He said don't worry about mixing units... but I have a feeling something is wrong with the m^3 in "G=" and the fact that the answer is in km.

Oh yeah, the answer is:

38, 008 km^2 kg^2/sec^2.

Also, he said in class to basically just integrate the whole F function. I did that, and it doesn't work.

The limits of integration are from 6378 to 6578.

 

the answer is TITS

 

You compute the work with an integral. The variable of integration is distance, so the limits are 0 km and 200 km. The integrand is F(x)dx, where F(x) is the force function.

It's a pretty straightforward integral.

Bon chance!

 

Except the limits of the integral are 6378 and 6578 kms. Since G is given in meters, convert the distance to meters as well so you have 6378000 m to 6578000 m. When you cancel out the terms, m^3 gets divided by m^2 and becomes m, kg^2 gets divided by the kg term in G, and s^2 stays so your new value is in terms of m*kg/s^2 which is also newtons.

Integrate the the equation in terms of x and set your bounds to 6378000 and 6578000 for part A and B.

 

Yes, it's supposed to be. Did you actually try and calculate it though?

 

You then get 3.800865x10^10 which is in m^2*kg^2/sec^2.
Divide it by km^2, or 1,000,000 m^2 to get 38008.65 for the first part.

 

Here's what I'm doing:

integrate ((6.673x10^-11)(5.9742x10^24)(20000)/6378000^2) from 6378000 to 6578000

and I'm getting

3.92005x10^10

 

(6.673x10^-11)(5.9742x10^24)(20000)/x^2)

Now try it.

 

So why do you keep it as x^2 even though the radius is given?!

 

and use the bounds you have, but don't forget to convert back to km^2 at the end by dividing the answer by 1x10^6