The Black Cloud (Fred Hoyle) читать бесплатно онлайн полную версию книги (ч. notes)

1

The details of Weichart’s remarks and work while at the blackboard were as follows: Write α for the present angular diameter of the cloud, measured in radians,

d for the linear diameter of the cloud,

D for its distance away from us,

V for its velocity of approach,

T for the time required for it to reach the solar system.

To make a start, evidently we have α = d/D

Differentiate this equation with respect to time t and we get

But so that we can write

Also we have Hence we can get rid of V, arriving at

This is turning out easier than I thought. Here’s the answer already

The last step is to approximate by finite intervals, , where Δt = 1 month corresponding to the time difference between Dr Jensen’s two plates; and from what Dr Marlowe has estimated Δα is about 5 per cent of α, i.e Therefore T = 20Δt = 20 months.