Energy phantoms

This is an optical image in the visual range of Theta Ursae Majoris. It is listed in SIMBAD as an F7V spectral type star with a parallax of 74.19 mas. Credit: Aladin at SIMBAD.

Students start from specific situations of motion, determine how to calculate energy and convert units, then evaluate types of energy.

Evaluation

evaluation activity

Energies

Def. a "quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent"[1] is called energy.

Def. "[a] physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)"[2] is called force.

In astronomy we estimate distances and times when and where possible to obtain forces and energy.

The key values to determine in both force and energy are (L/T²) and (L²/T²). Force (F) x distance (L) = energy (E), L/T² x L = L²/T². Force and energy are related to distance and time using proportionality constants.

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:[3]
F = G \frac{m_1 m_2}{r^2}\ ,

where:

  • F is the force between the masses,
  • G is the gravitational constant,
  • m1 is the first mass,
  • m2 is the second mass, and
  • r is the distance between the centers of the masses.
The diagram shows two masses attracting one another. Credit: .

In the International System of Units (SI) units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10−11
 N m2 kg−2.[4]

Observationally, we may not know the origin of the force.

Coulomb's law states that the electrostatic force F experienced by a charge, q at position r_q, in the vicinity of another charge, Q at position r_Q, in vacuum is equal to:

F = {qQ\over4\pi\varepsilon_0}{1\over {r^2}},

where \varepsilon_0 is the electric constant and r is the distance between the two charges.

Coulomb's constant is

k_e = 1 / (4\pi\varepsilon_0\varepsilon),

where the constant \varepsilon_0 is called the permittivity of free space in SI units of C2 m−2 N−1.

For reality, \varepsilon is the relative (dimensionless) permittivity of the substance in which the charges may exist.

The energy E for this system is

E = F \cdot D,

where D is the displacement.

Unknown forces

Newton's second law of motion is that F = ma, where F is the force applied, m is the mass of the object receiving the force, and a is the acceleration observed for the astronomical object. The newton is therefore:[5]

{1~{\rm N} = 1~{\rm kg} \frac{{\rm m}} {{\rm s}^2}}

where:

N: newton
kg: kilogram
m: metre
s: second.

In dimensional analysis:

{\mathsf F} = \frac{\mathsf {ML}} {{\mathsf T}^2}

where

M: mass
L: length
T: time.

But, for a force of unknown type, mass or charge may be meaningless until proven applicable.

So that

{\mathsf A} = {\mathsf {F/M}} = \frac{\mathsf L} {{\mathsf T}^2},
{\mathsf A} = {\mathsf {F/Q}} = \frac{\mathsf L} {{\mathsf T}^2},
{\mathsf P} = {\mathsf {E/M}} = \frac{{\mathsf L}^2} {{\mathsf T}^2},

and

{\mathsf P} = {\mathsf {E/Q}} = \frac{{\mathsf L}^2} {{\mathsf T}^2},

where {\mathsf P} may be called an energy phantom, or astronomical energy phantom.

Problem 1

The image is an optical negative centered on the SIMBAD coordinates J2000.0 for Van Maanen's star. Image is from the Palomar 48-inch Schmidt reflecting telescope. Van Maanen's star is the largest black dot center top right. Credit: NASA/IPAC Extragalactic Database.
The SIMBAD image is in natural color of Van Maanen's star. Credit: Aladin at SIMBAD.

In the image at right Van Maanen's star (largest dark spot) is not at the center of the coordinates where expected, but as a high proper motion star it is actually off-center to the center top right. This is an example of the change in radiation flux to a specific location of observation by a source undergoing a change in location for observation (but staying within the observation field of view) within an observable change in radiation flux (the star did not move close enough to blacken the entire frame nor change intensity sufficiently to disappear into the background of the detector).

Using a meter stick or smaller measuring device, measure the distance in mm that the star is displaced from the center of the negative. The image is 5' x 5' and may be considered from May 1.0, 1994.

According to SIMBAD, Van Maanen's star (designated VAN MAANEN STAR), is at optical coordinates: 00h 49m 09.902s +05° 23' 19.01".[6]

a. If the SIMBAD coordinates for the center of the image are the star's current position, how many milliarcseconds (mas) has the star moved since the above image was taken?

b. If the only direction of motion for the star is in the plane of the image, and the star is 14.1 ± 0.1 ly away, how fast is it moving?

c. The image at SIMBAD for the star [at left], also called Gliese 35, shows a split color image of the star (assume the position of the star is between the two color spots), where the image is 2.4' x 2.4'. The star is not at the coordinates but along the line of travel. If the star slowed down between these two images, what is its speed in the SIMBAD image?

d. Using the two speeds from above, calculate the deceleration, or acceleration, the star may have experienced.

Problem 2

In Problem 1, let the acceleration you've calculated be applied at the same magnitude over the entire time from the star's initial position to its position in the visual image at left. What is the value of the energy phantom for Van Maanen's star?

Problem 3

If the sole influence on Van Maanen's star is another star at the Sun's distance and mass, directly behind Van Maanen's star in the plane of the image, what is the force of gravity applied by this star to Van Maanen's star at its initial position in the image? Let the mass of Van Maanen's star be 0.68 ± 0.02 Mʘ.

Is this gravitational force enough to account for the deceleration?

Problem 4

If the sole influence on Van Maanen's star is another star at the Sun's distance directly in front of Van Maanen's star in the plane of the image, what is the force of electrostatics applied by this star to Van Maanen's star at its initial position in the image? Let the charge of the star be QS = -0.3 x 1028 e.s.u. and the amount of charge on Van Maanen's star be 0.68 ± 0.02 QS.

Is this electrostatic force enough to account for the deceleration?

Which is stronger, the gravitational force or the electrostatic force?

Problem 5

How much closer would the star have to be to produce the deceleration of Van Maanen's star for each force?

Research

Hypothesis:

  1. In astronomy observations usually consist of detection of radiation followed by analysis which usually includes assumptions about the forces and fields observed.
  2. The four known forces or interactions all stem from an electromagnetic type source that manifests itself at varying intensities depending on the collection of particles.

Control groups

This is an image of a Lewis rat. Credit: Charles River Laboratories.

The findings demonstrate a statistically systematic change from the status quo or the control group.

“In the design of experiments, treatments [or special properties or characteristics] are applied to [or observed in] experimental units in the treatment group(s).[7] In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.[8]"[9]

Proof of concept

Def. a “short and/or incomplete realization of a certain method or idea to demonstrate its feasibility"[10] is called a proof of concept.

Def. evidence that demonstrates that a concept is possible is called proof of concept.

The proof-of-concept structure consists of

  1. background,
  2. procedures,
  3. findings, and
  4. interpretation.[11]

See also

References

  1. ↑ "energy, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. July 12, 2013. Retrieved 2013-07-14.
  2. ↑ "force, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. September 1, 2011. Retrieved 2013-12-04.
  3. ↑ - Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4
  4. ↑ "CODATA2006".
  5. ↑ "Table 3. Coherent derived units in the SI with special names and symbols, In: The International System of Units (SI)". International Bureau of Weights and Measures. 2006.
  6. ↑ F. Van Leeuwen (November 1, 2007). "Validation of the new Hipparcos reduction". Astronomy & Astrophysics 474 (2): 653-64. doi:10.1051/0004-6361:20078357. http://adsabs.harvard.edu/abs/2007A%26A...474..653V. Retrieved 2013-12-05.
  7. ↑ Klaus Hinkelmann, Oscar Kempthorne (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (2nd ed.). Wiley. ISBN 978-0-471-72756-9. http://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover.
  8. ↑ R. A. Bailey (2008). Design of comparative experiments. Cambridge University Press. ISBN 978-0-521-68357-9. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579.
  9. ↑ "Treatment and control groups, In: Wikipedia". San Francisco, California: Wikimedia Foundation, Inc. May 18, 2012. Retrieved 2012-05-31.
  10. ↑ "proof of concept, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. November 10, 2012. Retrieved 2013-01-13.
  11. ↑ Ginger Lehrman and Ian B Hogue, Sarah Palmer, Cheryl Jennings, Celsa A Spina, Ann Wiegand, Alan L Landay, Robert W Coombs, Douglas D Richman, John W Mellors, John M Coffin, Ronald J Bosch, David M Margolis (August 13, 2005). "Depletion of latent HIV-1 infection in vivo: a proof-of-concept study". Lancet 366 (9485): 549-55. doi:10.1016/S0140-6736(05)67098-5. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1894952/. Retrieved 2012-05-09.

External links

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Educational level: this is a research resource.
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Subject classification: this is an astrophysics resource.
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