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The first direct observation of an exoplanet in orbit around its parent star was made by the Hubble Space Telescope. The observation is used to demonstrate the universal application and veracity of Newton's Universal Law of Gravitation, his general solution to Kepler's Third Law and Kepler's first 2 laws and that gravitation is the underlying driving principle behind it all.
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Fomalhaut Band
Newton’s General Solution To
Kepler’s Third Law
Professor Madigan
Fomalhaut
Fomalhaut is only 25 light years distant, is the
brightest star in Piscis Australis, The Southern
Fish and is visible during the late summer
Fomalhaut is twice the mass of the sun, over 17
times its luminosity and a productive life span of
only 10% of the sun’s
Results published in March of 2009 by Paul Kalas
and Eugene Chiang of UC, Berkeley show that
Fomalhaut B is the first exoplanet directly
imaged and orbit around its host star confirmed
by direct observation
Fomalhaut is only 25 light years distant; is the brightest star in Piscis Australis, The Southern Fish, and is visible during late summer
Fomalhaut is twice the mass of the sun and over 17 times its luminosity
Results published in March of 2009 by Paul Kalas and Eugene Chiang of UC, Berkeley show that
Fomalhaut B is the first exoplanet directly
imaged and orbit around its host star
confirmed by direct observation
Fomalhaut is only 25 light years distant; is the
brightest star in Piscis Australis, The Southern
Fish, and is visible during late summer
Fomalhaut is twice the mass of the sun, over 17
times its luminosity and a productive life span of
only 10% of the sun’s
Results published in March of 2009 by Paul Kalas
and Eugene Chiang of UC, Berkeley show that
Fomalhaut B is the first exoplanet directly
imaged and orbit around its host star confirmed
by direct observation
Fomalhaut is only 25 light years distant; is the
brightest star in Piscis Australis, The Southern
Fish, and is visible during late summer
Fomalhaut is twice the mass of the sun, over 17
times its luminosity and a productive life span of
only 10% of the sun’s
A study published in March 2009 by Paul Kalas
and Eugene Chiang of the University of
California, Berkeley:
Fomalhaut B is the first exoplanet directly imaged
whose orbit around its host star is confirmed by
direct observation
Fomalhaut is only 25 light years distant; is the
brightest star in Piscis Australis, The Southern
Fish, and is visible during late summer
Fomalhaut is twice the mass of the sun, over 17
times its luminosity and a productive life span of
only 10% of the sun’s
A study published in March 2009 by Paul Kalas
and Eugene Chiang of the University of
California, Berkeley:
Fomalhaut B is the first exoplanet directly imaged
whose orbit around its host star is confirmed by
direct observation
A quick review of Kepler’s laws1. All orbits are elliptical.
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
A quick review of Kepler’s laws1. All orbits are elliptical
Why?
Gravitation
2. Equal areas in equal times
Why?
Gravitation
3. The orbital period of any body in orbit about
another varies as the 3/2 power of its semimajor
axis
Why?
Gravitation
These laws are universally applicable and are not
restricted to any system
Using the Hubble Space Telescope,
Fomalhaut B was directly
imaged and its orbit empirically
measured over a 2 year period
We thus certify the veracity of all
Kepler’s Laws and their
inexorable link to gravity as the
universal driving principal and
the generality of Newton’s
Universal Law of Gravitation
We choose Kepler’s 3rd law and,
using Newton’s original
derivation, provide an
empirically demonstrable
solution for Fomalhaut B’s
orbital characteristics
2
31
P
A
2 3P A
What is the significance of the
“1” in this expression?
It represents the total mass of the
system
2
( )3 Tot
PM
A
In terms of Solar Masses and Earth
Years, we find:
2 3
( )TotP A M
3
( )TotP A M
Using the empirically determined
distance of 115 AU from Fomalhaut
to Fomalhaut B, we compute the
period of Fomalhaut B to be:
3(115) 2
11744 872
2
P x
SolarMassP x yrs
Deriving Newton’s General Form for
Kepler’s Third Law, equating the force
of gravity of the two bodies to the
centripetal force of the planet in orbit
around the center of mass, we find:
1 2( ) 2
2
2( )
2
1 2 2
2
G
Cent
M MF G
a
M vF
a
M M M vG
a a
22 2
1
2 2
2
1
2 2
2
1
3 2
3 2
1 2
1 2 4
4
4
4
M v a aG
a a a p p
M aG
a p
MG
a p
aGM
p
3 2
1 2
4aGM
p
Newton’s General Form
Of
Kepler’s 3rd Law
Solving this general equation for the
period, we find:
2 310
1
10
7 1
42.751 10 sec
2.751 10 sec872
3.156 10 sec
aP x
GM
xyrs
x yr
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