The Planets Spring 2024 Homework 9 Due 11:59 pm PT Friday, April 12 4. [20 pts] An astronomer on Earth has been obtaining spectra of a nearby star and noticed that the observed wavelength A | of a spectral line with a rest wavelength of A e 396. 84690 nm varies by +0. 00014 nm over a period of 4.217 days. re a. |4 pts] What is the observed wavelength (in nm) of the spectral line when the line is most blueshifted? b. [9 pts] At the moment when the line is most blueshifted, what is the radial velocity of the star towards or away from Earth? State your answer in m/s and clearly state whether the star is moving towards or away from Earth. The Planets Spring 2024 Homework 9 Due 11:59 pm PT Friday, April 12 c. [7 pts] If the observed Doppler shift occurs because the star is orbited by a planet in a circular orbit with an edge-on orientation, then the semi-amplitude K of the Doppler shift (in m/s) is related to the mass of the planet m , the mass of the star M , and the orbital period P (in years) by the following formula: K= (28. 4329 mm) malanet. Me In this formula, the constant m, is the mass of Jupiter and the constant M Sun is the mass of the Sun. The formula uses an approximately equal sign (~) rather than an equal sign (=) because we have assumed that the planet is much less massive than the star. Using this formula and the information given earlier in the question, estimate the mass of the planet. The star has mass M = 0. 8M . Show your work and express your answer in Jupiter masses. Hint: The semi-amplitude of the Doppler shift is the absolute value of the radial velocity you found in part b