3. The Andromeda Galaxy is one of the nearest galaxies to the Milky Way (only 2.5 million light- years from Earth). One of the characteristic spectral lines produced by ionized Hydrogen has a wavelength of 656.3 nm. If measured by an observer on Earth, Hydrogen spectral lines emitted from the Andromeda galaxy appear to have a wavelength of 655.6 nm. (a) How fast is the Andromeda Galaxy moving with respect to Earth? Is it moving towards or away from Earth? (b) If you answered \"towards": how long will it take the Andromeda Galaxy to collide with Earth? If you answered "away": how long will it take for the distance from Earth to the Andromeda Galaxy to double? (c) GN-z11 is one of the farthest galaxies from the Milky Way, moving away from Earth at a relative velocity of 0.986c. What wavelength would Hydrogen spectral lines emitted from GN- 211 appear to have according to an observer on Earth? . A ) is the change in wavelength. . ) is the original wavelength (656.3 nm). v is the velocity of GN-z11 relative to Earth . c is the speed of light. In this case, v is given as 0.986c, which means it's moving away from Earth at 98.6 of the speed of light. Let's calculate the change in wavelength: 0.986c 656.3x 10 9 m C Solving for 41: AX = 0.986 x 656.3 x 10 m Now, we can calculate 4 1: AX ~647.98 x 10 mthe two galaxies. This distance is approximately 2.5 million light-years. Sinc it's moving away, the distance will increase over time. However, a more realistic scena is that the Milky Way and Andromeda galaxies will eventually collide in about 4.5 billion years due to their mutual gravitation attraction. (c) To find the wavelength of Hydrogen spectral lines from GN-z11 as observed fro Earth, we can use the same Doppler shift formula: Where: A ) is the change in wavelength.: 656.3 X 109 m ow, we can solve for v: 9 __ '0 L7 x 10 3X108 olving for 'u: = 2.1 X 106 m/s he positive sign indicates that the *ndromeda Galaxy is moving away fro b) To calculate how long it will take fort 'ndromeda Galaxy to collide with Earth ere moving towards us, which it's not), eed to know the current distance betw he two galaxies. This distance is (a) To calculate the speed at which the Andromeda Galaxy is moving with respe Earth, we can use the Doppler shift form A Where: A ) is the change in wavelength (656.3 655.6 nm = 0.7 nm). ) is the original wavelength (656.3 nm). v is the velocity of the Andromeda Gala c is the speed of light (approximately 3 10^8 m/s). Let's convert the wavelengths to meters consistency: 41 = 0.7 x 10-9 m