Lab 1, due before the start of Lab 4/16/15

Name (8 pts):___________________
GSC307: Global Geophysics
Lab 1 (60 pts)
Due before start of next Lab 4/16/15
Use scientific notation, provide reasonable numbers of significant figures and provide the
correct units for all of your answers!
PROBLEM 1 (39 pts)
Introduction: In the oceans, the magnitude of the magnetic field is measured by towing a
magnetometer behind a ship. These measurements are a combination of two sources: Earth’s
present magnetic field and magnetism of rocks on the ocean floor. To gain information about
the latter, we subtract the regional value of the Earth’s magnetic field. What remains is the
magnetic anomaly. These anomalies can be explained by seafloor spreading and used to
derive the plate tectonic history of the area.
Part 1 (24 total)
Figure 1 shows part of the Eastern Pacific Ocean, showing the East Pacific Rise as a heavy
black line. It is offset between several fracture zones (FZs). The ridge is the divergent
boundary between the Pacific and Nazca plates. The numbered lines on each side of the ridge
are the magnetic anomalies. The age of these anomalies is known from the magnetic time
scale (Figure 2, numbers to the right of the column are anomaly numbers, short tick marks
indicate the age). This data will allow us to determine spreading rates of ridges.
1. (4 pts) Read the ages of magnetic anomalies 2,3 and 5 from Figure 2 and write them down
in Table 1, below, in the Age column. (Note the short line that indicates the exact age to the
left and above the anomaly number.)
2. (4 pts) Measure the distance between each pair of anomalies of the same age just south of
the Garrett fracture zone (Figure 1) and record these values in the table under the Distance
column for the East Pacific Rise (EPR).
3. (4 pts) Figure 3 shows a similar map of the Mid Atlantic ridge (MAR). Determine distances
and ages of all anomalies shown along the Ascension Fracture Zone and record in Table 1.
Anomaly 13 is shown on one side only, so you will find another way to estimate the total
distance!
4. (8 ps) Create a graph (and attach it!) with points of distance versus age (so distance along
the y-axis and age along the x-axis) for both the EPR and MAR. Fit a straight line to each set
of these points (so 2 lines in total) and label the lines “EPR” or “MAR”. Make sure to clearly
label your axes!
5. (4 pts) Use this graph to estimate full spreading rates for the two mid ocean ridges:
East Pacific Rise:
_________________ km/my = ______________________ mm/year
Mid-Atlantic Ridge: _________________ km/my = ______________________ mm/year
Anomaly Age in Millions Distance
between Distance
between
Number of Years
anomalies in km (EPR)
anomalies in km (MAR)
2
3
5
8
13
21
Table 1
Figure 1.
Figure 2.
Figure 3.
Part 2 (5 pts per question, 15 total)
The magnetic anomaly pattern in Figure 4 was recorded in an ocean basin on a long ship
traverse across a mid-ocean ridge.
1. Based on this pattern, explain at what distance this traverse crosses the mid-ocean ridge
and mark it on the magnetic anomaly pattern.
_____________________________________________________________________________
2. Using the expanded magnetic time scale of Figure 5, find magnetic anomaly 3A and
identify this anomaly on the traverse of Figure 4; mark it with an arrow. Measure the distance
of this anomaly from the ridge and write it down. Show how you determined this distance.
_____________________________________________________________________________
3. Use your answer from 2. to calculate the full(!) spreading rate of this ridge in mm/yr.
_____________________________________________________________________________
Figure 4.
Figure 5.
PROBLEM 2 (13 pts)
Derive an equation for the orbital velocity of the planets in our solar system, by using the (more)
complete version of Kepler’s 3rd law and approximating the orbits of these planets with a circle. Follow these
steps: first find an expression for orbital period in terms of orbital velocity for a circular orbit, then substitute
this expression in Kepler’s 3rd law and solve for orbital velocity. Clearly show your work and any derivations. (4
pts)
Describe in words the main pattern/characteristic of orbital velocity in our Solar System, based on the
form of this equation (e.g. are more massive planets faster?, smaller planets slower, etc.). Be clear and complete.
(4 pts)
Using the original version of Kepler’s 3rd law, determine at which distance above the Earth’s surface a
geosynchronous satellite orbits the Earth. A geosynchronous satellite remains fixed in the sky as seen from the
ground and is always in equatorial orbit. Assume a circular orbit. A page of useful numbers is provided in the
back of this assignment. Show your work, and remember to include your units! (5 pts)
N
口川 beLS
し se 十 口
Astronomical
al D iStan CeS
108km
light-year
ﾈ
3.09 X
1 kiloparsec(kpc)
1013km
^
Co
= 106pc
^
3.26 X
1 siderealmonth(average) ?= 27.32
106light-years
L
m
・
L 二
Planck's constant:
mass
of
ロass
of an electron
a
6 626
・
X
year
^
watt
・
we
= g.l X l0 ― 3lkg
BH
XS
on Earth: g = 9.8 m/s2
Vescape =
llkm/s
=
l1,000m/s
L
lL
8Y 1 @ 1
：
power:
Electron-volt:leV
1026watts
of the Earth: 1 inearth ^ 6,378 km
Escape velocity from surface of Earth:
t f
Basic unit of
of the Earth: 1 M^nh ^ 5.97 X l0-^kg
Acceleration of gravity
コ
Energy and Power Units
of the Sun: 1 A4sun ^ 2 X 1010kg
Radius (equatorial)
365.256 solar days
= l 67 X 10-27kg
proton:
Luminosity of the Sun: 1 Lsun % 3-8 x
A-2
1 sidereal
m2 X Kelvin4
Radius of the Sun: 1 ^gun ^ 696,000 km
Mass
?= 365.242 solar days
m
0- = 5.7 X 10 8
constant
Useful Sun and Earth
Reference Values
Mass
year
G=6 67Xlo-H
kS
@ XS2
constant
Stefan-Boltzmann
1 tropical
1 watt
=
days
solardays
止九 L L ま
口ヨ
3
Gravitational
2311
56"14.09'
1 synodicmonth(average) == 29.53 solar
3.26 light-years
= 1,000 pc s: 3.26 X 103light-years
1 megaparsec (Mpc)
Sh
1 siderealday ~
lo^ki-n
w 9.46 X
(pc)
1 parsec
1 solarday (average) = 24
・
1AU ^ 1.496 X
Times
-
1 joule/s
二 1.60 X lo ― lgjou た