You found the two main angular velocities of the Earth: one dueto the Earth's motion around the sun, and one due to its rotationabout its own axis. Now let's figure out the energy and momentumassociated with that motion. For the purposes of this problem,treat the Earth as a solid, uniform sphere with mass5.97×10²⁴ kg and radius 6.37×10⁶ m , andassume that the Earth's orbit around the sun is circular with aradius of 1.5×10¹¹ m .

Part A) What is the angular kinetic energy of the Earth due toits orbit around the sun?

Part B) What is the magnitude of the Earth's angular momentumdue to its orbit around the sun?

Part C) What is Earth's angular kinetic energy due to itsrotation around its axis?

Part D) What is the magnitude of the Earth's angular momentumdue to its rotation around its axis?

Part E) Which of the following best explains where the Earth'sangular kinetic energy and momentum came from?

Remember that energy and momentum are always conserved (thoughenergy can change forms). In other words, if you start with acertain amount of energy and momentum, you must end with the sameamount of energy and momentum. By conservation of energy andmomentum, the values you've calculated in this problem must havecome from somewhere.

Which of the following best explains where the Earth's angularkinetic energy and momentum came from?

a. The solar system formed from a massive cloud of gas and dust,which was slowly rotating. As the cloud collapsed under its owngravitational pull, the cloud started to spin faster, just as anice skater pulling his arms in will spin faster. Because all of thematerial that accreted to form the planet was rotating, the planetwas rotating as well.

b. As the Earth formed, it experienced a series of collisionswith asteroids and comets. These asteroids and comets hit the ballof rock that was forming into the planet off-center. Over time, theoff-center collisions gradually caused the planet to rotatefaster.

c. As the Moon orbits around the Earth, it creates tides on theEarth. Over time the tides have caused the Earth to rotate fasterand faster.

d. Sheer force of will.