The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?

The gravitational potential energy of a body of mass $m$ at the earth's surface is $-mgR_e$. Its gravitational potential energy at a height $R_e$ from the earth's surface will be (Here $R_e$ is the radius of the earth).

What is gravitational potential energy? Why is gravitational potential negative,and what does it mean?

What is the potential energy of a satellite at a height of $6.4 \times 10^6 \, m$ from the surface of the Earth? ($R_e$ = radius of the Earth)

The mass of the earth is $6.00 \times 10^{24} \ kg$ and that of the moon is $7.40 \times 10^{22} \ kg$. The gravitational constant is $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$. The potential energy of the system is $-7.79 \times 10^{28} \ J$. The mean distance between the earth and the moon is:

$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is: