Lab 3 measuring creater sizes (2)
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Apr 3, 2024
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Journeying Across the Cosmos: Investigating Distant Exoplanets Lab 4 Astronomy 101, L1F Professor: Aaron Boley TA: Justine Obidowski November 30
th
,2023 By: Bashar Adamat Student #: 22501787 Group members: Jimmy Gev, Ansh Garv
Introduction
When gazing into space, one frequently finds planets in star systems other than our own. These planets named "exoplanets"
—
can be studied in terms of both their unique features and those of their host star to explore and speculate on the possibility that they could support life on Earth. In this lab, we first use a combination of stellar spectroscopy to estimate the approximate temperature and mass of the star, and a light curve that shows the exoplanet's transits around a host star in terms of the star's observed flux over time. Following that, the acquired values will be utilized to compute details of the host star-exoplanet system, including the approximate size of the star and the primary lab objectives, which are the orbital period, semi-major axis, radius, mass, and temperature of the planet. We address the topic of whether human existence is possible on this exoplanet, focusing on these planetary values. We also speculate about potential features of other planets that might be present in the same star system.
Methods/Observations
By the end of the lab, we will determine: •
Orbital period of the Exoplanet •
Orbital Semi Major Axis of the Exoplanet •
Planetary Radius •
Planetary mass •
Planetary Temperature We first observe a light curve plotting the flux received from a distant host over time (see Figure 1). Along the graph are multiple dips in the flux value, taken to be due to the transit of the exoplanet across the visible surface of the host star to Earth. (Figure 1: A section of the known light curve, depicting flux received from the host star. Dips in the graph shows periods of time where the Exoplanet transits) For our purposes, and as a measure to reduce uncertainty, we take 5 arbitrary consecutive dips of the light curve and record information for each drop in flux, including the depth of the drop, the horizontal length of the drop (in hours, where each tick of the x-axis is 1 hour), and the time since the center of the previous drop. We observe the following: From these observations, we can easily determine the following: •
Average Transit Depth: 0.019
•
Average Transit Duration: 3 hours •
Average Time since previous transit: 84.5 hours Since multiple transits signify the movement of the exoplanet across a similar region of its orbit (the portion in front of its host star) the time since the previous transit directly taken from the light curve also yields to us that: •
Orbital Period of the Exoplanet = 84.5 hours We also again note that the average transit duration is 3 hours in length; this will be important for later. Next, we use stellar spectroscopy to determine a classification for the host star of this system. We compare a spectrum of the host star to that of a known classification to infer its approximate temperature. (Figure 2a: The recorded spectrum (Figure 2b: The spectrum of a star of the GOV for the observed star) classification) We can see that the two graphs comparing the host star to a general classification are identical. As such, the host star for our exoplanet's system is a GOV star. This gives us that: • Temperature of the host star (T
star
) = 6000 K Also, by spectroscopy, we also know that for a G-class star, the distance to it, which is the distance from which Earth receives its flux, is approximately 31.1 lightyears, or. 31.1 x (9.5 x 10
15
m) = 2.9545 x 10
17
m And that the flux received from a G-class star is: 2.14 x 10
−10
W/ m The following procedure is used to calculate the remaining information pertinent to our discussion: 1.
Determine the mass of the host star using the flux from and distance to a G-class star to first find its luminosity, as per:
F= 𝐿
(4𝜋𝐷
2
)
→ 𝐿 = 𝐹 × 4𝜋𝐷
2
Where D = 2.9545 x
10
17
𝑚
, as shown through the stellar spectroscopy and subsequently applying the luminosity-mass relation: Where M
sun = 1.99 × 10
30
𝑘𝑔
and L
sun = 3.828 × 10
26
𝑊
2.
Determine the orbital semi major axis of the exoplanet using Kepler's Third Law (Harmonic law) using standardized units of seconds and meters: Where G is the gravitational constant 6.67 × 10
−11
(
𝑚
3
𝑘𝑔×𝑠
2
)
because the planetary mass is expected to be of lesser magnitude than the mass of the host star, it may be considered negligible, for a simplification: 3.
Determine the radius of the host star using an approximate relation involving the transit duration (Hour):
simplified, > where R
sun = 696340 km or 6.9634 × 10
4
𝑚
4.
Calculate the planetary radius using an equation that relates the areas to the transit depth (previously recorded as 0.019) as the flux from the host star diminishes or lowers to an area of the Earth-facing surface being covered by an exoplanet transit:
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