If R represents the radius of the Earth, determine the work done in lifting a space probe of mass 100kg from the Earth's surface
a) to a height of 4R
b) to infinity
(Use G=6.67`xx`10^-11N m^2 kg^-2, Mass of Earth, M=6`xx`10^24 kg , radius of the Earth, R=6.4`xx`10^6 m )
My answers are 5.00`xx`10^9 J and 6.25`xx`10^9 J , but my teacher's answers have negative sign. Can explain why the answers have negative sign?
Gravity, work, force, and energy are all types of vectors. Vectors have both an amplitude (a numerical value signifying how much), and a direction. (usually defining the amplitude as positive or negative). For example. If I were to demonstrate the conservation of energy in a non-elastic collision, I would give the vehicle going right `->` a positive vector, and the vehicle going left `larr` a negative vector.
The most likely reason for your teacher's use of negative signs is that the teacher is making Gravity's vectors `darr` positive, and thus anti-gravity vectors `uarr` must be negative.
So long as your vector amplitudes (the absolute values) are the same, then your answer is correct. You should just show that you interpret Gravity as a negative vector, and energy countering it as positive.