Cepheid Variable Stars

For this discussion, the Cepheid RT Aurigae will be used, but any Cepheid where a significant number of accurate radial velocity measurements have been determined can be equally analyzed.

Acceleration Data, or Gravitational Force Data

The slope of a velocity versus time graph gives the acceleration. Therefore, in that upward sloping section, there is a change of radial velocity by around +27 km/sec which occurs over a time interval of around 167,000 seconds. This indicates that there is a relatively constant acceleration which is in effect in this portion of the cycle which is +27,000/167,000 or +0.161 meter/sec². (Plus here meaning receding from us, and therefore actually inward. Below, it is more appropriately described as negative, in the star's rest frame.)

The relative constancy of this slope suggests a relative constant accelerating force is acting during that extended portion of the velocity curve. That force is assumed to be the "surface gravity" of the star, and that the material involved is therefore following a normal ballistic path from soon after the point of having the most outward velocity to just before having the greatest inward velocity.

Since Newton's Laws show that only the mass and radius of an object are involved in establishing the surface gravity of any celestial object, this slope value seems to represent an extremely accurate value which can be used to establish either the radius or the mass if the other is known.

The actual calculations are as follows:

The current estimates for RT Aurigae are:
M_star = 5.0 * M_Sun
r_star = 38 * r_Sun
The surface acceleration on the Sun, G_Sun, is around 270 m/s²

These accepted values give a surface gravitational acceleration for RT Aurigae, G_star, of 0.93 m/sec². This value seems certainly incorrect by a factor of about six, as the slope of the velocity curve (calculated above, around 0.16 m/sec²) must certainly represent a very reliable value for that acceleration. This seems to suggest that the currently accepted values for either the radius or mass, or both, of RT Aurigae must be incorrect. This seems to suggest some serious problems. If the mass of that giant star is actually only 1/6 the accepted value, then its total mass is less than the Sun, which seems unlikely. If the radius is 2.4 times as large as the accepted value, the star seems unreasonably large.

A possible implication from this is that the glowing gases that we sense with our spectroscopes might be well above the actual surface of the star, which could allow the acceleration value found from the velocity slope to be compatible with a relatively realistic size and mass star.

The acceleration information for the entire cycle can be found by differentiating the velocity graph by time. The resulting values for RT Aurigae from the graph above are included in a table below. The good constancy of the amplitude of that acceleration from Phase 0.080 to 0.640 seems to imply that the glowing material is following a ballistic course, where only gravitational attraction is affecting it. If there was fluid resistance of any sort, as if in a volume that also contained other interfering gases, these glowing materials would certainly attain a Terminal Velocity and cease to further accelerate. Therefore, it seems reasonable to conclude that everything in the vicinity of the glowing material is moving ballistically together. In some Cepheids that appear to have a velocity curve distortion roughly in the center of that slope, that could be an indication of a harmonic pulsing, where a collapsing shell of material momentarily encounters an outward moving shell, causing a brief deceleration of both shells.

Radial Distance Data

The actual distance range is certainly greater than this because of the geometry of the situation. The spectrum that we receive is certainly an "average" spectrum for the full area of the star's disk that is exposed to us. The certain spherical shape of the star means that we would see a Doppler shift that is more representative of a large radiating area of the star centered on the sub-Earth point, and it is generally accepted that the actual radial velocity of the sub-Earth point would always be around 1.4 times what we measure. This implies that the total range of radial movement of RT Aurigae is probably in excess of 2.2 million km.

Finer Details

Differential Gravitation Effects

Differential Driving Accelerations, Forces

In addition, if that third derivative curve can be accurately developed for that portion of the cycle, and therefore accurate information regarding the dependency of necessary "rebounding force" on radius, then an additional dimension might be developed. A specific radius might be identified (inside the star) as being critical to defining the pulsation process, which would add additional information to our knowledge and theories regarding Cepheids. If the meager data from this sample could be relied on, then the rebounding / repulsive force, which was likely around zero at the median radius, had gotten to six times the local gravitational force, one to counteract that gravitation and five more to create the acceleration. This great change happened in around 806,000 km of radius difference. It is suggested that an accurate data plot might be extrapolated to a "critical radius" that would represent an apparent infinite repulsive force. This data seems to suggest that such a radius would not be very deep inside RT Aurigae. Further analysis in this direction was not done, due to the small number of data points in this sample.

Data on RT Aurigae derived from the Duncan Graph Above

After Phase 0.840, the Relative Velocity changes from positive to negative, which indicates the end of the collapse, at a star radius a little more than 806,000 km smaller than its median radius. at this time, the outward acting acceleration reaches its peak amplitude, around 5 times as large as the local gravitational acceleration would be.

In the (Measured) Radial Velocity column and Relative Radial Velocity column, plus numbers mean moving away from Earth. The opposite is true in the Acceleration column, where negative values indicate acceleration away from us, toward the center of the star, or a gravitational collapsing effect. The (Measured) Radial Velocity column is the value calculated from the Doppler shift of the lines of the spectrum. The (Center-of-mass) Relative Radial Velocity column is the value after the constant receding velocity (21.60 km/sec) of the star is eliminated, and is therefore the actual relative radial velocity of the surface, from the reference frame of the center of the star. In the distance column, the values indicate a differential radius of the star, so negative values represent a smaller star and positive values represent an expanded star.

Advanced Physics-related presentations in this Domain:

Conservation of Angular Momentum - An Exception or Violation (Sept 2006)
Galaxy Spiral Arms Stability and Dynamics A purely Newtonian gravitational explanation (Nov 1997, Aug 1998)
Twins Paradox of Relativity Is Absolutely Wrong (research 1997-2004, published Aug 2004)
Perturbation Theory. Gravitational Theory and Resonance (Aug 2001, Dec 2001)
Origin of the Earth. Planetary Gravitational Resonances (Dec 2001)
Rotation of the Sun (Jan 2000)
Origin of the Universe. Cosmogony - Cosmology (more logical than the Big Bang) (devised 1960, internet 1998)
Time Passes Faster Here on Earth than on the Moon (but only a fraction of a second per year!) (Jan 2009)

Globular Clusters. All Globulars Must Regularly Pass Through the cluttered Galaxy Plane, which would be very disruptive to their pristine form. (Nov 1997, Aug 1998)
Existence of Photons. A Hubble Experiment to Confirm the Existence of Individual Photons (experimental proof of quanta) (Feb 2000)
Origin of the Moon - A New Theory (June 2000)
Planetary Rotation of Jupiter, Saturn, and the Earth (Jupiter has a lot of gaseous turbulence which should have slowed down its rapid rotation over billions of years) (March 1998)
Cepheid Variable Stars. Velocity Graph Analysis (Feb 2003)
Compton Effect of Astrophysics. A Possible New Compton Effect (Mar 2003)
Olbers Paradox Regarding Neutrinos (Oct 2004)
Kepler and Newton. Calculations (2006)
Pulsars. Pulsars May Be Quite Different than we have Assumed (June 2008)
Sun and Stars - How the Sun Works - Nuclear Fusion in Creating Light and Heat (Aug 2006)
Stars - How They Work - Nuclear Fusion. Lives of Stars and You (Aug 2004)
Sundial Time Correction - Equation of Time. Sundial to Clock-Time Correction Factor (Jan 2009)
General Relativity - A Moon Experiment to Confirm It. Confirming General Relativity with a simple experiment. (Jan 2009)
General Relativity and Time Dilation. Does Time Dilation Result? (Jan 2009)
Geysers on Io. Source of Driving Energy (June 1998)
Mass Extinction, a New Explanation. A New Explanation for Apparent Periodicity of Mass Extinctions (May 1998, August 2001)
Precession of Gyroscopes and of the Earth. Gyroscope Precession and Precession of the Earth's Equinoxes (Apr 1998)
Ocean Tides - The Physics and Logic. Mathematical Explanation of Tides (Jan 2002)
Earth's Spinning - Perfect Energy Source (1990, Dec. 2009)
Earth's Magnetic Field - Source and Logic. Complex nature of the magnetic field and its source (March 1996)
Earth Spinning Energy - Perfect Energy Source From the Earth's Spinning (1990, Nov. 2002)

Nuclear or Atomic Physics Related Subjects:

Nuclear Physics - Statistical Analysis of Isotope Masses Nuclear Structure. (research 1996-2003, published Nov 2003)
Quantum Defect is NOT a Mathematical Defect- It Can Be Calculated The Quantum Defect is a Physical Quantity and not a Fudge Factor(July 2007)
Atomic Physics - NIST Atomic Ionization Data Patterns Surprising Patterns in the NIST Data Regarding Atomic Ionization (June 2007)
Nuclear Physics - Logical Inconsistencies (August 2007)
Neutrinos - Where Did they all Come From? (August 2004)
Neutrinos - Olbers Paradox Means Neutrinos from Everywhere (Oct 2004)
Quantum Nuclear Physics. A Possible Alternative (Aug 2001, Dec 2001, Jan 2004)
Quantum Physics - Quantum Dynamics. A Potential Improvement (2006)
Quantum Physics is Compatible with the Standard Model (2002, Sept 2006, Oct 2010)
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Ionization Potential - NIST Data Patterns. Surprising patterns among different elements (March 2003)

Mass Defect Chart. (calculation, formula) (research 1996-2003, published Nov 2003)

Assorted other Physics Subjects:

Precession of Gyroscopes and of the Earth. Gyroscope Precession and Precession of the Earth's Equinoxes (Apr 1998)
Earth's Magnetic Field - Source and Logic. Complex nature of the magnetic field and its source (March 1996)
Earth Spinning Energy - Perfect Energy Source (1990, Nov. 2002)

Earth Energy Flow Rates due to Precessional Effects (63,000 MegaWatts) (Sept 2006)
Accurate Mass of the Earth. Gravitational Constant - An Important Gravitation Experiment. (Feb 2004)
Tornadoes - The Physics of How They Operate, including How they Form. Solar Energy, an Immense Source of Energy, Far Greater than all Fossil Fuels (Feb 2000, Feb 2006, May 2009)
Radiometric Age Dating - Carbon-14 Age Determination. Carbon-14, C-14 (Dec 1998)
Mass Extinction, an Old Explanation. An Old Explanation for Apparent Periodicity of Mass Extinctions (Aug 2003)
Hurricanes, the Physics and Analysis A Credible Approach to Hurricane Reduction (Feb 2001)
Sundial Time Correction - Equation of Time. Sundial to Clock-Time Correction Factor (Jan 2009)

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago