PTYS_411_511_1_gravity_topography

PTYS_411_511_1_gravity_topography - Planetary Gravity and...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
PTYS 411/511 Geology and Geophysics of the Solar System Shane Byrne – [email protected] Background is from Lamb and Könemann 1998 Planetary Gravity and Topography
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
PYTS 411/511 – Planetary Gravity and Topography 2 Planetary wide gravity Planetary shapes Moments of inertia Gravitational potential Defining the reference surface Geoids Measurements from space Flybys vs. orbiters Correcting gravity observations Interpreting gravity anomalies Compensated? Crustal thickness Planetary gravity Lunar gravity Martian gravity Planetary comparisons In this lecture
Image of page 2
PYTS 411/511 – Planetary Gravity and Topography 3 Pythagoras (~550 BC) Speculation that the Earth was a sphere Eratosthenes (~250 BC) Calculation of Earth’s size Shadows at Syene vs. none at Alexandria Angular separation and distance converted to radius Estimate of 7360km – only ~15% too high Invention of the telescope Jean Picard (1671) – length of 1° of meridian arc Radius of 6372 Km – only 1km off! Length of 1° changes with latitude Controversy of prolate vs. oblate spheroids Pierre Louis Maupertuis - Survey 1736-1737 Equatorial degrees are smaller Earth is an oblate spheroid Quick History – The Shape of the World
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
PYTS 411/511 – Planetary Gravity and Topography 4 Galileo Galilei (~1600 AD) Accurately determined g All objects fall at the same rate 1 gal = 1 cm s -1 , g = 981 gals Quick History – Gravity Isaac Newton (1687) Universal law of gravitation Derived to explain Kepler’s third law Led to the discovery of Neptune 2 r GMm F = Henry Cavendish (1798) Attempt to measure the Earth’s density Measured G as a by-product Found ρ Earth ~5500 kg/m 3 > ρ rocks Density must increase with Depth Nineteenth century Everest and Bouguer both find mountains cause deflections in gravity field Deflections less than expected Airy and Pratt propose isostasy via different mechanisms
Image of page 4
PYTS 411/511 – Planetary Gravity and Topography 5 Planets are flattened by rotation Hydrostatic approximation Gravity at equator adjusted by centrifugal acceleration: Gravity at pole unaffected by rotation Planetary flattening described by: f for a perfectly fluid Earth 1/299.5 Difference due to internal strength Perhaps a relict of previously faster spin f for Mars ~ 1/170 – much more flattened Planets are represented by ellipsoids i.e. a = b ≠ c Triaxial ellipsoids can be used: a ≠ b ≠ c ..but only for a few irregular bodies Planetary Shape 257 . 298 1 10 352 . 3 3 = × = - = - a c a f g p g e ( 29 latitude a cos 2 ϖ
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
PYTS 411/511 – Planetary Gravity and Topography 6 Analogous to mass for linear systems Moment of Inertia Linear Rotational Momentum P = m v L = I ω Energy E = ½ m v 2 E = ½ I ω 2 Response to force t v m F δ δ = t I δ δϖ τ = ‘I’ can be integrated over entire bodies, usually I = k MR 2 For solid homogeneous spheres I = 0.4 MR 2 If extra mass is near the center (e.g. core of a planet) then I < 0.4
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern