PURPOSE: to discuss the possibilities of exploring the planets, exoplanets, and life in the Universe

MATERIALS: calculator, Light Curve graph (1 sheet)

INSTRUCTIONS: print out these pages and complete the activities according to the instructions below

2.1. (3 pts) The circumfrence of the Earth is about d = 24909 miles at the equator. If you drove a car at v = 65 miles/hr,
how long would it take you to travel around the Earth (at the equator) once?

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**EXPERIMENT**
Now let's figure more universal travel times using the "Astronomical Distances" applet, © D.P. Hamilton & M. Asbury.

First, open the applet. Then just to see what it does, press 'Launch'. Notice how the applet produces a table of various
destinations in the Universe and the time it would take to reach those destinations if travelling at the speed you selected.

2.2. (4 pts) Enter the following four travel speeds - car (65 mi/hr), a fighter jet (1200 mi/hr), and the space shuttle (17,500
mi/hr), space probe (30,000 mi/hr) - into the applet and compare the results by entering the data in the table below.

DESTINATION	CAR (65 mi/hr)	JET (1200 mi/hr)	SHUTTLE (17500 mi/hr)	PROBE (30000 mi/hr)
Earth's moon
The planet Mars
The planet Saturn
The planet Pluto
Closest star to the Sun (Proxima Centauri)
Center of Milky Way galaxy

2.3. (2 pts) List the planets considered inferior. List the planets considered superior.

2.4. (3 pts) Sketch a diagram of the Solar System showing the major planet configurations (opposition, quadrature,
elongation, inferior conjunction, superior conjunction).

2.5. (3 pts) Examine the sketch you drew in #2.4 or Figure 1 in the lab text to answer these questions:

a) Can an inferior planet ever be at opposition or quadrature?

b) Can a superior planet ever be at inferior conjunction?

c) Can more than one planet can be at a particular configuration at the same time?

2.6. (2 pts) The orbital period of Mercury is P = 87.96 days. What is its synodic period (S)?

2.7. (2 pts) The orbital period of Pluto is P = 90,700 days. What is its synodic period (S)?

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**EXPERIMENT**
Now we will study transfer orbits and interplanetary travel using the "Voyages" applet, © C. Mihos & B. Lee.

First, open this applet page and read the brief description of the "Mars Mission". Second, click on the menu option
'Controls' which is at the lefthand side of the page. Read these instructions on how to use the applet for the "Mars
Mission". When finished, click on the menu option 'Applets' and then select the 'Mars Mission' link. A new applet
window labeled 'Transfer' should open up. Examine the applet. Press 'Launch' and watch so you understand what
the applet does. Obviously, a transfer orbit was not successful in launching a satellite to Mars. You will need to
find the correct values of the satellite's semi-major axis (a) and the starting position (Phi) of Mars. To help with this,
note that a starting position of Phi = 0° puts Mars directly to the left of the Sun, with Phi increasing as you move counterclockwise (i.e., Phi = 90° puts Mars below the Sun, etc.). Also to help, here is a brief table of the semi-major
axis data for the nine planets:

Experiment with the applet, changing the various values of satellite semi-major axis, eccentricity, and Mars' starting
position, Phi. See if you can achieve a successful transfer orbit of a probe from Earth to Mars. It isn't easy, is it...?

2.8. (2 pts) Calculate the semi-major axis (a_T) for the Hohmann transfer orbit (in AU) from Earth to Mars.

2.9.   The transfer orbit you calculated (in other units) has a = 1.888 x 10¹¹ m. The period of Mars is P_MARS =
5.94 x 10⁷ s. In the applet, Earth's starting position is Phi_EARTH = 180°.

a) (3 pts) Using an equation from the Section 2.1 lab text, estimate the angular separation (φ_L) for Earth and Mars.









b) (1 pt) Calculate Mars' starting position Phi (i.e., find Phi_EARTH - φ_L).

Enter your results from #2.8 and #2.9b above into the applet and press 'Enter'. Do NOT change the eccentricity.
Then press 'Launch'. Did you successfully create a Hohmann transfer orbit to land a probe on Mars? If not, check
your calculations in #2.9 and try again. After you are successful, close the internet browser window containing
the "Mars Mission" applet.

2.10. (2 pts) Find the semi-major axis of a transfer orbit, a_T, for Earth to Saturn (in AU).

2.11. (2 pts) Could we successfully achieve a gravity-assist transfer orbit for a probe to Saturn? Give a reason why.

Back in your main browser window, select the 'Grand Tour' applet. This exercise shows how the Voyager probe
launched in 1977 was able to explore all the outer Jovian planets - Jupiter, Saturn, Uranus, and Neptune - even though
it was not expected to have enough energy or hold up (technically) long enough to successfully do so. When the window
opens, check the box labeled 'Voyager' and then click on the area where it says 'Click here to start'. Examine the planet's
positions and the a, e, and 'Planet starting angle' data at the top. Notice the interesting starting arrangement needed.

2.12. (3 pts) Press 'Launch' to see the probe travel from its Earth-sent trajectory to Jupiter. Watch what happens. The
applet will then give you some energy data. Then press 'Launch' 3 more times to see the Voyager probe move on to
Saturn, then Uranus, and finally Neptune. Watch the 'Time' data carefully during the last leg of the voyage.

a) Why is it necessary to have a staggered arrangment for the planets' starting positions? (Hint: think laws of motion)



b) How long in years did the Voyager 2 probe travel the Solar System?

c) A planet's gravitational strength is a direct result of how much mass it has. The masses of the Jovian planets (in
terms of M_EARTH) are as follows: Jupiter - 318    Saturn - 95    Uranus - 14.5    Neptune - 17.2. Given this information,
why was it possible to achieve a gravity-assist transfer orbit for the a probe to go from Earth to all the way to Neptune?

2.13. (2 pts) Give 2 reasons why gravity assisted transfer orbits are an efficient means of interplanetary exploration.

3.1. (2 pts) Examine a detailed light curve for the star HD209458 (from http://www.hao.ucar.edu/public/research/stare/).
(Note: you can view this animation to see how the light curve is generated.)

a) How long (in days) does it take the planet to occult the star?

b) What is the percent change in brightness of the star due to the occultation?

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**EXPERIMENT**
Now try generating your own occultation light curve for a star/extrasolar planet system.

3.2. (4 pts) Plot the following occultation data for a star/planet system on the graph paper provided. Then use a straight
edge to draw in the light curve, (i.e., connect the data points).

TIME (UT)	ΔMAG		TIME (UT)	ΔMAG
13:45	-0.010		16:45	-0.220
14:00	-0.012		17:00	-0.220
14:15	-0.011		17:15	-0.199
14:30	-0.033		17:30	-0.150
14:45	-0.050		17:45	-0.130
15:00	-0.097		18:00	-0.092
15:15	-0.128		18:15	-0.049
15:30	-0.155		18:30	-0.024
15:45	-0.180		18:45	-0.005
16:00	-0.218		19:00	-0.006
16:15	-0.220		19:15	-0.002
16:30	-0.220		19:30	-0.001

3.3. (4 pts) Points of contact are when the data suddenly changes direction. The four times of contact occurred at:

3.4. (1 pt) What was the elapsed time between first and second contact (in hours)?

3.5. (3 pts) Data shows that the planet orbits the star at a distance of a = 1.05 x 10⁸ km. Light curve data yields a
period of P = 3680 hrs. Use the equation v_ORB = 2πa / P, to find the orbiting planet’s speed (in km/hr).

3.6. (1 pt) Now multiply v_ORB by your result in #3.4 to find the orbiting planet's estimated diameter (in km).

3.7. (3 pts) We observe a hydrogen spectral line (λ₀ = 6563 Å) in the spectrum of the star HD 209458 to be
shifted by Δλ = 0.0019 Å. What is the radial velocity of the star?

3.8. (3 pts) The mass of the star HD209458 is approximately M_STAR = 2.189 x 10³⁰ kg and its inclination is i = 85.2°.
As found in #3.7, the velocity of the star (from spectroscopic analysis was V_STAR = 0.087 km/s. The velocity of the
planet was determined to be about V_PLANET = 145.24 km/s. Calculate a minimum mass estimate for the planet around
this star.

3.9. (1 pt) Jupiter’s mass is 1.9 x 10²⁷ kg. How much is this planet's mass in units of M_J?

3.10. (2 pts) Look at this table of detected extrasolar planet data.

a) Based on the data, list the least massive detected extrasolar planet. (Hint: list by its name AND its mass in units of M_J)

b) List the most massive detected extrasolar planet (Hint: list by its name AND its mass in units of M_J)

4.1. (3 pts) The average star formation rate in our Galaxy is 20 stars per year. Astronomers estimate that there are about
2 x 10¹¹ stars in the Milky Way. How many years ago may the Galaxy have formed?

4.2. (2 pts) Given your answer to #4.1 and the fact that humans have only been “communicating” for about 70 years, calculate
the probability that we will discover intelligent extraterrestrial life in our Galaxy in our lifetime.

4.3. (3 pts) Use the following commonly accepted values to solve the Drake Equation and find the number N of possible
intelligent civilizations able to communicate within our Galaxy:

R = 20 stars/yr      F_S = 0.1      F_P = 0.5      N_E = 3      F_L = 1       F_I = 0.5       F_C = 0.3       L = 70 yr


N = _______________

4.4. (1 pt) The above estimates for the number of stars with planets (F_P) and suitable planets (N_E) are both derived from
the limited knowledge of our Solar System and the few others we have found. Replace the above value of N_E = 1 (leaving
all others the same) and calculate the equation again.


N = _______________

4.5. (2 pts) In question #4.3 we assumed that half of all suitable planets would develop life and that if proper conditions
existed for the formation of life, it would in fact form 100% of the time. Perhaps this is too optimistic. Replace the #4.3
values of F_L = 0.5 and F_I = 0.2 (leaving all others the same) and recalculate.


N = _______________

4.6. (2 pts) Our calculations thus far have assumed that the lifetime (L) of our own ability to communicate (technologically)
is representative of all civilizations. It is also a lower limit for this factor. Recalculate the Drake Equation if we assume that
an intelligent communicating civilization (in the future?) can survive for L = 1000 yrs. (Again, only change the value of L.
Use all others from #4.3)


N = _______________

4.7. (2 pts) List the terms in the Drake Equation that, at present, can be constrained somewhat by scientists based on
collected data. Then list those terms that at present are extremely uncertain and lack support from scientific data.

4.8.   Look at this plot of extrasolar planets we have discovered. The shaded gray box-like area is the "habitable
zone."

a) (4 pts) Based on the extrasolar data in the table below, determine whether the orbiting planet can support Earth-like
life or not. If you answer 'no', list the factor that caused you to answer this way.

STAR	STELLAR TYPE	STELLAR MASS	PLANET DISTANCE FROM STAR (AU)	SUPPORT LIFE?	REASON IT FAILS
A	K2	0.8	0.038
B	M0	0.47	0.13
C	G5	1.1	5.25
D	B9	4.5	1.13

b) (1 pt) Based on this graph, what mass range must a star be within in order to have planets that can support life?


c) (1 pt) Based on this graph, what is the minimum and maximum semi-major axis for life-supporting extrasolar planets?

4.9. (3 pts) Based on the factors and issues that must be taken into consideration when discussing the possibilities of
intelligent extraterrestrial life forming and evolving and your results above, comment on the scientific probability of life
existing elsewhere in our Galaxy.

**If you would like to play more with various Drake equation calculations, try this "Life Beyond Earth" applet.

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