Sun calculates to be less massive for planets which are further out - sun mass anomaly

It is a fairly easy matter to calculate the mass of the sun based upon
the velocity and the orbital period of the planets. I obtained a list
of the parameters from:

http://janus.astro.umd.edu/astro/calculators/scalc.html

According to Kepler's third law, Mass = Velocity^2*radius/G where
G=6.672E-11

The radius can be determining from the circumference of the orbit which
is just velocity multiplied by the orbital period. The relationship of
radius to circumference for a circle is radius = (circumference/pi)/2.
This relationship holds for a perfect circle instead of an orbital
ellipse. However, from what I can see, the way orbital mechanics work
is that the same gravitational body will produce the same average
velocity and period no matter whether the orbit is highly eliptical or
perfectly circular. So it appears fair to circularize the orbit to do
the calculation.

We would expect that to a high degree of accuracy, the mass of the Sun
should calculate out to be exactly the same for all planets. We do know
these planetary parameters to a high degree of accuracy. Any
descrepencies ought to be randomly distributed. However, when I did the
actual calculations, a definite pattern emerges. Here are the masses of
the sun as calculated from the planetary velocity and period.

Planet Calculated sun mass
MERCURY 1.9894791993181600E+30
VENUS 1.9894791810937200E+30
EARTH 1.9894791808340100E+30
MARS 1.9894791769989200E+30
JUPITER 1.9894791570266600E+30
SATURN 1.9894791987710100E+30
URANUS 1.9894791941358700E+30
NEPTUNE 1.9894791973551700E+30
PLUTO 1.9894791888597400E+30

At first glance, they look all the same at about 1.99E30 Kg, but if you
look at the digits further down, you see a pattern emerging that from
Mercury to Jupiter, the calculated mass of the sun DECREASES
consistently. It then jumps back up for Saturn and then appears to
generally (except for Neptune) decrease again through Pluto.

This is very strange indeed! The Sun appears to have smaller mass the
further you go out.

Since anyone with a calculator and a basic knowledge of orbital
mechanics could do this calculation, surely someone must have noticed
this anomaly before. Is there a generally accepted scientific
explanation for this anomaly? I would imagine that this would have a
huge impact on planetary navigation of space probes.

I suppose the most obvious explanation would be that this is just the
normal expectation for the degree of precision that is avaliable.
However, if that were the case, I would think that the mass of the Sun
would bounce up and down randomly instead of distinctly trending
downward. Also the digit where we see the differences correspond to a
mass difference of 1E22 Kg, or a trillion, trillion kilograms. Not an
insignificant amount of mass.

It is really odd that there is a significant break in the trend between
Jupiter and Saturn. The mass of the Sun appears to reset back to nearly
the mass of the sun as measured by Mercury and then trends down again,
but not as rapidly as for the inner planets.

If someone could fill me on on the possible explanations for this
phenomenon, I would greatly appreciate it.

fhumass

wrote in news:1147324390.881010.78010
@j73g2000cwa.googlegroups.com:

It is a fairly easy matter to calculate the mass of the sun based upon
the velocity and the orbital period of the planets. I obtained a list
of the parameters from:

http://janus.astro.umd.edu/astro/calculators/scalc.html

According to Kepler's third law, Mass = Velocity^2*radius/G where
G=6.672E-11

The radius can be determining from the circumference of the orbit which
is just velocity multiplied by the orbital period. The relationship of
radius to circumference for a circle is radius = (circumference/pi)/2.
This relationship holds for a perfect circle instead of an orbital
ellipse. However, from what I can see, the way orbital mechanics work
is that the same gravitational body will produce the same average
velocity and period no matter whether the orbit is highly eliptical or
perfectly circular. So it appears fair to circularize the orbit to do
the calculation.

We would expect that to a high degree of accuracy, the mass of the Sun
should calculate out to be exactly the same for all planets. We do know
these planetary parameters to a high degree of accuracy. Any
descrepencies ought to be randomly distributed. However, when I did the
actual calculations, a definite pattern emerges. Here are the masses of
the sun as calculated from the planetary velocity and period.

Planet Calculated sun mass
MERCURY 1.9894791993181600E+30
VENUS 1.9894791810937200E+30
EARTH 1.9894791808340100E+30
MARS 1.9894791769989200E+30
JUPITER 1.9894791570266600E+30
SATURN 1.9894791987710100E+30
URANUS 1.9894791941358700E+30
NEPTUNE 1.9894791973551700E+30
PLUTO 1.9894791888597400E+30


Errors in the values plugged into the equations. What are the error bars on
the data you used. If your source doesn't tell you then the results are not
meaningful. The differences above are in the eighth decimal place. i.e one
part in one hundred million.

Klazmon






fhumass

wrote:
It is a fairly easy matter to calculate the mass of the sun based upon
the velocity and the orbital period of the planets. I obtained a list
of the parameters from:

http://janus.astro.umd.edu/astro/calculators/scalc.html

According to Kepler's third law, Mass = Velocity^2*radius/G where
G=6.672E-11

The radius can be determining from the circumference of the orbit which
is just velocity multiplied by the orbital period. The relationship of
radius to circumference for a circle is radius = (circumference/pi)/2.
This relationship holds for a perfect circle instead of an orbital
ellipse. However, from what I can see, the way orbital mechanics work
is that the same gravitational body will produce the same average
velocity and period no matter whether the orbit is highly eliptical or
perfectly circular. So it appears fair to circularize the orbit to do
the calculation.

We would expect that to a high degree of accuracy, the mass of the Sun
should calculate out to be exactly the same for all planets. We do know
these planetary parameters to a high degree of accuracy. Any
descrepencies ought to be randomly distributed. However, when I did the
actual calculations, a definite pattern emerges. Here are the masses of
the sun as calculated from the planetary velocity and period.

Planet Calculated sun mass
MERCURY 1.9894791993181600E+30
VENUS 1.9894791810937200E+30
EARTH 1.9894791808340100E+30
MARS 1.9894791769989200E+30
JUPITER 1.9894791570266600E+30
SATURN 1.9894791987710100E+30
URANUS 1.9894791941358700E+30
NEPTUNE 1.9894791973551700E+30
PLUTO 1.9894791888597400E+30

At first glance, they look all the same at about 1.99E30 Kg, but if you
look at the digits further down, you see a pattern emerging that from
Mercury to Jupiter, the calculated mass of the sun DECREASES
consistently. It then jumps back up for Saturn and then appears to
generally (except for Neptune) decrease again through Pluto.

This is very strange indeed! The Sun appears to have smaller mass the
further you go out.

Since anyone with a calculator and a basic knowledge of orbital
mechanics could do this calculation, surely someone must have noticed
this anomaly before. Is there a generally accepted scientific
explanation for this anomaly? I would imagine that this would have a
huge impact on planetary navigation of space probes.

I suppose the most obvious explanation would be that this is just the
normal expectation for the degree of precision that is avaliable.
However, if that were the case, I would think that the mass of the Sun
would bounce up and down randomly instead of distinctly trending
downward. Also the digit where we see the differences correspond to a
mass difference of 1E22 Kg, or a trillion, trillion kilograms. Not an
insignificant amount of mass.

It is really odd that there is a significant break in the trend between
Jupiter and Saturn. The mass of the Sun appears to reset back to nearly
the mass of the sun as measured by Mercury and then trends down again,
but not as rapidly as for the inner planets.

If someone could fill me on on the possible explanations for this
phenomenon, I would greatly appreciate it.

fhumass


Do suppose that having the great mass of Jupiter either inside or
outside the planet's orbit might make the difference?

Double-A

"Double-A" writes:

wrote:
At first glance, they look all the same at about 1.99E30 Kg, but if you
look at the digits further down, you see a pattern emerging that from
Mercury to Jupiter, the calculated mass of the sun DECREASES
consistently. It then jumps back up for Saturn and then appears to
generally (except for Neptune) decrease again through Pluto.

fhumass


Do suppose that having the great mass of Jupiter either inside or
outside the planet's orbit might make the difference?

Double-A's got a good point here. I would expect the mass to rise
steadily though as more and more planets on the inside of it...

/Fredrik

"Fredrik Bulow" wrote in message ...
"Double-A" writes:

wrote:
At first glance, they look all the same at about 1.99E30 Kg, but if you
look at the digits further down, you see a pattern emerging that from
Mercury to Jupiter, the calculated mass of the sun DECREASES
consistently. It then jumps back up for Saturn and then appears to
generally (except for Neptune) decrease again through Pluto.

fhumass


Do suppose that having the great mass of Jupiter either inside or
outside the planet's orbit might make the difference?

Double-A's got a good point here. I would expect the mass to rise
steadily though as more and more planets on the inside of it...

Planets appear to eachother as point masses, not as
spherical shells that sit around the Sun. They cause
perturbations in eachother's orbits (precessions,
changes in eccentricity, small radial changes) that
tend to average out, for the most part, over time.

In article ,
Greg Neill wrote:
Do suppose that having the great mass of Jupiter either inside or
outside the planet's orbit might make the difference?
Double-A's got a good point here. I would expect the mass to rise
steadily though as more and more planets on the inside of it...

Planets appear to eachother as point masses, not as
spherical shells that sit around the Sun.

Yes and no. If an inner planet orbits much more rapidly than the planet
whose orbit you're calculating, then it's often a reasonable approximation
to treat the inner planet as a disk around the Sun. If you're ignoring
the third dimension, that's pretty much equivalent to a spherical shell.

They cause
perturbations in eachother's orbits (precessions,
changes in eccentricity, small radial changes) that
tend to average out, for the most part, over time.

Exactly, and the averaging turns out to be surprisingly close to just
treating the inner planet as a disk or shell. For precise work like
long-term perturbation effects, you can't get away with that, but for
first-approximation work and overall properties of the orbit, you often
get very good results that way.
--
spsystems.net is temporarily off the air; | Henry Spencer
mail to henry at zoo.utoronto.ca instead. |

wrote:
It is a fairly easy matter to calculate the mass of the sun based upon
the velocity and the orbital period of the planets. I obtained a list
of the parameters from:

http://janus.astro.umd.edu/astro/calculators/scalc.html

According to Kepler's third law, Mass = Velocity^2*radius/G where
G=6.672E-11

The radius can be determining from the circumference of the orbit which
is just velocity multiplied by the orbital period. The relationship of
radius to circumference for a circle is radius = (circumference/pi)/2.
This relationship holds for a perfect circle instead of an orbital
ellipse. However, from what I can see, the way orbital mechanics work
is that the same gravitational body will produce the same average
velocity and period no matter whether the orbit is highly eliptical or
perfectly circular. So it appears fair to circularize the orbit to do
the calculation.

We would expect that to a high degree of accuracy, the mass of the Sun
should calculate out to be exactly the same for all planets. We do know
these planetary parameters to a high degree of accuracy. Any
descrepencies ought to be randomly distributed. However, when I did the
actual calculations, a definite pattern emerges. Here are the masses of
the sun as calculated from the planetary velocity and period.

Planet Calculated sun mass
MERCURY 1.9894791993181600E+30
VENUS 1.9894791810937200E+30
EARTH 1.9894791808340100E+30
MARS 1.9894791769989200E+30
JUPITER 1.9894791570266600E+30
SATURN 1.9894791987710100E+30
URANUS 1.9894791941358700E+30
NEPTUNE 1.9894791973551700E+30
PLUTO 1.9894791888597400E+30

At first glance, they look all the same at about 1.99E30 Kg, but if you
look at the digits further down, you see a pattern emerging that from
Mercury to Jupiter, the calculated mass of the sun DECREASES
consistently. It then jumps back up for Saturn and then appears to
generally (except for Neptune) decrease again through Pluto.

This is very strange indeed! The Sun appears to have smaller mass the
further you go out.

Since anyone with a calculator and a basic knowledge of orbital
mechanics could do this calculation, surely someone must have noticed
this anomaly before. Is there a generally accepted scientific
explanation for this anomaly? I would imagine that this would have a
huge impact on planetary navigation of space probes.

I suppose the most obvious explanation would be that this is just the
normal expectation for the degree of precision that is avaliable.
However, if that were the case, I would think that the mass of the Sun
would bounce up and down randomly instead of distinctly trending
downward. Also the digit where we see the differences correspond to a
mass difference of 1E22 Kg, or a trillion, trillion kilograms. Not an
insignificant amount of mass.

It is really odd that there is a significant break in the trend between
Jupiter and Saturn. The mass of the Sun appears to reset back to nearly
the mass of the sun as measured by Mercury and then trends down again,
but not as rapidly as for the inner planets.

If someone could fill me on on the possible explanations for this
phenomenon, I would greatly appreciate it.

fhumass

A wonderful example of significant figure abuse.
The periods are known to eight significant digits.
Any number calculated with a number known to eight significant digits
is only known (at best) to eight significant digits. The remaining
digits are garbage. This is a basic numerical literacy skill, hammered
in relentlessly the first two weeks of freshman physics lab.
To eight significant digits, these mass values are identical.

PD

You also need to use the total mass of the system (Solar mass +
planetary mass), not just the solar mass. And, the orbit of the
objects are around the center of mass of the system, not the center of
the Sun.

muddy wrote:
You also need to use the total mass of the system (Solar mass +
planetary mass), not just the solar mass. And, the orbit of the
objects are around the center of mass of the system, not the center of
the Sun.


Welllll ... that's an OK approximation in some cases. For instance,
it's common to lump Mercury through Mars into the Sun when you're doing
long-term integrations of Pluto.

You can *define* Keplerian elements of any body relative to any other
body. That's nothing more than a mathematical transformation of six
degrees of freedom (three components of relative position, three of
relative velocity) into six other quantities. From that perspective,
given an appropriate value for the "mass of the barycenter", yes, you
can establish a set of barycentric orbital elements.

The rub, as always, lies in the perturbations. Do barycentric elements
show less variation with time than heliocentric elements? I don't know
the answer, but it's an interesting question.

JPL's planetary ephemeris files are barycentric, because that's how we
do the numerical integration.

-- Bill Owen

I just wanted to take a second to say wow! This is the most scientific
discussion that I've read in sci.astro for a long time.
Congratulations to all the contributors for not giving up on this
forum.

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