σ1=C[5-3cos(2δ)]
σ2=-C[1-9cos(2δ)]
C=3h2Mμ(1+ν)/(8πρa3)
Distance between area of interest and the tidal bulge: δ
Measured in degrees. The tidal bulge has the greatest induced stress.
Tidal Love Number: h2 ⋍ 0.95-1
Measures how a planet deforms due to tidal influences on a scale of 0-1. A solid body has a love number of 0, a liquid body has a love number of 1.
Mass of Jupiter: M= 1.898*1027kg
Calculated using the orbital period and mean orbital distance of satellites
Shear Moduli: μ 0.25-0.33 3.5-4MPa
Ratio of shear stress to shear strain. Also known as rigidity. How much force is needed to deform the material. Strong materials have high shear moduli, liquids have values of zero.
Poisson's Ratio: ν⋍ 0.25-0.33
Ratio of transverse strain to axial strain. Also known as compressibility. If a material is stretched in one direction, how much is it compressed in another.
Density: ρ⋍ 920 kg/m3
Colder ice tends to be more dense.
Distance between Europa and Jupiter: a⋍6.71*105km
Changes throughout Europa's orbit due to ellipticity of the orbit.
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| A) Stress Map of Europa's Surface when Europa is at Apojove. Image Credit: (Greenberg et al., 2003) B) Tidal Stress over 1 orbital period for Astypalaea Linea, the red star on Panel A. Image Credit : (Hoppa et al., 1999) |
Nice presentation, Angela. I think your discussion was clear, but I could have benefited from a diagram of the orientation of the stress components, or showing what shear strain/shear stress looks like. It was nice to hear some of how you were thinking about applying the equation to Europa.
ReplyDeleteMissed opportunity for great band/song name: Tidal Love Number 9.
ReplyDeleteI like the format in which you explained your variables. Not a lot of eye contact, but it's probably difficult when you're explaining equations at 8am.
How do they measure the tidal love number and shear moduli for something distant in the solar system?
ReplyDeleteIt seems like there is a huge uncertainty associated with shear moduli. Consequently, I wonder how much this uncertainty affects your calculations. You did a good job answering questions and carried yourself well during your talk.
ReplyDeleteYou lay out the terms nicely with a brief sentence for explanation on the post. I thought your discussion of uncertainty was useful.
ReplyDeleteYour presentation is quite detailed, though could possibly be simplified in certain ways. Question: why is the shear moduli mu instead of G? I doubt your wrong, but I usually encounter it represented as a capital "G."
ReplyDeleteI'm not sure. Seismology uses mu and I think planetary scientists studying Europa tend to have seismic or tectonic background and that's why they use mu.
DeleteI'm a little confused by the delta term. You describe it as distance but it is measured in degrees. This is counterintuitive to me. You did a good job describing a complex equation. I liked that you gave ranges for each variable as they relate to Europa.
ReplyDeleteGood presentation. You explained all the parameters in the equations well and the last two figures are also helpful to understand the equations.
ReplyDeleteVery nice presentation. I like you listes all the terms here.
ReplyDelete