I have to write an essay on the following problem. I don\'tquite understand exac

Question

I have to write an essay on the following problem. I don'tquite understand exactly how to go about answering it. Anysuggestions and ideas will be greatly appreciated and I will giveyou a lifesaver rating.

As you well know, our illustrious governor takes a keen interest inphysics, and likes to use his knowledge of the subject to makeinformed and rational decisions about state policy. In an effort toshow up our long-time foes, the Coloradoans, the governor hasdecided the state should start its own space program. Unfortunately, our illustrious governor never excelled at PHYS 2010like the rest of you, and is slightly confused about some pointsregarding the Utah Space Agency’s plans.
He is hip to getting the astronauts into orbit.“We put themon a big rocket! We use the impulse
provided by the rocket to give them momentum, which means they havekinetic energy. This gets them off the launch pad and intoorbit.”
“But wait!” he exclaims. “How will they get home?When you are up high, you are supposed to
have gravitational potential energy which you convert into kineticenergy as you fall. Our astronauts clearly have some kinetic energybecause they are going around in an orbit, but they are weightless!If they are weightless, that means there is no gravity. If there isno gravity, they have no gravitational potential energy. How willthey get home?” The Treasury Secretary pipes in and tries tohelp. “They have rockets. If they fire their rockets, theycan increase their kinetic energy and come home.” TheSecretary of Transportation disagrees. “No, they are incircular motion because there is gravity, so they have potentialenergy. They need to use their rockets to get rid of their currentkinetic energy and they will start to fall.”

“This is crazy,” shouts the governor. “Eitherthey have potential energy or they don’t. Either they
need to increase their kinetic energy or they don’t. Someonebetter start making sense soon.
In a short (1-2 page) essay, explain which of these people (all,some or none!) actually understand
what is going on, and the physics of how the astronauts will gethome.

Explanation / Answer

The major falacy in this is the statement: " If they areweightless, that means there is no gravity." For example, the value of g at the surface of the earthis   ge = G Me /Re2 , which works out to be approx 9.8m/s2 . In space at a distance from the earth's surface of about 4,000miles (which is 1 earth radius from the surface), the value of gthere is      gspace = GMe / (2Re )2 = GMe / 4 Re2 = ge / 4 = 9.8 / 4   = 2.45m/s2 Thus, there is a force of gravity since there is a value of gin space. Thus, there is gravitational PE. The person in space is "weightless" because they are infree-fall.   If you jumped off a tall building with abathroom scale strapped to your butt, the scale would read zerosince you are in free-fall.   However, there is still aforce of gravity acting on your body pulling you rapidly downtoward earth and g is still 9.8. In a circular orbit in space, the non-zero force of gravitydoes not pull you down to the ground but pulls you inward and keepsyou going in a circular path, ie, prevents you from flying offtangentially in a straight line.   This non-zero force ofgravity supplied the centripetal force that is always required fora circular orbit to exist.

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