# Method of Isochrons and Gravity Flashcards

1
Q

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

A
• 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
2
Q

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

A
• 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
3
Q

What is the closure temperature?

A

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

4
Q

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

A

Rock may have exchanged isotopes with its environment.

5
Q

What are 4 widely used radiometric dating systems?

A
• Rubidium-Strontium
• Potassium-Argon
6
Q

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

A
• 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.

7
Q

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?

A
• 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

8
Q

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

A

-N = Uranium-238
OR
-N = Uranium-235

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

9
Q

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

A
• N = Thorium-232

Provide further cross checking with Uranium method

10
Q

What is Newtons law of gravitation?

A

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

11
Q

What is the integral version of newtons law of gravitation?

A

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

12
Q

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

A
• Knowledge of ρ leads to knowledge of F

- Knowledge of F does not lead to knowledge of ρ

13
Q

What is the integral equation for the gravitational potential energy?

A

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

14
Q

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

A

g(r) = -∇V(r)

15
Q

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

A
• 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

16
Q

What is the equation for the gravity outside a spherical shell?

A

g(R) = -GM/R^2

17
Q

What are gravity anomalies?

A

Local deviation in Earth’s gravitational field

18
Q

How are gravity anomalies measured?

A

Using gravimetres- can be as simple as a calibrated mass on a spring or can be complex interferometer

19
Q

What is 1 Gal equal to?

A

1 Gal = 0.01ms^-2

20
Q

What is the Earth’s gravitational field strength to 5 decimal places?

A

9.80665 ms^-2