similarly the centrifugal acceleration is proportional to r: gcent = W^2r So equating the two g0*r/R = W^2*r W = sqrt(g0/R) rad/sec (1) 2pi/W = period for 1 revolution (84.4 min) (1) produces a net zero gravity everywhere in the earth or planet. That is the same period as a low flying shuttle orbit. At this angular rate, there is no gravity anywhere (assuming constant density) in earth so it would tend to come apart. John Polasek |
#12
|
|||
|
|||
Finding minimum rotation period
Ricky Romaya wrote: "oriel36" wrote in ups.com: The actual mechanism for the deviation of the Earth's shape from a perfect sphere is differential rotation in the flexible and molten interior across the Entire length of the Earth's axis and certainly not from the dead center as contemporary notions have it*. For once,do something productive and pick up on latitude dependent differential rotation and apply the lessons learned from observing rotating celestial objects with exposed flexible conditions such as the Sun's plasma and the correlation to a deviation from a perfect sphere.It then becomes a matter of adjusting the Earth's interior composition,its viscosity,rotation rate from Equator to pole ect. - http://www.astronomynotes.com/starsun/sun-rotation.gif Just think 'across the entire length of the Earth's axis' and you will get to love the mechanism for the planetary deviation from a perfect sphere. Could you point me to some inet resources where I can learn more about this? The resourses are scattered all over the internet but not in an organised way and certainly not linking the dynamics of the Earth's shape and crustal motion under a common mechanism - differential rotation perpendicular to the planetary rotational axis. There are informal discussions on Saturn's large deviation from a perfect sphere but none exist for the Earth either through unfamiliarity or oversight.It becomes easier to assign a differential rotation to the Earth by considering the molten and flexible interior alone and then grafting in the fractured surface crust later as the rotational dynamics create a basis for the motion of the crust.Even in outlines,these dynamics look far more exciting that remaining with stationary Earth/convection cell mechanisms. I suppose you are best ploughing your own course on this exciting material,think of it as updating the already known correlation between rotational dynamics and the Earth's shape with data based on a flexible and molten interior and replacing vague descriptions based on models which reference the bulge from the dead center of the Earth rather than the more accurate conception based on rotational dynamics perpendicular across the entire length of the Earth's axis. Good luck in your endeavors. |
#13
|
|||
|
|||
Finding minimum rotation period
In article ,
Ricky Romaya writes: If given a planet's mass, radius, and density, how can I find out the minimum rotation period, or maximum rotation speed, assuming the planet is rotating around it's own axis and is a perfect sphere? Wikipedia only give a hint that for celestial bodies, the body's tensile strength is the one supplying the centripetal force... If Wikipedia really says this about _planets_, then it's wrong. As someone else noted, for large masses, tensile strength is negligible compared to gravity. Also, a planet near breakup will (in general) be very far from spherical. The general solution of this problem is complicated. As others have written, the maximum rotation speed is where the gravitational force at the surface equals the centripetal force needed for a circular orbit, but calculating the gravitational force for a non-spherical body is not always trivial. You need to know the shape of your planet and how density changes within it, and those depend on what the planet is made of (in particular on the "equation of state" of the material, i.e., how its density changes as a function of pressure). Composition may not be uniform, so you may have multiple materials to consider. I'd be surprised if there is an analytic solution in the general case. If you are willing to accept simplifying assumptions, there can be analytic solutions. For example, the case of uniform density results in the "Maclaurin spheroids," http://www.phys.lsu.edu/astro/H_Book...aclaurin.shtml There are also "Jacoby ellipsoids," but I forget exactly what simplifying assumption is made to derive those. (Anybody remember?) By the way, a few people who have responded to this thread don't seem to know much about physics. Be careful about which answers you take seriously. -- Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA (Please email your reply if you want to be sure I see it; include a valid Reply-To address to receive an acknowledgement. Commercial email may be sent to your ISP.) |
#15
|
|||
|
|||
Finding minimum rotation period
In article ,
John C. Polasek writes: I don't see that it is complicated at all. It is plain that the dirt would peel off at the equatorial bulge, where only the surface condition governs. In Eq. (1) g0 = W^2R so you measure g0 at the equator (regardless of shape) and knowing Rbulge you can calculate W^2. How do you know Rbulge? I suggest you try writing down the equation for density as a function of radius and latitude, given some assumed equation of state. (If you do this right, you will find yourself writing down the equation of hydrostatic equilibrium in cylindrical coordinates, then solving it for some equation of state.) Once you have that, write an equation for gravitational force. Remember that the mass distribution is not spherically symmetric nor is density constant. Perhaps there's some simplification I don't see, but the general case looks hard to me. Of course it's easy to get an approximate answer by assuming spherical symmetry. That may not be a bad approximation if much of the mass is concentrated near the center of the planet. -- Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA (Please email your reply if you want to be sure I see it; include a valid Reply-To address to receive an acknowledgement. Commercial email may be sent to your ISP.) |
#16
|
|||
|
|||
Finding minimum rotation period
|
|
Thread Tools | |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Spacecraft Doppler&Light Speed Extrapolation | ralph sansbury | Astronomy Misc | 91 | August 1st 13 01:32 PM |
Pioneer 10 looks like red shift, not blue | [email protected] | Astronomy Misc | 71 | January 5th 06 02:04 PM |
Scientists Find That Saturn's Rotation Period Is A Puzzle | Ron | Astronomy Misc | 2 | June 30th 04 10:41 AM |
Pioneer 10 anomaly: Galileo, Ulysses? | James Harris | Astronomy Misc | 58 | January 28th 04 11:15 PM |
Thanks George | Oriel36 | Astronomy Misc | 31 | January 5th 04 02:16 PM |