Cosmology: Suppose That the Hubble Constant Had the Value 35

question 38

Essay

Cosmology: Suppose that the Hubble constant had the value 35.0 km/s per million light-years. (1 y = 3.156 × 10⁷ s, m_H ≈ m_proton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s, 1 light-year = 9.461 × 10¹⁵ m, G = 6.67 × 10^-11 N ∙ m²/kg²)
(a) What would be the maximum density the universe could have that would still allow it to expand forever?
(b) Under the conditions of part (a), how many hydrogen atoms would we expect to find, on the average, in a volume of space measuring 3.00 m by 8.00 m by 8.00 m?

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