(40 pts) Imagine a rocky asteroid wandering into Earth's orbit at the wrong time, so that it is hit by our planet. Remem

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40 Pts Imagine A Rocky Asteroid Wandering Into Earth S Orbit At The Wrong Time So That It Is Hit By Our Planet Remem 1 (738.12 KiB) Viewed 30 times

(40 pts) Imagine a rocky asteroid wandering into Earth's orbit at the wrong time, so that it is hit by our planet. Remembering that the kinetic energy (KE) per unit mass (m) of a body moving at velocity v is KE/m = vẽ/2 (this is another way of writing KE = 1/2 mv²), and that the temperature increase is 1 K for each kJ/kg energy put into rock (this is the same as saying that the heat capacity of rock is 1 kJ/kg/K) at ambient and high temperatures, how much is our planet heated in the impact zone? Is this enough to boil water – that is, to sterilize the impact area? We will help you through the calculation: a. (10 pts) Using the information that the Earth takes 1 year to orbit the Sun and has an orbital semimajor axis of 1 AU, determine Earth's orbital velocity (v in km/s). b. (15 pts) Determine the asteroid's kinetic energy per unit mass (J/kg) for an impact at this velocity (v?/2 in J/kg). This is the amount of energy put into the impact zone, and also into the asteroid. c. (10 pts) Use the heat capacity of rock to calculate the corresponding temperature increase of the asteroid and our planet's rock in the impact zone. d. (5 pts) Compare your result with the temperature required to boil water, 100° C. Note: This calculation is not quite right because it ignores the heat required to boil water, but the correction is not big enough to change the general result.