Is Isaac Asimov's Moon-Planet Theory Valid?

[Starfleet2222]

I recently read an interesting theory by Issac Asimov. Here is a link to a summery of the article, including the equation mentioned below... http://www.jmp.com/news/jmpercable/fall97/just_mooning_around.html
Asimov calculates a ratio of the force a planet (primary) is exerting over the force the sun is exerting. His equation is an aplication of Issac Newtons gravitational attraction equation. Using his equation, Asimov can calculate a band around a planet in which a satillite can truly exist. He sets the ratio to be equal to 30, or the planet having a 30x stronger grip on the satillite than the sun. He then defines a interior limit based upon the roche limit. My question is... Are his equations right? If they are, then, the moon is not a true sattilite of earth, and would fall into the planet category, or atleast something between a planet and a satillite. If his equations are correct, the sun is "winning" the "tug of war" between the Earth and the sun by a factor of over 2. Is he right and everyone else has been wrong about the moon all these years, or am I missing something?? Thanks

 

[Simfish]

Interesting...

 

[Nereid]

Are his equations right?

Well, the link you gave has only one formula, and it's 'right', as far as it goes. The first two paragraphs of the article, plus Newton's equation, give you enough info to derive the TOW formula quoted.

If they are, then, the moon is not a true satellite of earth, and would fall into the planet category, or at least something between a planet and a satellite.

What Asimov may have been trying to do (I've no way of telling; I've not seen his article - I doubt he'd have called it a theory though ) was probe the conventional understanding of 'satellite' and 'planet'.

This TOW exercise raises a good question - what else, other than the gravitational forces acting on the Moon (Sun, Earth), determine its orbit? What determines the long term stability of a satellite's orbit?

BTW, at least two of the recently discovered satellites of Jupiter, plus the recently discovered outermost satellite of Neptune also have a TOW <1 (the Neptunian one is lower than the 0.455 for the Moon).

 

[Simfish]

What puzzles me, is how the Moon formed, if Earth has a ToG value of less than 1. I know that the Moon is also receding from the Earth every year.

 

[Nereid]

Originally posted by Simfishy
What puzzles me, is how the Moon formed, if Earth has a ToG value of less than 1. I know that the Moon is also receding from the Earth every year.

(Inelastic!) collision between the proto-Earth and a Mars-sized object. The core of the impactor sank to the centre of the Earth (that's why the Earth has such a high density), and much of the debris - mostly from the impactor's mantle - coalesced to form the Moon (that's why the Moon is both very 'dry' - mostly refractory minerals - and under-dense).

If it hadn't been for the collision, the impactor would have remained as an independent planet (until it collided with something else in the young solar system).

 

[wolram]

This TOW exercise raises a good question - what else, other than the gravitational forces acting on the Moon (Sun, Earth), determine its orbit? What determines the long term stability of a satellite's orbit?
---------------------------------------------------------------------
1 mass of planet
2 orbital distance
3 speed
i would guess that the closer a planet is to its star the faster
its orbit would have to be.
please excuse intrusion, but if there is a teacher willing to
teach I am all eyes and ears.

 

[Nereid]

Originally posted by wolram
This TOW exercise raises a good question - what else, other than the gravitational forces acting on the Moon (Sun, Earth), determine its orbit? What determines the long term stability of a satellite's orbit?
---------------------------------------------------------------------
1 mass of planet
2 orbital distance
3 speed
i would guess that the closer a planet is to its star the faster
its orbit would have to be.
please excuse intrusion, but if there is a teacher willing to
teach I am all eyes and ears.

Glad you contributed wolfram If this is an 'intrusion', I say let's have more of them.

 

[Jenab]

The Earth and moon are a double planet. The crucial point is that the moon's orbit with respect to the sun is concave toward the sun at all points, even those at which it is between Earth and Sun. There are two classes of planetary satellites, then: (1) true moons (Io, Titan) and planetary companions (the moon). The requirement that the satellite be within the orbital stability radius (versus tidal disruption by their sun) applies to both cases.

Jerry Abbott

 

[pervect]

I recently read an interesting theory by Issac Asimov. Here is a link to a summery of the article, including the equation mentioned below... http://www.jmp.com/news/jmpercable/fall97/just_mooning_around.html
Asimov calculates a ratio of the force a planet (primary) is exerting over the force the sun is exerting. His equation is an aplication of Issac Newtons gravitational attraction equation. Using his equation, Asimov can calculate a band around a planet in which a satillite can truly exist. He sets the ratio to be equal to 30, or the planet having a 30x stronger grip on the satillite than the sun.

There is a much better criterion for the furthest a moon can get away from its primary than to require such a large force ratio.

This is to use the "Hill Sphere" approximation.
See for instance the Wikipedia article on the Hill Sphere

http://en.wikipedia.org/wiki/Hill_sphere

The detailed derivation of this distance gets a bit technical, it involves a conserved quantity known as the Jacobi intergal.