# Why is Gravitational Potential Energy Negative?

Student's learn in HSC and IB Physics classes that the gravitational potential energy of two attracting masses is negative. Why is this? Let us consult the popular Physics textbooks to see what their authors say.

Resnick, Halliday and Walker Fundamentals of Physics (10th edition, page 365)...we choose a reference configuration with U equal to zero when the separation distance between the masses is infinite. The gravitational potential energy decreases when the separation decreases. Since U=0 for r=infinity, the potential energy is negative for any finite separation and becomes progressively more negative as the particles move closer together..

Serway and Jewett Physics for Scientists and Engineers (8th edition, page 386)...the potential energy is negative because the force is attractive and we have chosen the potential energy as zero when the particle separation is infinite. Because the force between the particles is attractive, an external agent must do positive work to increase the separation between the particles. The work done by the external agent produces an increase in potential energy as the two particles are separated.

Knight Physics for Scientists and Engineers (4th edition, page 366)...All a negative potential energy means is that the potential energy of the two masses at separation r is less than their potential energy at infinite separation.

Tipler and Mosca Physics for Scientists and Engineers (6th edition, page 374)....this means that U approaches zero as r approaches infinity. At first this may seem like a strange choice because for finite values of r all values of U are negative. This just means, however, that the potential energy is at a maximum when Earth and particle are at infinite separation.

Sears, Zemansky, Young, Freedman University Physics (14th edition, page 429)...in defining U we have chosen U to be zero when the body is infinitely far from the Earth. As the body moves towards the Earth, gravitational potential energy decreases and becomes negative.

Ohanian and Markert Physics for Engineers and Scientists (3rd edition, page 289)...the potential energy is always negative and its magnitude is inversely proportional to r. If the distance r is small, the potential energy is low (the potential energy is much below zero); if the distance r is large, the potential energy is higher (the potential energy is still negative but not so much below zero). Thus the potential energy increases with distance; it increases from a large negative value to a smaller negative value or to zero. Such an increase of potential energy with distance is characteristic of an attractive force. For instance, if we want to lift a communications satellite from a low initial orbit (just above the Earth's atmosphere) into a high final orbit (such as a geostationary orbit) we must do work on this satellite (by means of a rocket engine). The work we do while lifting the satellite increases the gravitational potential energy from a large negative value (much below zero) to a smaller negative value (not so much below zero).

Comment