Lab 7
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University of Delaware *
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Course
133
Subject
Astronomy
Date
Apr 3, 2024
Type
Pages
2
Uploaded by ElderSnow13489
Discovering
Exoplanets
Using
Transits
Version
of
November
1
7
,
20
21
1.
Open your NAAP Labs software. From the main menu, click "12. Extrasolar Planets" and then select "Exoplanet Transit Simulator." From
the
Presets
menu,
select
HD
209458
b,
the
first
transiting
exo-planet
ever
found. 2.
The error on the mean of a set of data, or the amount by which the
√ estimate of the mean may be wrong, is σ
μ = σ/ N
, where σ is the standard deviation of the data and N is the number of data points. For a transit to be detected, its depth must be greater than 5
σ
μ
, or five errors on the mean. (That way there is only a 1-in-3.5-million chance that the transit is not real. With depth= 3
σ
μ
, there is a chance of 2.7 in 1000 that the transit is not real.) Click the button labeled “show simulated measurements” in the upperright panel. Add 50 simulated measurements to your light curve. Count the number of points that trace the full transit (when the flux is at minimum)
—
that will be the number of data points in your series. What is the maximum noise level you could have in order to detect the transit? After testing multiple noise levels / standard deviation data points, I have found that 0.017 is the maximum before 5
σ
μ > depth (0.0181). I have found this by comparing the two points 0.017 and 0.018. When computing 0.017/
√
24, I found 0.01735 which is less than 0.0181. Now, when I computed .018/
√
28, I found that 5
σ
μ (0.01837) > 0.0181. 3.
Suppose the best measurement you can get has σ = 0
.
01. This is about right for telescopes on the ground (as opposed to in space). Use pencil, paper, and calculator to estimate the smallest planet size you could detect with 50 total data points (some will not be during transit). Then use the simulator to adjust the planet radius until you find the eclipse depth equal to 5
σ
μ given σ = 0
.
01. How close was your penciland-paper estimate? Hint: eclipse depth scales as what power of planet radius? Firstly, the equation I used to find the size of the planet was: (x * 43441)^2/432690^2 Solving for x, we get .007
Now, finding the eclipse depth with the given information, we get .01/
√
50 = .0014 5*.0014 = .007, which is the number that we cannot exceed when finding the size of the planet So, testing multiple x values for radius, I found .82 to be the maximum radius for a given planet before exceeding 5
σ
μ 4.
Suggest a strate
gy for detecting smaller planets from Earth’s surface.
Speculate about how your noise value would change if you could put your telescope in space, and why. Firstly, your noise value would change potentially due to the obscuring properties of the atmosphere when it comes to imaging astronomical entities. Now, as for detecting smaller planets from Earth
’
s surface, one possible strategy would be to correct this disruption using AI or other computer programs. 1
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