* Updated: Solar System Foci

Alright, it was my fault. She said each planet's orbit has two foci. One is
the sun. She wants to know any new theories on what the other focal point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot. All
replies appreciated.

"the97fan" wrote in
news:A29Bb.30610$Bk1.17269@fed1read05:

Alright, it was my fault. She said each planet's orbit has two foci.
One is the sun. She wants to know any new theories on what the other
focal point is. My fault. I need some opinions from some
astronomers/professors from around the world. I'd figure this
newsgroup could help me out. When replying, please post exactly what
you do in this field. Thanks alot. All replies appreciated.


New theores?. Isaac Newton pretty much wrote the last word on this. Even
if you want the additional accuracy provided by Albert Einstein, You are
still looking back 88 years or so, when Albert published his theory of
gravity (a later last word ;-)). I suspect your teacher is just trying to
get you to do a bit of research. Try using google for the following
subjects:

Orbit focal points
Planetary orbits
Celestial Mechanics
Newton's theory of gravity
Kepler's three laws
Lagrange points
General Relativity Solar System
Mercury's perihelion advance

That should keep you going for a while.

Llanzlan

"Llanzlan Klazmon The 15th" wrote in message
7.6...
"the97fan" wrote in
news:A29Bb.30610$Bk1.17269@fed1read05:

Alright, it was my fault. She said each planet's orbit has two foci.
One is the sun. She wants to know any new theories on what the other
focal point is. My fault. I need some opinions from some
astronomers/professors from around the world. I'd figure this
newsgroup could help me out. When replying, please post exactly what
you do in this field. Thanks alot. All replies appreciated.


New theores?. Isaac Newton pretty much wrote the last word on this. Even
if you want the additional accuracy provided by Albert Einstein, You are
still looking back 88 years or so, when Albert published his theory of
gravity (a later last word ;-)). I suspect your teacher is just trying to
get you to do a bit of research. Try using google for the following
subjects:

Orbit focal points
Planetary orbits
Celestial Mechanics
Newton's theory of gravity
Kepler's three laws
Lagrange points
General Relativity Solar System
Mercury's perihelion advance

That should keep you going for a while.

Llanzlan

I'm not sure how much googling I can take. But will defiantly take a look at
that list and googling more tonight. Thanks.

"the97fan" wrote in message
news:A29Bb.30610$Bk1.17269@fed1read05...
Alright, it was my fault. She said each planet's orbit has two foci. One
is
the sun. She wants to know any new theories on what the other focal point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot. All
replies appreciated.

There's actually not a lot to say about the empty focus of an elliptic
orbit. I suspect your teacher may be having a bit of fun with the class.
However, the following may be of interest and may giver her a surprise (I
know it surprised me when I read it).

The result applies to objects that are in a 1:1 spin-orbit resonance around
their primary. This includes all (most???) of the major moons of the solar
system. For the purposes of this discussion, lets consider the Earth-Moon
system.

The Moon is locked into a 1:1 spin-orbit resonance around the Earth. This
means that its rotational period is equal to its orbital period. It is often
said that this causes the Moon to always present (sort-of/kind-of) the same
face to the Earth. Strictly speaking this is not entirely true. In the
course of one orbit the face of the Moon wobbles back and forth. We actually
see about 59% of the Moons surface during the course of one orbit. This
wobble is called "libration". You can get a good sense of it from this site
http://antwrp.gsfc.nasa.gov/apod/ap991108.html

The classic explanation of libration is that for short periods of time (on
the order of an orbital period) the rotation rate is constant but the
orbital speed is not (the orbital speed will be greatest at perigee and
least at apogee) and this leads to the wobble. Up until about a year ago
this is the only explanation of libration that I had ever heard but I found
a result in a book that I bought that leads to a very elegant explanation of
libration (the underlying reasons are of course the same, this is just a
different description of it).

(I'm getting to the interesting bit ... finally)

The book is ...

Solar System Dynamics, C. D. Murray, S. F. Dermott, Cambridge University
Press, 1999

In it, the authors derive a result that is summarized as follows ...

"... a synchronously rotating satellite rotates with one face pointing
toward the empty focus of its orbit."

This means that the Moon would *actually* keep the *exact* same face toward
the empty focus of its orbit. If we could image the Moon from the vantage
point of the empty focus during the course of an orbit, there would be *no*
libration (there would still be a slight bobbing up and down but that is due
to something else). Since it keeps the exact same face pointed toward its
empty focus during the course of an orbit it can't possibly keep the same
face pointed toward the full focus (the Earth) hence the wobble from our
perspective.

I honestly don't know if this is a "new" result (it was new to me) and I
would be interested to hear from anyone who had heard of this before from
another source.

(Note: I'm guessing you are in high school. The material in this book is
well beyond high school level but hopefully just a reference will do. If you
would like to try and contact one of the authors, you can find his e-mail
address here ...
http://ssdbook.maths.qmw.ac.uk/ )

Good Luck

"the97fan" wrote in message
news:A29Bb.30610$Bk1.17269@fed1read05...
Alright, it was my fault. She said each planet's orbit has two foci. One
is
the sun. She wants to know any new theories on what the other focal point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot. All
replies appreciated.


It's not really a "what". All of the orbits of the planets have two foci.
One is occupied by the sun. The other is just a mathematical abstraction
rather than a "thing". For a very elliptical orbit it is just a point in
empty space. I wonder: is the second foci of planets with very circular
orbits within the body of the sun?

R

"Ron Miller" wrote...
in message ...

"the97fan" wrote in message
news:A29Bb.30610$Bk1.17269@fed1read05...

Alright, it was my fault. She said each planet's orbit has two foci. One is
the sun. She wants to know any new theories on what the other focal point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot. All
replies appreciated.

It's not really a "what". All of the orbits of the planets have two foci.
One is occupied by the sun. The other is just a mathematical abstraction
rather than a "thing". For a very elliptical orbit it is just a point in
empty space. I wonder: is the second foci of planets with very circular
orbits within the body of the sun?

R

'Lo Ron --

Since the orbits of all the major planets are *almost* circular,
both foci must indeed be very close together and within the
Sun. Jupiter would be a distinct exception since its orbital
focus is outside the surface of the Sun, so the other focus,
being nearer to Jupiter, would also be outside the Sun's
surface.

And John Z.'s post would indicate that the non-orbital focus
of the Moon's orbit around the Earth is more than just a
mathematical abstraction. If he is right, then this focus is
where the Moon always faces with no libration effect. So
this focus must move around within Earth's surface. It might
be interesting to correlate these movements with seismic
readings!

happy days and...
starry starry nights!

--
Our heads up in the sky,
We're so clueless of our worth...
Whose sky no longer shines
As we lose our Mother-Earth?

As people we must learn
About the care of planet parts,
To leave the world a better turn--
Empower brand new hearts!

Paine Ellsworth

"Ron Miller" wrote in message
...

"the97fan" wrote in message
news:A29Bb.30610$Bk1.17269@fed1read05...
Alright, it was my fault. She said each planet's orbit has two foci. One
is
the sun. She wants to know any new theories on what the other focal
point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot.
All
replies appreciated.


It's not really a "what". All of the orbits of the planets have two foci.
One is occupied by the sun. The other is just a mathematical abstraction
rather than a "thing". For a very elliptical orbit it is just a point in
empty space. I wonder: is the second foci of planets with very circular
orbits within the body of the sun?

The distance between the foci can be calculated as

d = 2*e*a

where e is the eccentricity and a the semi-major axis of
the orbit. Running down the list of planets:

e a(10^6 km) d(10^6 km)
Mercury 0.2056 57.9 23.81
Venus 0.0068 108.2 1.47
Earth 0.0167 149.6 5.00
Mars 0.0934 227.9 42.57
Jupiter 0.04845 778.3 75.42
Saturn 0.05565 1427.0 158.8
Uranus 0.04724 2887.9 272.8
Neptune 0.00858 4529.3 77.8
Pluto 0.2482 5913.5 2935.5

The Sun's diameter is 1.392x10^6 km. So Venus' foci almost,
but not quite, fit within the diameter of the Sun. The rest
of the planet's foci are much too far apart.

"Greg Neill" wrote in message...
. ..

"Ron Miller" wrote in message
...

"the97fan" wrote in message
news:A29Bb.30610$Bk1.17269@fed1read05...

Alright, it was my fault. She said each planet's orbit has two foci. One is
the sun. She wants to know any new theories on what the other focal point
is. My fault. I need some opinions from some astronomers/professors from
around the world. I'd figure this newsgroup could help me out. When
replying, please post exactly what you do in this field. Thanks alot. All
replies appreciated.

It's not really a "what". All of the orbits of the planets have two foci.
One is occupied by the sun. The other is just a mathematical abstraction
rather than a "thing". For a very elliptical orbit it is just a point in
empty space. I wonder: is the second foci of planets with very circular
orbits within the body of the sun?

The distance between the foci can be calculated as

d = 2*e*a

Damn! I KNEW i should've looked it up. Sorry, Ron.

I just *assumed* that since the eccentricities were so close to
zero that both of the foci would be within the Sun, except for
Jupiter's. I was wrong. I looks like only Venus falls within this
category.

Thanks, Greg, for your clarification!

happy days and...
starry starry nights!

--
Gaia shadow come November,
Does this bode well for December?
Moon aglow as I remember,
Tremble, tremble glowing ember,
Seems my life's a severed member.

Paine Ellsworth

"Painius" wrote in message
...

And John Z.'s post would indicate that the non-orbital focus
of the Moon's orbit around the Earth is more than just a
mathematical abstraction. If he is right, then this focus is
where the Moon always faces with no libration effect. So
this focus must move around within Earth's surface. It might
be interesting to correlate these movements with seismic
readings!

The focus to focus distance is given by ...

F-F' = 2*e*a were ...

e = eccentricity
a = semi-major axis

The radius of the Earth is 6.378E3 km

e(Moon) = 0.0549
a(Moon) = 3.844E5

F-F' = 4.221E4 km

Outside of the Earth

"Ron Miller" wrote in message
...

I wonder: is the second foci of planets with very circular
orbits within the body of the sun?

The focus to focus distance is given by ...

F-F' = 2*e*a were ...

e = eccentricity
a = semi-major axis

The radius of the Sun is 6.9599E5 km

Planet Semi-Major (km) Eccentricity
------ ------------------ ------------
Mercury 5.79E7 0.206
Venus 1.082E8 0.007
Earth 1.496E8 0.017
Mars 2.279E8 0.093
Jupiter 7.783E8 0.048
Saturn 1.429E9 0.056
Uranus 2.875E9 0.046
Neptune 4.504E9 0.009
Pluto 5.916E9 0.249


Planet F-F' (km) In/Out of Sun
------ ------------- ---------------
Mercury 2.385E7 Out
Venus 1.515E6 Out
Earth 5.086E6 Out
Mars 4.239E7 Out
Jupiter 7.472E7 Out
Saturn 1.600E8 Out
Uranus 2.645E8 Out
Neptune 8.107E7 Out
Pluto 2.946E9 Out


Although you would think that the foci would be very close to each other,
you have to keep in mind the enormous distances involved in relation to the
radius of the Sun