Figure 1 highlights the likely appearance of the environment surrounding a super massive black hole (less the inset). In this question you will use Newton's Universal Law of Gravitation to estimate the 'spaghettification' an astronaut would experience in close proximity to a black hole. WARNING! BLACK HOLE! KEEP AWAY Figure 1: A Super Massive Black Hole and its surrounding Event Horizon. a) An astronaut whose height h is 1.7 m floats 'feet down' at a distance of r = 6.77 x 106 m above the center of the Earth (ME = 5.98 x 1024 kg). What is the difference between the gravitational acceleration on the astronaut's feet versus the astronaut's head? Show all of your work. = b) Repeat the calculation from part a), but now for an astronaut floating 'feet down' at a distance of r = 6.77 x 106 m above the center of a black hole with MBH 1.99 x 1031 kg. What is the difference between the gravitational acceleration on the astronaut's feet versus the astronaut's head? Show all of your work.