Download The Sun and Planets Homework 2.

The Sun and Planets
Homework 2.
Spring Semester 2017
Prof Dr Ravit Helled
Due by: 09.03.2017
TURN IN YOUR SOLUTIONS NEXT WEEK IN CLASS
or
EMAIL THEM AS A PDF
Exercise 1.
Days
The Earth–Moon system is coupled through tidal interactions. Due to these interactions,
the rotation of the Earth is slowing down and the distance between the Earth and Moon
is increasing. In the past there were more days per year and in the future there will be
fewer days per year. However, the length of the year is not changing perceptibly. Instead,
it is the rotation of the Earth that is changing; the rotation is slowing down which causes
longer days. Likewise, the revolution of the Moon around Earth has been slowing down
as its orbit expands.
How do we know this? We know this because corals deposit a single, very thin layer of
lime once a day. It’s possible to count these layers to obtain the the number of days in
a year (since you can also demarcate the annual growth of the coral). Therefore, given a
piece of coral, you can measure how many days occurred in a year. These measurements
can also be made on fossilized coral, which allows you to measure the number of days
that occurred in a year at times in the past.
1. Coral from Pennsylvanian (290–325 Mya) rockbeds have about 387 daily layers per
year; Devonian (360–410 Mya) rockbeds about 400 daily layers per year. In the Cambrian
(500–570 Mya) a year was 412 days. A Precambrian (550–4500 Mya) stromatolite yielded
a measurement of 435 days per year.
a) Note the time—or range of times—for each of the above geologic periods. Use graph
paper and a ruler (or a computer-based plotting program) to make a plot where the
x-axis is millions of years before the present (zero being today) and the y-axis is
the length of a day in hours. The plot should trend towards shorter days as you go
back in time. Note that a geologic period is a range of time, for which you have
measured value for the length of the day. The purpose is not to get things perfectly
right, but rather to show the general evolution of the length of the day.
b) Approximately how many seconds are added to a day every century, assuming that
you can extrapolate your line forwards through the present?
c) Extrapolate back to 4.567 billion years ago. How fast do you predict that the Earth
was spinning originally? Express your answer in hours per day.
d) Comment upon whether you think that the extrapolation made in part c is a valid
assumption. Why or why not?
1
Exercise 2.
Months
Similar to the coral problem above, you can use bivalves (e.g., clams) to count the number
of days occurring in a month. These measurements are controversial, but for the purpose
of the homework, assume the following numbers:
Table 1. — Days in the lunar month
Millions of years ago
Duration of lunar month†
900
25.0
600
26.2
300
28.7
0 (today)
29.5
† Measured in days with the present length of a day (24 hrs)
a) Draw a plot of this tabulated data (days per month versus millions of years ago).
b) Use Kepler’s 3rd law1 to derive the distance of the Moon to the Earth as a function
of time. Express your answers in terms of the present day Earth–Moon distance
(i.e., d = 1 today) and draw a plot of lunar distance versus millions of years ago.
c) How fast, on average, is the Moon presently receding from Earth? Express your
answer in cm/yr.
Exercise 3.
Origin of the Moon
Write down the three main hypotheses for the Moon’s origin and briefly describe the main
problems (if any) with each. This should take about one page of text or itemized points.
You can use diagrams as well.
Exercise 4.
Mission Timeline
Pick any of the following Solar System bodies: Venus, the Moon, Mars, Pluto, asteroids,
or comets. Write down a complete timeline of all missions that have flown to that body (or
in the case of asteroids or comets, all asteroid or all comet missions). Your timeline should
begin at the first mission and end on 1. January, 2017. Include six columns: launch year,
nationality(s), type of mission (e.g., flyby, orbital, rover), mission objective(s), outcome
(i.e., success/partial success/failure), and mission duration.
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Kepler’s 3rd law states that a planet’s orbital period, P , is proportional to its semi-major axis, a. In
the Solar System this relationship is: P 2 = a3
2