Calculation of Energy Carried by Emitted Solar Particles Using Their Masses

Author: G. Mustafa Shahzad
Research Partner: ChatGPT
Affiliation: Director, Qalim Institute | Theorist of Al-Asr Dynamic Number System (ADNS)

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Abstract

The Sun continuously emits not only light (photons) but also massive particles such as electrons, protons, alpha particles, and heavier ions, particularly through the solar wind and solar energetic particle (SEP) events. This paper calculates the energy contribution of these particles based on their rest mass and kinetic energy, using Einstein’s equation $E = mc^2$ and classical kinetic energy principles. Realistic particle velocities are considered to determine the energy per particle type. The purpose is to understand the quantitative energy profile of solar particle emissions and their impact on space weather, satellites, and Earth's ionosphere.

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1. Introduction

Solar emissions include:

• Photons (massless, energy via frequency)

• Electrons, Protons, Alpha particles (He²⁺), and occasionally heavier ions

These are emitted through:

• Solar Wind (steady flow)

• Solar Flares

• Coronal Mass Ejections (CMEs)

Each massive particle carries energy due to:

• Its rest mass energy: $E_0 = mc^2$

• Its kinetic energy: $KE = \frac{1}{2}mv^2$ (non-relativistic case)

This paper calculates these energies and compares their roles in solar-terrestrial interactions.

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2. Rest Masses of Emitted Solar Particles

Particle	Symbol	Mass (kg)	Mass (MeV/$c^2$)
Electron	e−	$9.11 \times 10^{-31}$	0.511
Proton	p+	$1.67 \times 10^{-27}$	938.3
Alpha particle	$\mathrm{ \; \; H}{e}^{2+}$	$6.64 \times 10^{-27}$	3727.4
Photon	$\gamma$	0	Energy from $E = hf$

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3. Rest Mass Energy $E = mc^2$

Using:

$$E = mc^2,  c = 3 \times 10^8 m/s}$$

3.1 Electron

$$E_e = (9.11 \times 10^{-31}) \cdot (3 \times 10^8)^2 = 8.2 \times 10^{-14}J}$$

3.2 Proton

$$E_p = (1.67 \times 10^{-27}) \cdot (3 \times 10^8)^2 = 1.5 \times 10^{-10}J$$

3.3 Alpha Particle

$$E_\alpha = (6.64 \times 10^{-27}) \cdot (3 \times 10^8)^2 = 5.98 \times 10^{-10} J$$

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4. Kinetic Energy of Solar Particles

Typical solar wind velocity: $v=400\text{km/s}=4\times$10^5$\text{m/s}$

Using:

$$KE = \frac{1}{2}mv^2$$

4.1 Electron

$$KE_e = \frac{1}{2}(9.11 \times 10^{-31})(4 \times 10^5)^2 = 7.3 \times 10^{-20}J$$

4.2 Proton

$$KE_p = \frac{1}{2}(1.67 \times 10^{-27})(4 \times 10^5)^2 = 1.34 \times 10^{-16}J$$

4.3 Alpha Particle

$$KE_\alpha = \frac{1}{2}(6.64 \times 10^{-27})(4 \times 10^5)^2 = 5.31 \times 10^{-16}J$$

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5. Energy Contribution Comparison

Particle	Rest Mass Energy (J)	Kinetic Energy (J)	Total per Particle (J)
Electron	$8.2 \times 10^{-14}$	$7.3 \times 10^{-20}$	≈ $8.2 \times 10^{-14}$
Proton	$1.5 \times 10^{-10}$	$1.34 \times 10^{-16}$	≈ $1.5 \times 10^{-10}$
Alpha	$5.98 \times 10^{-10}$	$5.31 \times 10^{-16}$	≈ $5.98 \times 10^{-10}$

Observation:

• Rest mass energy dominates, especially in slower solar wind scenarios.

• Kinetic energy becomes important in solar energetic particles (SEPs) which may travel at relativistic speeds (up to 0.9c).

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6. Impact of Emitted Particles on Earth

6.1 Ionospheric Disturbances

• Protons and electrons penetrate Earth’s magnetic field at poles.

• Result: Auroras, HF communication blackouts, ionospheric heating

6.2 Satellite Hazards

• High-energy protons and ions damage electronics via single-event upsets (SEUs).

• Accumulated charge causes material degradation in solar panels.

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7. ADNS Viewpoint: Particle Energy Flow

In the Al-Asr Dynamic Number System (ADNS):

• Every emitted particle represents a time-directed energy quantum (+).

• The zero point (Al-Asr) is the present moment when that energy reaches and interacts with Earth.

• Particles with greater mass (like alpha particles) are seen as heavier time packets, capable of deeper disruption — representing delayed or prolonged events.

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8. Conclusion

By using particle masses and velocities, we quantified the energy carried by solar particles:

• Rest mass energy is constant and large, but mostly not released unless via annihilation or nuclear fusion.

• Kinetic energy depends on particle velocity and becomes significant in high-speed solar events.

These energetic particles shape Earth's ionosphere, magnetosphere, and space weather environment, with major consequences for communication, power grids, and space infrastructure.

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9. References

1. Kivelson, M. & Russell, C. (1995). Introduction to Space Physics.

2. Serway, R., & Jewett, J. (2018). Physics for Scientists and Engineers.

3. NASA Solar Wind Data Repository

4. Shahzad, G. M. (2025). Al-Asr DNS and Energy-Particle Duality. Qalim Institute

5. NOAA Space Weather Prediction Center (SWPC)