# 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...

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?

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### 1 Answer

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.