ASTRONOMY FUNDAMENTALS - Chapter 5, Exercise 2 Solution
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Estimating the Sun's Remaining Main-Sequence Lifespan

PROBLEM
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The Sun's main-sequence phase began roughly 4.6 billion years ago, and
its total main-sequence lifespan is approximately 10 billion years. Use
these real figures to estimate how many years remain before the Sun
leaves the main sequence.

SOLUTION
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Step 1 - identify the two real figures given:
    Total real main-sequence lifespan: ~10 billion years
    Time already elapsed since the Sun joined the main sequence:
    ~4.6 billion years

Step 2 - subtract the elapsed time from the total lifespan:
    Remaining time = Total lifespan - Elapsed time
    Remaining time = 10 billion years - 4.6 billion years
    Remaining time = 5.4 billion years

ANSWER: Approximately 5.4 billion years remain before the Sun leaves
the main sequence and becomes a red giant.

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WHY THIS WORKS AS AN ANSWER

A star's real main-sequence lifespan is essentially a fixed total
"budget" of time, set mainly by its own mass, during which core
hydrogen fusion can continue before running low. Since the Sun has
already spent roughly 4.6 billion years of its own real ~10-billion-year
budget, simple subtraction gives the real time genuinely remaining. This
matches closely with the chapter's own rounder estimate of "roughly 5
billion years remaining," since that figure is itself an approximation
built from the same two real underlying numbers - a small, expected
rounding difference (5.4 billion vs. "roughly 5 billion") rather than a
contradiction, given that both the 10-billion-year total lifespan and
the 4.6-billion-year current age are themselves real, but not
perfectly precise, astronomical estimates.