**8. The extra-solar planets which donot fit in any model**

Lately many exoplanets have been discovered apart from hot-jupiters which donot fit any Model of planet birth and evolution and hence present a conundrum. Table (7) presents the list of the exoplanets and the reasons why they have become an enigma.


Enigma of the Birth and Evolution of Solar Systems

lom(length of month)/lod(length of day) equation:

= (Jspin )planet + (Jorbital)system + (Jspin)satellite ;

around host planet which in case of our satellite Moon is 27.3 days);

JT = total angular momentum of the Satellite- Planet System,

C = Principal Moment of Inertia around the spin axis of the Planet;

G = Gravitational Constant = 6.67 × 10-11 N-m2/Kg2 ;

When lom/lod = 1 we have geosynchronous orbit.

outer geo-orbit is a stable equilibrium orbit.

Charon is doing or it may be deflected as our Moon will be.

**9. Planetary satellite dynamics** 

day);

E = JT/(BC);

B = √[G(M + m)];

F = m/[C(1+m/M)];

M = mass of the host planet; m = mass of the satellite;

May Be Solved by Invoking Planetary-Satellite Dynamics 87

On 21st July 1994, the Silver Jubilee Celebration Year of Man's landing on Moon, NASA gave a press release stating that Moon has receded by 1 meter in 25 years from 1969 to 1994. Using this piece of data, the first Author redid the analysis of Earth-Moon System [Sharma 1995]. In a subsequent paper the Authors [Sharma, B. K. and Ishwar, B " Basic Mechanics of Planet-Satellite Interaction with special reference to Earth-Moon System", 2004, http://arXiv.org/abs/0805.0100 ] found that Satellites-Planet Systems have a characteristic

LOM/LOD = E×a3/2 – F×a2 [The proof is given in SOM\_Appendix A] Where l.o.m. = length of month ( sidereal period of orbital rotation of the natural satellite

l.o.d. = length of day ( spin period of the host planet which in our case is 24 hours or 1 solar

 E×a3/2 – F×a2 = 1 (1) Equation (1) has two roots and hence planet -satellite systems have two geo-synchronous. Only at these two Geo-synchronous orbits the system is in equilibrium because the orbits are non-dissipative. Elsewhere the system is dissipative hence in non-equilibrum either spiraling out to the outer geo-synchronous orbit or spiraling inward to its certain doom. The inner Geo-synchronous orbit lies at energy maxima whereas the outer Geosynchronous orbit is at energy minima. Therefore the inner geo-orbit is an unstable equilibrium orbit and the

When the natural satellite is at the inner geo-orbit it is easily perturbed by solar wind or cosmic particles or solar insolation. It tumbles out on an expanding outward spiral path or it falls short of the inner geo-orbit on inward collapsing spiral path. Inward collapsing spiral path is entirely a runaway path. The outward spiral path, because of energy conservation, is initially an impulsive gravitational runaway phase which quickly terminates because of tidal dissipation in the central host body due to tidal streching and squeezing . This runaway phase is the gravitational sling shot phase. After the gravitational sling shot phase, the natural satellite coasts on its own towards the outer geo orbit. Our Moon is on a midway course in its journey towards the outer geo-orbit. Charon, a satellite of Pluto, has already arrived at the outer geo-orbit. The satellite may remain stay put in the outer geo-orbit as

a = semi- major axis of the elliptical orbit of the satellite ( for Moon it is 3,84,400 Km);


\* Initially it was thought that Giant planets must have formed in colder region far from their parent stars. Icy nuggets act as seeds that accumulate enough dust to build up to a critical mass where by runaway accretion it is enveloped by a large mass of gas giving birth to gas giants. These icy nuggets can form only beyond snowline[Sasselov & Lecar 2000]. But in HD 188753 this could not have happened. This is because the secondary system of star pair would truncate the disk to 1.3AU leaving nothing beyond in the colder region that could nucleate and grow into a giant planet. "Giant planets in circumstellar disks can migrate inward from their initial formation positions. Radial migration is caused by inward torques between the planet and disk, by outward torque between the planet and the spinning star and by outward torques due to Roche lobe overflow and consequent mass loss from the planet." [Trilling, Benz et al 1998]. Through numerical solutions it has been shown that taking all the torques into consideration, Jupiter-mass planets can stably arrive and survive at small

Table 7. The exoplanets which are conundrum.[Konacki 2005, Hatzes & Wuchterl 2005, Mugrauer 2005, Hatzes et al 2003]

heliocentric distance just as hot-jupiters do in scorchingly tight orbits.
