Question

With a lifespan of 10 billion years, the sun has about 315 quadrillion seconds in its lifetime.
Every second, the sun produces about 380 septillion joules.

380 septillion joules times 315 quadrillion seconds = approximately 120 tredecillion.
Give the sun's 120 tredecillion joules produced in its lifetime, calculate similarly for other stars, to form an estimate for the average amount of joules that each star can produce. Then find out how much of it can be harnessed.

The purpose of this study is to theorize how much energy awaits mankind's use throughout the universe.

Answer 1

Short answer (headline): a typical star will produce of order 10^44 joules over its lifetime. Multiplying by numbers of stars gives roughly 10^55 J available in a single large galaxy like the Milky Way, and ~10^66–10^68 J in the observable universe (depending on the star count you use). With megastructures (Dyson spheres) you could in principle capture essentially all of a star’s radiative output; with hypothetical total mass->energy conversion you could access ~1,000–2,000 times more energy per star.

Below I show the assumptions, the simple calculations, example numbers for different stellar masses, and what fraction can realistically be harnessed.

1) Basis: Sun as a worked example
- Solar luminosity L☉ ≈ 3.828×10^26 W.
- Main-sequence lifetime ~10^10 yr ≈ 3.156×10^17 s.
- Total radiative energy emitted by the Sun over its main-sequence lifetime:
E☉ ≈ L☉ × t ≈ 3.828×10^26 W × 3.156×10^17 s ≈ 1.2×10^44 J.
(Your “120 tredecillion” matches ≈1.2×10^44 J in scientific notation.)

2) Scaling to other stars (simple physical scaling)
- To first approximation the total luminous energy a star emits over its main-sequence lifetime scales roughly linearly with mass: E ∝ M. That follows because luminosity roughly L ∝ M^3.5 while lifetime t ∝ M/L ∝ M^-2.5, so E = L·t ∝ M.
- A convenient scaling constant is the Sun’s energy per unit mass:
E☉/M☉ ≈ 1.2×10^44 J / (1.989×10^30 kg) ≈ 6×10^13 J/kg.
- Therefore a star of mass M will emit roughly
E ≈ (M/M☉) × 1.2×10^44 J,
with an uncertainty of order a few× because of stellar-structure effects (core fraction, metallicity, etc.).

Example lifetimes/total energies (order‑of‑magnitude):
- 0.1 M☉ (low-mass red dwarf): E ≈ 1×10^43 J (but see caveat on red dwarfs below).
- 0.5 M☉: E ≈ 6×10^43 J.
- 1.0 M☉ (Sun): E ≈ 1.2×10^44 J.
- 10 M☉: E ≈ 1.2×10^45 J.

Caveats: very low-mass red dwarfs are fully convective and can burn a much larger fraction of their hydrogen before dying; they also have lifetimes ≫ 10^10 yr, so their total lifetime energy can be comparable to or even exceed the Sun’s output per unit mass over their full lifetimes. Massive stars have shorter lives but more energy per star by the linear scaling above.

3) Population (averaging) and totals
- Number-weighted average stellar mass in a typical galaxy is often estimated ~0.3–0.7 M☉ (the initial mass function is very bottom-heavy). Using Mavg ≈ 0.5 M☉ gives an average per-star lifetime radiative energy of order
Eavg ≈ 0.5 × 1.2×10^44 J ≈ 6×10^43 J.
- Milky Way (≈2×10^11 stars) total stellar radiative energy (main-sequence output) ≈ 2×10^11 × 6×10^43 J ≈ 1–2×10^55 J.
- Observable universe: estimates of total stars vary from ~10^22 to 10^24 stars.
- For 10^22 stars: total ≈ 10^22 × 6×10^43 J ≈ 6×10^65 J ≈ 10^66 J.
- For 10^24 stars: total ≈ 6×10^67 J ≈ 10^68 J.
(So a conservative observable‑universe luminous-energy total is ∼10^66–10^68 J.)

4) How much of that could be harnessed?
Scenarios and fractions:
- Natural interception by a planet (Earth example): Earth intercepts ≈1.74×10^17 W from the Sun, which is ≈4.5×10^-10 of the Sun’s luminosity. Over the Sun’s lifetime the energy that hits Earth ≈ 1.2×10^44 J × 4.5×10^-10 ≈ 5×10^34 J. So planets collect a tiny fraction of a star’s output unless we build collectors much larger than planetary cross sections.
- Dyson-type collectors: a full Dyson sphere or complete collector around a star could in principle intercept ~100% of that star’s radiative output. So harnessable ≈ the full E values above (e.g., ≈1×10^44 J for a Sun-like star over its lifetime), minus engineering and conversion inefficiencies.
- Total mass->energy conversion (hypothetical ultimate limit): converting the entire rest mass to energy (annihilation) yields E = M c^2. For a 1 M☉ star that is ≈1.8×10^47 J. That is ≈1,500 times larger than the star’s main-sequence luminous output (~1.2×10^44 J). So if a civilization could convert mass directly (annihilation, black‑hole evaporation, etc.), the accessible energy is orders of magnitude larger than ordinary fusion output.
- Practical harnessable fraction for humans/near-future civilization: very small. Even if we could capture all sunlight on Earth’s orbit, we still tap only a small fraction of what’s available from the Sun; interstellar capture requires large engineering projects and enormous material/energy investments. For a Kardashev-type technological civilization that builds star-encompassing collectors, you could approach 100% of stellar luminous output. For entire-galaxy harvesting you need correspondingly greater scale and logistics.

5) Summary (order-of-magnitude numbers you can quote)
- Typical per-star lifetime luminous energy: ~10^43–10^45 J; a reasonable average by number ≈ a few×10^43 to 10^44 J per star.
- Milky Way total (main-sequence luminous energy): ~10^55–10^56 J.
- Observable-universe luminous energy (stars): ~10^66–10^68 J (depending on star count).
- Harnessable: up to ~100% of the luminous output with megastructures (Dyson spheres). Ultimate theoretical maximum (full mass annihilation) is ~1,000–2,000× larger per star than its fusion output.

6) Final notes and uncertainties
- These estimates are order-of-magnitude and depend on assumptions (initial mass function, what fraction of a star’s mass can be fused, whether you include post-main-sequence fusion phases, and whether you count future long-lived red dwarfs that have not yet exhausted fuel).
- “Available to mankind” also depends on transport, engineering, economics, and physics limits (we cannot practically reach or control many stars, redshifts, or convert mass to energy efficiently with known physics).
- If you want, I can: (a) do a more detailed population-weighted integral using a chosen initial-mass function (Salpeter or Kroupa) to give a refined number-weighted average star energy, (b) compute precise per-galaxy totals for a specific galaxy star count, or (c) model harnessable energy under different engineering scenarios (planetary collectors, Dyson swarms, interstellar resource limits). Which would you like next?