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 Mercury Work done at ROBTides

The universal force of gravitation depends on the distance from the body. Masses located at different distances in the gravitational field will experience a different force and induce therefore a different acceleration. This force is called tidal force. If one drops two particles at the same time but at different distances in the gravitational field, they will not suffer the same force, will not have the same acceleration and therefore not the same speed. The distances between them will then vary. If one considers a celestial body, the same phenomenon will happen except that in this case, the particles are linked together by forces of cohesion that will oppose to this change distance. The tide is the deformation of the body due to tidal forces, causing distortion, and to the cohesive force, which is opposing to distortion. The closer to the Sun, the more the gravitational tidal force, and thus the tide, is important. On Mercury, the tide phenomenon is complicated because its amplitude is modulated by two phenomena: Mercury on its orbit gets closer then away from the Sun, and Mercury's rotation causes a shift in the tide on the surface of Mercury. The study of the tide phenomenon is essential to learn more about the internal structure of Mercury. If the core of Mercury is a liquid, the forces of cohesion are lower in the core. Following the existing interface between the liquid core and mantle, it has the ability to distort much. The amplitude of the tides is more important if the core is liquid than if it is solid. This dependency between the effect of tide and the internal structure of Mercury is quantified by the Love numbers (h, k).

δr = h Vt / g

δr is the tide amplitude
h is a Love number
Vt is the external potential of the planet
g is the acceleration due to gravity

δV = (1 + k ) Vt

δV is the deformation potential associated with the tide
k is a Love number
Vt is the external potential of the planet

The Observatory works on the relationship between the Love numbers, the tides and the internal structure of Mercury. BELA will characterize the topography and its changes over time. MORE will allow determining the changes in the mass distribution resulting from the deformation of Mercury, and therefore the effect of the tides with a high accuracy. This will allow determining the Love number and learn more about the internal structure of Mercury. Click here to view the phenomenon of tide.

Scientists at the ROB have calculated the potential to generate tides of Mercury. They showed that due to the spin-orbit coupling of Mercury, the tides have periods of the order of Mercury days or a Mercury year. They built models of the interior of Mercury and calculated the tides for these models. They have shown that the observations of the tides of Mercury will be extremely helpful to better understand the interior of Mercury and in particular the liquid outer core and inner core. For more informations : see Van Hoolst and Jacobs (2003).

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