Why is gravitational potential energy negative? How is it different from other forms of energy? I recently saw a video by Dr. Michio Kaku, he said that the total energy content of the universe is zero, since gravitational potential energy is negative, thus balancing all the positive energy. Can anyone help me out here?
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1possible duplicate of [Total energy of the Universe](http://physics.stackexchange.com/q/2838/ – John Rennie Sep 04 '14 at 05:18
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1Also consider Why is gravitational potential energy negative, and what does that mean? – BMS Sep 04 '14 at 05:41
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This can be understood in the following way: one may define the potential energy of a body of mass $m$ in the gravitational field of a mass $M$ as the energy (work) required to take it from its current position $r_i$ to infinity. The force exerted by M on m is, at least in Newtonian Gravity, which should suffice to give an intuitive understanding of the concept, given by
$\mathbf{F}(\mathbf{r})=-G\frac{mM}{r^2}\hat{r},$
where $\mathbf{r}$ is the vector pointing from $m$
to $M$, $\hat{r}$ is the associated unit vector and $r$ is the distance.
The required work is now given by the usual formula $W=\int Fds$ as
$$W=\int_{r_i}^{\infty}\mathbf{F}(\mathbf{r})\mathbf{\mathbb{d}s},$$ which leads to
$$W=E_{pot}=-G\frac{mM}{r}.$$ As one can see, the origin of the negative sign can be traced back to the fact that gravity is attractive.
Frederic Brünner
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