## Energy to move mass (potential energy)

1. The problem statement, all variables and given/known data
How much energy is required to move a 900 kg mass from the Earth's surface to an altitude 3 times the Earth's radius?

2. Relevant equations
$$\Delta U = GMm[\frac{1}{R_1} - \frac{1}{R_2}]$$
$$G = 6.67 x 10^{-11} Nm^2/kg^2$$
$$R_1 = R_E = 6.37 x 10^6 m$$
$$M = 5.98 x 10^{24} kg$$

3. The attempt at a solution
I plugged in everything with $$R_1$$ = radius of earth
and $$R_2$$ = 3(radius of earth) + 1 radius of earth = 4 radius of earth...and got $$\Delta U = 4.23 x 10^{10}$$.

The answer is $$3.76 x 10^{10}$$, where $$R_2$$ = 3(radius of earth).

Why don't you use the radius of the earth plus the altitude (i.e. 4x radius of earth)? For the first potential energy, I use the radius as the radius of the earth, so I don't see why you use only the altitude for the second potential energy.
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Recognitions:
Homework Help
 Quote by merced 1. The problem statement, all variables and given/known data How much energy is required to move a 900 kg mass from the Earth's surface to an altitude 3 times the Earth's radius? 2. Relevant equations $$\Delta U = GMm[\frac{1}{R_1} - \frac{1}{R_2}]$$ $$G = 6.67 x 10^{-11} Nm^2/kg^2$$ $$R_1 = R_E = 6.37 x 10^6 m$$ $$M = 5.98 x 10^{24} kg$$ 3. The attempt at a solution I plugged in everything with $$R_1$$ = radius of earth and $$R_2$$ = 3(radius of earth) + 1 radius of earth = 4 radius of earth...and got $$\Delta U = 4.23 x 10^{10}$$. The answer is $$3.76 x 10^{10}$$, where $$R_2$$ = 3(radius of earth). Why don't you use the radius of the earth plus the altitude (i.e. 4x radius of earth)? For the first potential energy, I use the radius as the radius of the earth, so I don't see why you use only the altitude for the second potential energy.
Your reasoning is entirely correct, $r_f$ {\em should} be $4 R_E$. If they used three times the radius of the Earth, they made a mistake, since "altitude" is defined to be measured above ground.