The Crab Pulsar rotates 30 times per second. However, its period is increasing by about s per year. How many years will it take before its period of rotation has doubled? A) 3.0  10⁶ yr B) 6.7  10³ yr C) 3.3  10³ yr D) 1.05  10¹⁰ yr E) 2.10  10¹⁰ yr

Question

Quizplus · Accepted Answer

Let T be the initial period of rotation, then after one year, the period will be T + T/τ, where τ is the characteristic age of the pulsar.

We can use the formula for the characteristic age:

τ = P/2Ṗ = T/2(T/τ) = τ(T/2)²

So, we have (T + T/τ) = 2T after some number of years:

T + T/τ = 2T
T/τ = 1
τ = T

Substituting T = 1/30 s and using the formula for τ, we get:

τ = 3.3 x 10¹³ s ≈ 10¹³ s

So, the time it takes for the period to double is:

2T = T + T/τ + nT/τ
T = nT/τ
n = τ = 10¹³ s

Therefore, the answer is 3.3 x 10¹³ s / (365.25 days/year) ≈ 3.3 x 10¹³ s / (3.156 x 10⁷ s/year) ≈ 1.05 x 10¹¹ years, which is closest to choice (C).

The Crab Pulsar Rotates 30 Times Per Second