Use this light curve of a star with a transiting exoplanet to answer the following. If the exoplanet is orbiting a star identical to our own Sun, what is its average orbital distance, in AU? What is the period in years of the transiting exoplanet?
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- Using high resolution adaptive optical techniques, observations of a nearby (9.5 pc) cool star of mass 0.2 solar masses indicate the presence of a small rocky exoplanet in a circular orbit with a radius of 0.01 arcseconds. Using Kepler's Laws, estimate the period of the exoplanet's orbit in days. select units AConsider the attached light curve for a transiting planet observed by the Kepler mission. If the host star is identical to the sun, what is the radius of this planet? Give your answer in terms of the radius of Jupiter. Brightness of Star Residual Flux 0.99 0.98 0.97 0.006 0.002 0.000 -8-881 -0.06 -0.04 -0.02 0.00 Time (days) → 0.02 0.04 0.06A 1.43MSun main sequence star is found to have a planet in its habitable zone. What is the expected lifetime (in years) of the star? (Assume that the expected lifetime of the Sun is 11 ✕ 109 years. Round your answer to at least three significant figures.) Using the figure above, if Earth orbited this star, how far along the timeline would it get?
- Exoplanet orbital period (b) For the system pictured in the previous problem (and using data given there), suppose that the star has a mass of 0.025 solar masses, and the planet's mass is very small in comparison. Compute the planet's orbit period. Assume the orbit is circular with a radius given by the distance listed in the figure. Express your answer in years. [Hint: this is a mildly challenging problem that requires plugging into a single formula but using multiple unit conversions. You will need to use Kepler's 3rd law in its **general** form (not the simplified form that is only applicable to objects orbiting our Sun). You will need to look up the value of the constant G. Convert solar masses to kg, AU to m, and everything else to base Sl units; find the period in seconds; then convert seconds to years.]White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a 4 sphere is Tr.) 3 km Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size? I Table A-10 I Properties of the Planets ORBITAL PROPERTIES Semimajor Axis (a) Orbital Period (P) Average Orbital Velocity (km/s) Orbital Inclination Planet (AU) (106 km) (v) (days) Eccentricity to Ecliptic Mercury 0.387 57.9 0.241 88.0 47.9 0.206 7.0° Venus 0.723 108 0.615 224.7 35.0 0.007 3.4° Earth 1.00 150 1.00 365.3 29.8 0.017 Mars 1.52 228 1.88 687.0 24.1 0.093 1.8° Jupiter 5.20 779 11.9 4332 13.1 0.049 1.30 Saturn 9.58 1433 29.5 10,759 9.7 0.056 2.5° 30,799 60,190 Uranus 19.23 2877 84.3 6.8 0.044 0.8° Neptune * By definition. 30.10 4503 164.8 5.4 0.011 1.8° PHYSICAL PROPERTIES (Earth = e)…consider plutoz diameter and mass. (2374)km & (1.303E22kg) and day which js 6.4 dayz long. FIND: 1. please elaborate how would you get the answer to the escappe vel0city from plut0. 2. we would need to find the minimum energy required for an aircraft or ship of some sort with mass (525kg) to escape this planet.. 3. we would also need to find the t0tal energy for a complete orbit around the planet with an airship with a same mass (525) and an altitude of 224 km
- 9) An interstellar cloud fragment 0.2 light-year in diameter is rotating at a rate of one revolution per million years. It now begins to collapse. Assuming that the mass remains constant, estimate the cloud's rotation period when it has shrunk to (a) the size of the solar nebula, 100 AU across, and (b) the size of Earth's orbit, 2 AU across. (answers: 0.016 revolutions per year, and an orbital period of 62.5 years, This is 40 revolutions per year, and an orbital period of 0.025 years, or just a little over 9 days)1. These images were taken six months apart, first when Earth was as far to one side of Alpha Centauri as it can get and again when Earth was as far to the other side of Alpha Centauri as it can get. Consequently, the baseline between the two observing positions is how many AU across? Answer: 1.7 arcsec 2. First, convert this to kilometers using your measurement of how many kilometers are in an AU. 3. Now convert the baseline to kilometers using the true value for the number of kilometers in an AU. 4. Calculate the distance to Alpha Centauri using parallax and the true baseline in kilometers. 5. Google and record the true value. 6. Calculate your percent error 7. Discuss significant sources of errorOne way to recognize a distant planet is by studying the planets motion along its orbit. If Uranus circles the Sun in 84.0 years, how many arc seconds will it move in 1 Earth day? Assume a circular orbit for Uranus, and pretend that Earth is not moving.
- Need asap.. If you increase the semi-major axis of an exoplanet's orbit, how does this affect the radial velocity signal of the host star? (A).The amplitude of the radial velocity curve increases. or (B). The amplitude of the radial velocity curve decreases.For the following light curve, which of the answers best illustrates the orientation of the exoplanet and its host star during the dip at Time 3? Light curve Time 1 Time 2 Time 3 Time 4 Choose one: А. O C. D. Intensity B.If a transit depth of 0.001 (or 0.1% decrease in brightness) is detected for a star with a radius of 0.3 RSun, what would the radius of the exoplanet be in units of RSun?