ASTRONOMY FUNDAMENTALS - Chapter 9, Exercise 2 Solution
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Could Parallax Measure TRAPPIST-1's Distance?

PROBLEM
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Using TRAPPIST-1's real distance (40.66 light-years) and Chapter 1's
real Hipparcos parallax limit (~1,600 light-years), explain whether
Hipparcos-style parallax measurement could have been used to directly
measure TRAPPIST-1's distance, and why.

SOLUTION
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Compare the two real distances directly:

    TRAPPIST-1's real distance: 40.66 light-years
    Hipparcos's real parallax measurement limit: ~1,600 light-years

    40.66 light-years is far smaller than 1,600 light-years
    (40.66 / 1,600 ≈ 0.025, or about 2.5% of the limit)

Since TRAPPIST-1's real distance is well within the real range Hipparcos
could reliably measure, parallax measurement absolutely could have been,
and in real practice can be, used to directly determine TRAPPIST-1's
own distance from Earth.

ANSWER: Yes - TRAPPIST-1, at 40.66 light-years, sits comfortably inside
the real ~1,600-light-year range Hipparcos-style parallax measurement
can reach, using only about 2.5% of that maximum real range. Its
distance could be, and has been, measured directly through parallax.

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WHY THIS WORKS AS AN ANSWER

Chapter 1 established that parallax only works reliably for relatively
nearby stars, since the parallax angle shrinks as distance grows -
Hipparcos's own real ~1,600-light-year limit marks roughly where that
angle becomes too small to measure reliably. TRAPPIST-1's real distance
of 40.66 light-years is genuinely close by comparison - nowhere near
that limit - meaning the same real technique Bessel first used on 61
Cygni in 1838 remains a perfectly viable way to measure it directly,
without needing any of the more specialized techniques (like redshift,
covered in Chapter 8) that become necessary only for objects far beyond
what parallax can reach.