fomalhaut b and newton's general solution to kepler's third law

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

imaged and orbit around its host star

confirmed by direct observation

Fomalhaut is only 25 light years distant; is the

Fish, and is visible during late summer

Results published in March of 2009 by Paul Kalas

and Eugene Chiang of UC, Berkeley show that

imaged and orbit around its host star confirmed

by direct observation

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 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.

Gravitation

2. Equal areas in equal times

Gravitation

3. The orbital period of any body in orbit about

another varies as the 3/2 power of its semimajor

Gravitation

These laws are universally applicable and are not

restricted to any system

A quick review of Kepler’s laws1. All orbits are elliptical

Gravitation

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 3P A

What is the significance of the

“1” in this expression?

It represents the total mass of the

system

( )3 Tot

In terms of Solar Masses and Earth

Years, we find:

( )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

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

M MF G

M M M vG

M v a aG

a a a p p

Newton’s General Form

Kepler’s 3rd Law

Solving this general equation for the

period, we find:

42.751 10 sec

2.751 10 sec872

3.156 10 sec

fomalhaut b and newton's general solution to kepler's third law

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