# Method of Isochrons and Gravity Flashcards

What are the first three steps in the method of isochrons?

- Take samples of several different minerals from rock
- Choose decay system such that D and R are same element, N is different
- Measure isotopic ratios D/R and N/R for each mineral sample by mass spectrometry and plot graphs

What are the last 3 steps in the method of isochrons?

- If data lies on straight line, system has been closed, and M gives age of rock, C gives initial ratio
- Scatter indicates poor ‘closure’, i.e. that isotopes have been exchanged with the environment
- Line of best fit through many points reduces random error

What is the closure temperature?

Diffusion of a mineral behaves exponential with temperature - diffusion starts after specific temp (closure temp)

What does it mean if a rock is heated past the closure temperature since its formation?

Rock may have exchanged isotopes with its environment.

What are 4 widely used radiometric dating systems?

- Rubidium-Strontium
- Potassium-Argon
- Uranium-Lead
- Thorium-Lead

What are N, D and R equal to for the Rb-Sr system? What can we assume here? What is this system used for?

- N = Rubidium-87
- D = Strontum-87
- R = Strontium-86

Sr-87/Sr-86 (now)= Sr-87/Sr-86 (0) + Rb-87/Sr-86 (now) * λt

Used for ancient rocks as has very long half life.

What are N, D and R equal to for the K-Ar system? What is effective here and what is the closure temp like? What is this system used for?

- N = Potassium-40
- D = Argon-40
- R = Argon-36

can have effective λ(effective). Closure temp relatively low

Used for determining thermal history of a rock

What are N, D and R equal to for the U-Pb system? What is this system used for?

-N = Uranium-238

-D = Lead-206

-R = Lead-204

OR

-N = Uranium-235

-D = Lead-207

-R = Lead-204

Can determine age of rock and time at which disturbance causing system to lose or gain lead might have occurred.

What are N, D and R equal to for the Th-Pb system? What is this system used for?

- N = Thorium-232
- D = Lead-208
- R = Lead-204

Provide further cross checking with Uranium method

What is Newtons law of gravitation?

F = GMm/(|r1-r2|^2) * (r1-r2)/|r1-r2|

What is the integral version of newtons law of gravitation?

F(r) = triple integral over u of G*m*ρ(r1)*(r1-r)/(|r1-r|^3) dr1

What can we infer from knowing the density or the force on object u?

- Knowledge of ρ leads to knowledge of F

- Knowledge of F does not lead to knowledge of ρ

What is the integral equation for the gravitational potential energy?

V(r) = triple integral over u of -G*ρ(r)/|r1-r| dr1

What is the equation for the acceleration of a test mass due to gravity?

g(r) = -∇V(r)

What are the key points to consider when calculating the gravity due to a spherical shell?

- Gravity inside uniform spherical shell g(r) = 0

- Gravity outside of spherical shell is equivalent to having a point mass at centre of the shell