If not, what are the other applications?

Calculating the relativistic precession of Mercury, for one. This post-diction was one of the key things that helped with the rapid acceptance of general relativity.

Modeling GPS, and calculating the orbits of LAGEOS and Gravity Probe B, for another. A full-blown general relativistic formulation works quite nicely on (and is absolutely essential for) black holes and neutron stars precisely because gravity about those extremely massive objects is simple. Earth's gravity field isn't so nice and simple. It's rather lumpy compared to a neutron star. One of the more recent models of the Earth's gravity field, Earth Gravity Model 2008 (EGM2008), is a 2159x2159 spherical harmonics model. How are you going to handle that with general relativity? The answer is to linearize the field equations.

Modeling the behavior of the solar system, for yet another. All three of the leading models of planetary ephemerides use a first order post-Newtonian approximation of gravity. (But apparently they're starting to wonder if they need to step beyond that. To second order.)

One last use: "weigh" the Earth. See my answer to the question "How is the mass of the Earth determined?" at the earth science stackexchange sister site.

If not, what are the other applications?

Calculating the relativistic precession of Mercury, for one. This post-diction was one of the key things that helped with the rapid acceptance of general relativity.

Modeling GPS, and calculating the orbits of LAGEOS and Gravity Probe B, for another. A full-blown general relativistic formulation works quite nicely on (and is absolutely essential for) black holes and neutron stars precisely because gravity about those extremely massive objects is simple. Earth's gravity field isn't so nice and simple. It's rather lumpy compared to a neutron star. One of the more recent models of the Earth's gravity field, Earth Gravity Model 2008 (EGM2008), is a 2159x2159 spherical harmonics model. How are you going to handle that with general relativity? The answer is to linearize the field equations.

Modeling the behavior of the solar system, for yet another. All three of the leading models of planetary ephemerides use a first order post-Newtonian approximation of gravity. (But apparently they're starting to wonder if they need to step beyond that. To second order.)

One last use: "weigh" the Earth. See my answer to the question "How is the mass of the Earth determined?" at the earth science stackexchange sister site.

If not, what are the other applications?

Calculating the relativistic precession of Mercury, for one. This post-diction was one of the key things that helped with the rapid acceptance of general relativity.

Modeling GPS, and calculating the orbits of LAGEOS and Gravity Probe B, for another. A full-blown general relativistic formulation works quite nicely on (and is absolutely essential for) black holes and neutron stars precisely because gravity about those extremely massive objects is simple. Earth's gravity field isn't so nice and simple. It's rather lumpy compared to a neutron star. One of the more recent models of the Earth's gravity field, Earth Gravity Model 2008 (EGM2008), is a 2159x2159 spherical harmonics model. How are you going to handle that with general relativity? The answer is to linearize the field equations.

Modeling the behavior of the solar system, for yet another. All three of the leading models of planetary ephemerides use a first order post-Newtonian approximation of gravity. (But apparently they're starting to wonder if they need to step beyond that. To second order.)

If not, what are the other applications?

Calculating the relativistic precession of Mercury, for one. This post-diction was one of the key things that helped with the rapid acceptance of general relativity.

Modeling GPS, and calculating the orbits of LAGEOS and Gravity Probe B, for another. A full-blown general relativistic formulation works quite nicely on (and is absolutely essential for) black holes and neutron stars precisely because gravity about those extremely massive objects is simple. Earth's gravity field isn't so nice and simple. It's rather lumpy compared to a neutron star. One of the more recent models of the Earth's gravity field, Earth Gravity Model 2008 (EGM2008), is a 2159x2159 spherical harmonics model. How are you going to handle that with general relativity? The answer is to linearize the field equations.

Modeling the behavior of the solar system, for yet another. All three of the leading models of planetary ephemerides use a first order post-Newtonian approximation of gravity. (But apparently they're starting to wonder if they need to step beyond that. To second order.)

One last use: "weigh" the Earth. See my answer to the question "How is the mass of the Earth determined?" at the earth science stackexchange sister site.