Surface motion of a fluid planet induced by impacts

In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a ( for cases of a/R = 0.001 to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r(0) (for cases of r(0)/R = 0.90 to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a/R, and slightly on r(0)/R. For example, in our base-line case, a/R = 0.03, r(0)/R = 0.96, the free-surface velocity above the source is 0.26c, whereas antipodal to the source, the peak free surface velocity is 0.19c. Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.