Original teaching data give (distance in 10²² m, speed in km/s) (1, 720), (2, 1390), (3, 2110), (4, 2780), (5, 3510). (a) Find endpoint gradient. (b) Convert it to s⁻¹ and estimate 1/H in years using 3.16 × 10⁷ s/year. (c) Explain redshift evidence. (d) Explain sample scatter. (e) State limitations of treating 1/H as exact cosmic age.

Question

Accepted Answer

Gradient 697.5 km s⁻¹ per 10²² m = 6.98 × 10⁻¹⁷ s⁻¹; illustrative expansion timescale 4.54 × 10⁸ years. Using endpoints, gradient = (3510 − 720)/(5 − 1) = 697.5 km s⁻¹ per 10²² m. Wide separation limits relative reading uncertainty. Convert: H = 697.5 × 1000/10²² = 6.975 × 10⁻¹⁷ s⁻¹. Its reciprocal is 1.434 × 10¹⁶ s = 4.54 × 10⁸ years. The dataset is intentionally simplified original teaching data, not a current cosmological measurement. Spectral lines shifted to longer wavelengths provide recession evidence by comparison with laboratory wavelengths. Galaxies have local peculiar velocities and distance uncertainty, so one v/d value is unreliable. A large sample and best-fit trend reveal the expansion relation. The expansion rate changes with cosmic contents and history, and distance calibration affects the gradient. Therefore 1/H is a model timescale, not automatically exact age.

Galaxy recession and expansion age

What a complete response should do

Illustrative galaxy data

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Illustrative galaxy data — supplied values
Distance / 10²² m	Speed / km s⁻¹
1	720
2	1390
3	2110
4	2780
5	3510