# Cosmic circuits

Voyager 1 has found only electrons streaming into the heliosphere from elsewhere in the galaxy. This problem set poses several problems to calculate the possibility that a simple electrical circuit is involved. The arcing, graceful structure is actually a bow shock about half a light-year across, created from the wind from the star L.L. Orionis colliding with the Orion Nebula flow. Credit: NASA.

## Circuit astronomy

The diagram at right suggests a simple electrical circuit.

Def. an enclosed path of an electric current is called a circuit.

In the diagram at right are three components:

1. a voltage (V), or current (i), source,
2. an enclosed path, and
3. a resistance, or resistor, (R).

According to Ohm's law:

$V=iR.$

With respect to an enclosed path, consider a path from outside the heliosphere, inward toward the Sun, and out again. Let the incoming electrons have 500 MeV of energy and a flux of 8.5 x 104 e- cm-2 s-1.

Def. a time rate of flow of electric charge is called a current.

Def. that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10–7 newton per metre of length is called an ampere.

Def. an amount of electrostatic potential between two points in space is called a voltage.

## Problem 1

Using the energy and electron flux described above, what is the apparent current in Amperes (A), flowing toward the Sun?

Considering the Sun to be a natural light source like the halogen light bulb at right, what is the resistance (R) and the voltage (V) of this circuit?

## Problem 2

If the luminosity (in Watts, W) of the Sun is 3.846 x 1026 W, pick a combination of resistance (R) and voltage (V) for this circuit.

## Problem 3

If the total number of protons being carried away from the Sun by the solar wind is about 1.3×1036 per second, with 10 keV of energy, what is the proton (p+) flux away from the Sun?

What is the amperage (A) of this solar wind?

Pick a combination of resistance (R) and voltage (V) for this circuit for the luminosity of the Sun.

## Problem 4

Using your electron and proton currents calculated above, where the current vector toward the Sun is the same as away from the Sun as part of the circuit, does the proton current increase or decrease the total current?

In a household circuit, the voltage may be 110 V and the current 15 A, considering it a direct current circuit, what is the number of electrons per second for these 15 Amps?

If the Sun is a 110 V source, and the number of electrons leaving the Sun in all directions is 15 Amps, what is the resistance of the enclosed path?

## Problem 5

The Voyager 1 data suggests that no electrons or protons are leaving the heliosphere into the galaxy. Some of the incoming electrons may be converted into neutrons. Some are being turned back toward the Sun as part of the circuit. If ten per cent of the incoming interstellar electrons are those leaving the Sun and being turned back toward the Sun, and another portion are being neutralized by the proton solar wind, what is the maximum number that may be turned into neutrons if no electrons are lost and only their energy is used to make the Sun luminescent?

If the only electrons leaving the Sun have the same numbers and energy of the protons leaving the Sun, how many electrons are being turned into radiant energy, if 50 % are being turned into neutrons?

If the radiant energy leaving the Sun combines with incoming interstellar gamma-rays at 500 MeV or greater, what gamma-ray flux is needed to complete the circuit if half are converted to electrons?

## Hypotheses

1. A complete circuit exists regarding the Solar System.