Portal:Radiation astronomy/Problems/4

Energy phantoms

Main resource: 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.

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 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) 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:
$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: Dna-Dennis.

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.

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:

$F={qQ \over 4\pi \varepsilon _{0}}{1 \over {r^{2}}},$

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.