stevebd1

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## Main Question or Discussion Point

A quote from the 'Light-dragging effects' section from wikipedia states-

"Under general relativity, the rotation of a body gives it an additional gravitational attraction due to its kinetic energy.."

Based on this, does rotational kinetic energy contribute the gravity of an object?

[tex]E_{rotation}=\frac{1}{2}I\omega^{2}[/tex]

[tex]I=mr^{2}0.4[/tex] (0.4 for a solid sphere)

[tex]\omega= Rads/sec[/tex] or [tex]f\pi2[/tex] (f- frequency)

Rotational energy for 2 objects-

Earth-

= 1/2 x (5.9736x10^24 x 6.371x10^6^2 x 0.4) (7.29x10^-5 (rads/sec))^2

= 2.5771X10^29 joules

equivalent mass = 2.8674x10^12 kg

2 sol neutron star, 12 km radius, 1000 Hz freq-

= 1/2 x (2 x 1.9891x10^30 x 12000^2 x 0.4) (2 x pi x 1000)^2)

=4.5232x10^45 joules

equivalent mass = 5.0327x10^28 kg (which is ~2.5% of a sol mass)

While the equivalent mass for the kinetic rotational energy of the Earth is negligible compared to the Earth's overall mass, for the neutron star, it becomes significant. Technically, could it be added when calculating the gravity?

Steve

"Under general relativity, the rotation of a body gives it an additional gravitational attraction due to its kinetic energy.."

Based on this, does rotational kinetic energy contribute the gravity of an object?

[tex]E_{rotation}=\frac{1}{2}I\omega^{2}[/tex]

[tex]I=mr^{2}0.4[/tex] (0.4 for a solid sphere)

[tex]\omega= Rads/sec[/tex] or [tex]f\pi2[/tex] (f- frequency)

Rotational energy for 2 objects-

Earth-

= 1/2 x (5.9736x10^24 x 6.371x10^6^2 x 0.4) (7.29x10^-5 (rads/sec))^2

= 2.5771X10^29 joules

equivalent mass = 2.8674x10^12 kg

2 sol neutron star, 12 km radius, 1000 Hz freq-

= 1/2 x (2 x 1.9891x10^30 x 12000^2 x 0.4) (2 x pi x 1000)^2)

=4.5232x10^45 joules

equivalent mass = 5.0327x10^28 kg (which is ~2.5% of a sol mass)

While the equivalent mass for the kinetic rotational energy of the Earth is negligible compared to the Earth's overall mass, for the neutron star, it becomes significant. Technically, could it be added when calculating the gravity?

Steve

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