2.5) If the planet takes significantly less time for the transit than described, what are likely...

 

 

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2.5) If the planet takes significantly less time for the transit than described, what are likely explanations? A. passage does not pass through stellar center (a secant). B. Non circular passage orbit with passage close to periastron. C. Inaccurate measurement of stellar properties, mass and radius D. General relativity distortions E. Third body perturbations Answer:___ 2.6) If the planet is in circular orbit about the star as described above, what would be its greatest separation be in arc seconds as observed from Earth? A.)2 B). 0.5 C.) 0.2 Answer: Answer: 2.6) Later a Neptune-like planet IS detected with a four year period. What is its semi-major axis (AUS)? A.)1.8 B). 2.28 C.) 3.14 D.) 3.28 E.) 3.35 Answer: 2.7) This will help for what follows: The K5 Neptune's velocity at its semi major axis distance (km/sec)? A.) 12.3 B). 15.4 C.) 17.0 D.) 19.5 E.) 21.8. A.) 1.77 2.8) It is discovered that "Neptune" parameter p is aligned with line of sight! Eccentricity = 0.3. and periastron to viewer's left, heading to the right. The radial distance at "p" or r(p) in AUs? C.) 1.97 Answer:___ A.)12.81 Answer: D.) 0.07 B) 1.87 Answer: E.) 0.35 2.9 What is Neptune's projected transit velocity (km/sec)? Hints: The conic, the definition of p and the flight path angle in rv cos gamma = h and energy equation are all involved. Find the radius in AUS at p, the velocity and h with Rp Vp = Ra Va... B.) 13.45 Answer: D.) 2.07 C). 14.02 2.10) Excitement mounts about imaging at apoastron. How far out is that (AUS)? A.) 2.8 B.) 2.96 C.) 3.12 D.) 3.28 D.) 17.45 2.11) What is the angular separation for the above in arc seconds at 5 parsecs out? A.) 1.8 B.) 1.2 C.) 0.6 D.) 0.4 E.) 2.47 E.) 21.8. E.) 3.42 E.) 0.2 Table-1 Calculation Aids Normalized Units on Main Sequence Stellar Class Mass Radius Luminosity M8 0.13 0.10 0.0008 M5 0.32 0.21 0.0079 0.51 0.60 0.74 0.69 MO K5 КО G5 G2 GO F5 FO A5 AO B5 BO 06 0.85 0.78 0.93 1.0 1.05 1.2 1.3 1.7 2.5 3.8 7.4 18 0.072 0.16 0.40 0.93 0.79 1.0 1.0 1.1 1.3 B; (T5800, A500) 1.7 2.1 20 3.2 80 6.5 18 40 Solar Radius: Terrestrial Planet radius: Jovian Planet radius Neptunian Planet radius 1.26 2.5 6.0 Planck Function in Wavelength Form Centimeter units = 800 20000 500,000 h k C Kelvin A500 T5800 Temperature 2660 3120 3800 4410 5240 5610 5800 5920 6540 7240 8620 10,800 16,400 30,000 38,000 Absolute Magnitude 18.7 7.50 5.49 4.83 (for expansion to 1 AU, 400 K vs. 5777) Planck constant Boltzmann constant Vacuum light speed 1 nanometer 500 nanometers: Solar Effective Temp For what follows, we use B. (T) as derived by Swihart (Astrophysics & Stellar Astronomy) to simplify application. Ba (T, λ) = 1.191 x10³) ³/(exp(1.439/(2T)) - 1.0) (Eq. 2.2) = 1.191 x10-5 A500 ³/[(exp(1.439/(500 T5800))-1.0)] 1.191x10-5/(5x10-) / [exp (1.439/(5 x1075.8 x10³))-1.0] =.... 5 x10 centimeters 5800 K 2.93 2.41 Earth Orbital velocity: 29.7859... km/s =Sqrt(GMsun/1AU) 700,000 kilometers 7,000 kilometers 1/100th Solar 70,000 kilometers 1/10th Solar 28,000 kilometers 1/25th Solar B₂ (T) = 2 hc²/25 [ exp( hc/2 KT)-1], 6.63 x10-27 erg second 1.38 x10-16 erg /deg Kelvin 3.0 x 10¹0 cm/sec 1x10⁹ meters 2.5) If the planet takes significantly less time for the transit than described, what are likely explanations? A. passage does not pass through stellar center (a secant). B. Non circular passage orbit with passage close to periastron. C. Inaccurate measurement of stellar properties, mass and radius D. General relativity distortions E. Third body perturbations Answer:___ 2.6) If the planet is in circular orbit about the star as described above, what would be its greatest separation be in arc seconds as observed from Earth? A.)2 B). 0.5 C.) 0.2 Answer: Answer: 2.6) Later a Neptune-like planet IS detected with a four year period. What is its semi-major axis (AUS)? A.)1.8 B). 2.28 C.) 3.14 D.) 3.28 E.) 3.35 Answer: 2.7) This will help for what follows: The K5 Neptune's velocity at its semi major axis distance (km/sec)? A.) 12.3 B). 15.4 C.) 17.0 D.) 19.5 E.) 21.8. A.) 1.77 2.8) It is discovered that "Neptune" parameter p is aligned with line of sight! Eccentricity = 0.3. and periastron to viewer's left, heading to the right. The radial distance at "p" or r(p) in AUs? C.) 1.97 Answer:___ A.)12.81 Answer: D.) 0.07 B) 1.87 Answer: E.) 0.35 2.9 What is Neptune's projected transit velocity (km/sec)? Hints: The conic, the definition of p and the flight path angle in rv cos gamma = h and energy equation are all involved. Find the radius in AUS at p, the velocity and h with Rp Vp = Ra Va... B.) 13.45 Answer: D.) 2.07 C). 14.02 2.10) Excitement mounts about imaging at apoastron. How far out is that (AUS)? A.) 2.8 B.) 2.96 C.) 3.12 D.) 3.28 D.) 17.45 2.11) What is the angular separation for the above in arc seconds at 5 parsecs out? A.) 1.8 B.) 1.2 C.) 0.6 D.) 0.4 E.) 2.47 E.) 21.8. E.) 3.42 E.) 0.2 Table-1 Calculation Aids Normalized Units on Main Sequence Stellar Class Mass Radius Luminosity M8 0.13 0.10 0.0008 M5 0.32 0.21 0.0079 0.51 0.60 0.74 0.69 MO K5 КО G5 G2 GO F5 FO A5 AO B5 BO 06 0.85 0.78 0.93 1.0 1.05 1.2 1.3 1.7 2.5 3.8 7.4 18 0.072 0.16 0.40 0.93 0.79 1.0 1.0 1.1 1.3 B; (T5800, A500) 1.7 2.1 20 3.2 80 6.5 18 40 Solar Radius: Terrestrial Planet radius: Jovian Planet radius Neptunian Planet radius 1.26 2.5 6.0 Planck Function in Wavelength Form Centimeter units = 800 20000 500,000 h k C Kelvin A500 T5800 Temperature 2660 3120 3800 4410 5240 5610 5800 5920 6540 7240 8620 10,800 16,400 30,000 38,000 Absolute Magnitude 18.7 7.50 5.49 4.83 (for expansion to 1 AU, 400 K vs. 5777) Planck constant Boltzmann constant Vacuum light speed 1 nanometer 500 nanometers: Solar Effective Temp For what follows, we use B. (T) as derived by Swihart (Astrophysics & Stellar Astronomy) to simplify application. Ba (T, λ) = 1.191 x10³) ³/(exp(1.439/(2T)) - 1.0) (Eq. 2.2) = 1.191 x10-5 A500 ³/[(exp(1.439/(500 T5800))-1.0)] 1.191x10-5/(5x10-) / [exp (1.439/(5 x1075.8 x10³))-1.0] =.... 5 x10 centimeters 5800 K 2.93 2.41 Earth Orbital velocity: 29.7859... km/s =Sqrt(GMsun/1AU) 700,000 kilometers 7,000 kilometers 1/100th Solar 70,000 kilometers 1/10th Solar 28,000 kilometers 1/25th Solar B₂ (T) = 2 hc²/25 [ exp( hc/2 KT)-1], 6.63 x10-27 erg second 1.38 x10-16 erg /deg Kelvin 3.0 x 10¹0 cm/sec 1x10⁹ meters

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