Physics

Physics · mechanics

Problem

a - Calculate the flattening factor, given that the gravitational constant is

6.67 \times 10^{-11}

N.m

\cdot \mathrm{kg}^{-2}

. Given constants: The rotating neutron star. A 'millisecond pulsar' is a source of radiation in the universe that emits very short pulses with a period of one to several milliseconds. This radiation is in the radio range of wavelengths; and a suitable radio receiver can be used to detect the separate pulses and thereby to measure the period with great accuracy. These radio pulses originate from the surface of a particular sort of star, the so-called neutron star. These stars are very compact: they have a mass of the same order of magnitude as that of the sun, but their radius is only a few tens of kilometers. They spin very quickly. Because of the fast rotation, a neutron star is slightly flattened (oblate). Assume the axial cross-section of the surface to be an ellipse with almost equal axes. Let

r_{p}

be the polar and

r_{e}

the equatorial radii; and let us define the flattening factor by:

\epsilon=\frac{\left(r_{e}-r_{p}\right)}{r_{p}}

a mass of	$2.0 \cdot 10^{30} \mathrm{~kg}$ ,
an average radius of	$1.0 \cdot 10^{4} \mathrm{~m}$ ,
and a rotation period of	$2.0 \cdot 10^{-2} \mathrm{~s}$ .

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