Galaxies give (distance in Mpc, recession speed in km/s) (20, 1380), (40, 2860), (60, 4210), (80, 5650), (100, 7040). Use 1 Mpc = 3.086 × 10¹⁹ km and 1 year = 3.156 × 10⁷ s. (a) Find H₀. (b) Convert to s⁻¹ and calculate 1/H₀ in years. (c) Predict speed at 150 Mpc. (d) Explain population fitting. (e) Explain standard candles and redshift. (f) Explain two age limitations and two other hot-Big-Bang observations.

Question

Accepted Answer

H₀ ≈70.8 km s⁻¹ Mpc⁻¹ = 2.29 × 10⁻¹⁸ s⁻¹; Hubble time 1.38 × 10¹⁰ years; predicted 150 Mpc speed 1.06 × 10⁴ km/s. Endpoint gradient H₀ = (7040 − 1380)/(100 − 20) = 70.75 km s⁻¹ Mpc⁻¹; full regression would use all points. Convert H₀ = 70.75/(3.086 × 10¹⁹) = 2.29 × 10⁻¹⁸ s⁻¹. Reciprocal is 4.36 × 10¹⁷ s = 1.38 × 10¹⁰ years. At 150 Mpc, v = H₀d = 70.75 × 150 = 1.06 × 10⁴ km/s under the fitted linear relation. Peculiar velocities and distance uncertainty make one galaxy unreliable. Standard candles infer distance from known luminosity and measured flux; shifted spectral lines provide recession evidence. Expansion rate changes through history and distance calibration affects H₀, so 1/H₀ is not exact age. Cosmic microwave background and primordial light-element abundances independently support a hot early Universe.

Hubble plot and cosmological evidence

What a complete response should do

Galaxy recession relation

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Galaxy recession relation — supplied values
Distance / Mpc	Recession speed / km s⁻¹
20	1380
40	2860
60	4210
80	5650
100	7040