The Universe Table — A Periodic Table for Astronomy

   

Galaxy Name Mass of Galaxy Center ( ×1030 kg)
Star Name Mass ( ×1030 kg) Distance ( ×1010 km) Velocity (km/s) Period (years)
Gravity (m/s2) Radius (km) Density (kg/m3)    
   
Planet Name Mass ( ×1020 kg) Distance ( ×1010 km) Velocity (km/s) Period (days)
Gravity (m/s2) Radius (km) Density (g/cm3)    
   


Category: Physics and Astronomy
The Universe Table—A Periodic Table for Astronomy

Andrew Hu
Red River High School
Grand Forks, ND 58201
AndrewHu1997@gmail.com

Abstract

The periodic table of chemistry is well known and is an essential tool for chemistry study. This research applies the idea of the periodic-table construction of chemistry to astronomy and builds the Universe Table, which provides useful information to astronomy as the periodic table to chemistry. Seven characteristics for each of stars and planets, (i) mass, (ii) distance between an object and the orbital center, (iii) velocity, (iv) orbital period, (v) gravity, (vi) object radius, and (vii) density, are displayed or yet to be found. The Universe Table like the Universe is unlimited and is expandable because users can always add more galaxies, stars, and planets to the table. In order to find the unknown characteristics, various constants, symbols, laws, formulas, and methods are used, proposed, or implemented. The Universe Table successfully fulfills the two missions of the hypothesis: (i) Classify galaxies, stars, and planets into groups with similar properties. (ii) Predict the characteristics of galaxies, stars, and planets based on other characteristics. This research is related to several subjects including physics, astronomy, and computer science. The future works and directions include: (i) finding more characteristics, (ii) planet and star predictions, (iii) a more realistic model, and (iv) able to save the data entered.

Introduction
The periodic table of chemistry as shown in Figure 1 is well known and is an essential tool for chemistry study. It has the elements arranged in order of increasing atomic number. A vertical column contains elements with similar properties. A period runs from left to right with the atomic number of the elements increasing from left to right. The main purpose of the periodic table includes Scientists took many years to complete the periodic table, whose elements were discovered in various years. However, before the table was complete, scientists had already known the existence of the not-yet-discovered elements. It is because the elements are ordered in sequence. If the sequence was broken, then elements were needed to complete the sequence. This research applies the idea of the periodic-table construction of chemistry to astronomy and builds the universe table, which provides useful information to astronomy as the periodic table to chemistry.


Figure 1. A periodic table (http://old.iupac.org/reports/periodic_table/)

Hypothesis
There is a universe table for astronomy as the periodic table for chemistry. Additionally, the main purpose of the universe table includes Methods Used and Proposed
In order to build the universe table, this research uses, designs, and implements a wide variety of concepts, formulas, laws, and methods including: gravity, Kepler’s laws, the mass of a star or galaxy center.
Constants and symbols used
The following constants and symbols are used in this research:

  • d (distance): the distance between two objects or orbital radius
  • g (gravity of Earth): 9.81 m/s2
  • G (the gravitational constant): 6.673×10-11 N⋅m2/kg2,   where N is Newton
  • m (mass): the mass of an object
  • N (Newton): 1 kg⋅m/s2
  • p (period): the period of an orbit
  • r (radius): the radius of an object
  • v (velocity): the velocity of an object

Centripetal acceleration
The acceleration is directed inward toward the center of the orbit and is given by 
     a = v2/d
where
  • v is the speed of the object and
  • d is the radius of the orbit.

Centripetal force
Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force having the magnitude 
   F = m⋅v2/d
where
  • m: the mass of the object,
  • v: the velocity of the object, and
  • d: the orbital radius.

Density
The density of a star or planet is equal to its mass divided by its volume 
    s = m/((4/3)⋅r3⋅π)
where
  • s is the density
  • m is the mass
  • r is the radius

Distance between the object and the orbit center
The circular velocity of an object in orbit is equal to the circumference of an orbit divided by the period of the orbit: 
     v = (2⋅π⋅d)/p ⇒ d = (v⋅p)/(2⋅π)
where
  • p is the period of orbit and
  • v is the velocity of the object.

Escape velocity
From Newton’s law of universal gravitation and the centripetal acceleration we find that, for a circular orbit, 
     v2/d = G⋅M/d2  ⇒  v = (G⋅M/d)½
where
  • G is the gravitational constant,
  • M is the mass of the object at the orbit center, and
  • d is the radius of the orbit.

Kepler’s laws of planetary motion
First law
The path of each planet about the Sun is an ellipse with the Sun at one focus.

Second law
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.

Third law
The ratio of the squares of the periods (the time needed for one revolution about the Sun) of any two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from the Sun: 
     (p1/p2)2 = (d1/d2)3  ⇒  d13/p12 = d23/p22
where
  • p1: the period of an planet 1,
  • p2: the period of an planet 2,
  • d1: the distance between the planet 1 and the Sun, and
  • d2: the distance between the planet 2 and the Sun.

This law means that d3/p2 should be the same for each planet.

Mass of a star or galaxy center
For finding the mass of a star, because the gravitational attraction of the star for the planet is the centripetal force causing the planet's circular motion around the star, we can use Newton’s law of universal gravitation to find the mass of the star: 
      Fgravity = Fcentripetal
  ⇒  (G⋅M⋅m)/d2 = (m⋅v2)/r
  ⇒  M = (v2⋅d2)/(G⋅r)
  ⇒  M = (v2⋅r)/G     ∵ r = d
where
  • M: the mass of the star,
  • m: the mass of the planet,
  • d: the distance between the star and the planet,
  • v: the velocity of the planet, and
  • r: the orbital radius of the planet around the star.

Mass of the Earth
Use the following formulas to find the mass of the Earth: 
      Fgravity = F
  ⇒  G⋅m⋅m1/r2 = m1⋅a
  ⇒  G⋅m/r2 = g
  ⇒  m = g⋅r2/G
where
  • G is the gravitational constant,
  • g is the gravity of Earth,
  • m is the mass of the Earth, and
  • r is the radius of the Earth.

Newton's laws of motion
First law
The velocity of a body remains constant unless the body is acted upon by an external force.
Second law
The acceleration a of a body is parallel and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = m⋅a.
Third law
The mutual forces of action and reaction between two bodies are equal, opposite and collinear.

Newton's law of universal gravitation
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them: 
   F = G⋅m1⋅m2/d2
where:
  • F is the force between the masses,
  • G is the gravitational constant,
  • m1 is the first mass,
  • m2 is the second mass, and
  • d is the distance between the centers of the masses.

Orbital period
The orbital period p of a small body orbiting a central body in a circular or elliptic orbit is: 
     p = 2⋅π[d3/(G⋅M)]½
where
  • d is the orbital radius,
  • G is the gravitational constant, and
  • M is the mass of the central body.

Conclusions
The proposed Universe Table successfully fulfills the two missions of the hypothesis:
To classify galaxies, stars, and planets into groups with similar properties
Related galaxies, stars, and planets are grouped by the Universe Table. Wrongly-grouped objects can be found by checking their characteristics; for example, if a planet does not belong to a star system, its mass might not be predicted correctly.

To predict the characteristics of galaxies, stars, and planets based on other characteristics.
Users can use the proposed Universe Table to predict various characteristics by leaving the characteristic blank and clicking the Update button.
This research is related to several subjects: Also, it involves huge amount of works; for example, more than 30 constants, symbols, laws, formulas, and methods are used, proposed, or implemented in this research. The proposed Universe Table like the Universe is unlimited and is extensible because users can always add more galaxies, stars, and planets to the table.

Future Directions
The proposed Universe Table is not finished yet because there are many other ways to find the characteristics; for example, orbital periods can be found by a couple of methods, which are based on different characteristics. The periodic table can be used to predict unknown elements, but my system is not yet able to do that. Also, the model I proposed is greatly simplified. For example, a star system may include more than one star, but my system can only handle one star. The future works and directions therefore include:
References
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  7. Wikipedia. (n.d.). Milky Way. Retrieved October 19, 2011, from http://en.wikipedia.org/wiki/Milky_way.

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