Instructions for space travel to exoplanets:
Is the solar system unique in the universe? No. More than 3,000 extra solar planets (exoplanets) have been discoverd. For more information, you
may visit the following website: http://planetquest.jpl.nasa.gov/
Suppose we have developed two very fast space crafts named Condor and Griffin. The Condor travels at a speed of v=0.93c and t he Griffin moves at
that of v=0.99c relative to the earth. Here, c is the speed of light (=300,000 km/sec). For this activity, we are going to figure out how much the
travelers will have aged when they travel from earth to their desired exoplanets. In order to do that, we will use Einstein's time dilation formula:
t
p
= t
1 −
v
c
2
2
Here, tp is proper time, t is dilated time, and v is the speed of the space craft. The proper time is the time interval for travelers who measure their own
age using their clock during the journey. The dilated time is the time interval measured by a person on earth, who sees that the events occur at
different places.
The selected exoplanets with some physical properties are as follows. Kepler- 452b is located at about 1,400 light years away from earth. Its size is
1.6 times of Earth's radius and it has 5 times Earth's mass. 51 Pegasi b is about 41 light years away from us. Its mass is ab out half of that of Jupiter.
Its size is about twice of that of Jupiter. Jupiter's mass is 318 times Earth's mass and Jupiter's size is about 11 times Ear th's size. Keper-78b is
located about 400 light years from us. Its mass is double of Earth's mass and its size is 1.2 times Earth's radius. The dista nce from 'Super-Earth'
exoplanet, OGLE-2005-BLG-390 Lb, is about 22,000 light years. Its size is about half of that of Earth. It is five times heavier than that of Earth. The
distance between WASP-18b and Earth is about 325 light years. The mass of WASP-18b is 10 times of Jupiter's mass, that is, about 3180 times
greater than Earth's mass. Its size is 11 times bigger than that of Earth's radius.
Look at the table below. The first column is the name of planet, the second column is the distance in light years, and the third and the fourth columns
are the dilated and the proper times when you select Condor for space travel. The fifth and the sixth columns are the dilated and the the proper
times when you travel by Griffin. Using the above information regarding the five exoplanets, e nter the distance in the table below. The dilated time
and the proper time for each space craft will be automatically evaluated. After completing the table, answer the questions.
Microsoft excel software is required to use the table below for automated calculation. However, if you do not have this, you can use your own
calculator. It should be no problem to answer the questions.
1. Fill out Distance column below using above information (50 points).
Condor (v=0.93c)
Exoplanet name
Distance[light years]
Dilated time t [years]
Griffin (v=0.99c)
Proper time tp [years] Dilated time t [years] Proper time tp [years]
51 Pegasi b
WASP-18b
Kepler -78b
Kepler-452b
OGLE-2005-BLG-390 Lb
2. Which planet is the most plausible to visit when you travel by Condor? If you could bring some of your personal items that weigheda total of 5 kg in
a given box that has a dimension of one cubic meter, what items would you choose? (10 points)
3. If you choose Griffin, how many planets could we visit within our lifetime? If you can change the names of the planets, what would you change them
to and why? (10 points)
4. Look at the data of Kepler-452b. The distance determined by the earth observer is 1400 light years, as you can see in the table.
If you are on Griffin, what is the distance to Kepler-452b when you measure? Hint: distance=speed x time. If you are in charge of designing the space
craft, what would you consider to be the most important thing? (10 points)
5. We can't arrive at OGLE-2005-BLG-390 Lb within our lifetime using Condor or Griffin, even if they travel extremely fast.
If we can travel at the speed of light, do you think it is possible? Show your approximate estimation of the cost to constr uct the space craft based on
your purpose of travel. (20 points) Your response should be at least 50 words in length.
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