diff --git a/doc/modules/changes/20250716_hyunseong96 b/doc/modules/changes/20250716_hyunseong96
new file mode 100644
index 00000000000..360e963c29f
--- /dev/null
+++ b/doc/modules/changes/20250716_hyunseong96
@@ -0,0 +1,4 @@
+Added: ASPECT now has a new gravity model plugin called 'Radial linear with tidal potential' for tidal forces.
+This plugin is useful for modeling long-term interior and surface evolution in moons orbiting a large planet.
+
+(Hyunseong Kim, Antoniette Greta Grima, Wolfgang Bangerth 2025/07/16)
diff --git a/include/aspect/gravity_model/radial_with_tidal_potential.h b/include/aspect/gravity_model/radial_with_tidal_potential.h
new file mode 100644
index 00000000000..6107417f9e0
--- /dev/null
+++ b/include/aspect/gravity_model/radial_with_tidal_potential.h
@@ -0,0 +1,90 @@
+/*
+ Copyright (C) 2014 - 2019 by the authors of the ASPECT code.
+
+ This file is part of ASPECT.
+
+ ASPECT is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2, or (at your option)
+ any later version.
+
+ ASPECT is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with ASPECT; see the file LICENSE. If not see
+ .
+*/
+
+
+#ifndef _aspect_gravity_model_radial_with_tidal_potential_h
+#define _aspect_gravity_model_radial_with_tidal_potential_h
+
+#include
+#include
+#include
+
+namespace aspect
+{
+ namespace GravityModel
+ {
+ /**
+ * A class that describes gravity as a radial vector of linearly
+ * changing magnitude, which is modified by a tidal potential from flattening and non-synchronous rotation.
+ *
+ * The equation implemented in this gravity model is from Tobie et al. (2025) (https://doi.org/10.1007/s11214-025-01136-y),
+ * which is defined as:
+ * g = -magnitude - gradient (-(tidal potential)).
+ * Tidal potential is positive because the formula follows conventions from geodesy research, where potential is taken as positive.
+ * (tidal potential) = (3 G M_p) / (2 a_s^3) * r^2 * (Tstar + T0)
+ * Tstar = 1/6 *(1-3*cos(theta)^2) and T0=1/2sin(theta)^2*cos(2*lambda + 2*b*t)
+ * where G = gravitational constant, M_p = mass of the perturbing body, a_s = semimajor axis of the orbit, b = angular rate of non-synchronous rotation.
+ * b = 2 * pi / P where P is period of NSR.
+ * r, theta and lambda are radial distance, polar angle and azimuthal angle, respectively.
+ *
+ * @ingroup GravityModels
+ */
+ template
+ class RadialWithTidalPotential : public Interface, public SimulatorAccess
+ {
+ public:
+ /**
+ * Return the gravity vector as a function of position.
+ */
+ Tensor<1,dim> gravity_vector (const Point &position) const override;
+
+ /**
+ * Declare the parameters this class takes through input files.
+ */
+ static
+ void
+ declare_parameters (ParameterHandler &prm);
+
+ /**
+ * Read the parameters this class declares from the parameter file.
+ */
+ void
+ parse_parameters (ParameterHandler &prm) override;
+
+ private:
+ /**
+ * Mass of the perturbing body
+ */
+ double M_p;
+
+ /**
+ * Semimajor axis of the orbit that causes the tidal perturbation
+ */
+ double a_s;
+
+ /**
+ * Period of the non-synchronous rotation in year or second
+ */
+ double P;
+ };
+ }
+}
+
+#endif
diff --git a/source/gravity_model/radial_with_tidal_potential.cc b/source/gravity_model/radial_with_tidal_potential.cc
new file mode 100644
index 00000000000..0cc840acf3a
--- /dev/null
+++ b/source/gravity_model/radial_with_tidal_potential.cc
@@ -0,0 +1,150 @@
+/*
+ Copyright (C) 2011 - 2020 by the authors of the ASPECT code.
+
+ This file is part of ASPECT.
+
+ ASPECT is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2, or (at your option)
+ any later version.
+
+ ASPECT is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with ASPECT; see the file LICENSE. If not see
+ .
+*/
+
+
+#include
+#include
+#include
+
+#include
+
+#include
+
+namespace aspect
+{
+ namespace GravityModel
+ {
+ template
+ Tensor<1,dim>
+ RadialWithTidalPotential::gravity_vector (const Point &/*p*/) const
+ {
+ // This plugin is not implemented for 2D models
+ AssertThrow(false, ExcNotImplemented());
+ return Tensor<1,dim>();
+ }
+
+ template <>
+ Tensor<1,3>
+ RadialWithTidalPotential<3>::gravity_vector (const Point<3> &p) const
+ {
+ const unsigned int dim = 3;
+ /**
+ * Notation of this potential equation is converted from spherical coordinates to cartesian coordinates.
+ * Therefore, gradient of potential is (3 G M_p) / (2 a_s^3) * ( 1 / 6 * ( x^2 + y^2 - 2 * z^2) + 1 / 2 * (C1*(x^2 + y^2) - 2 * C2 * x * y)))
+ * where C1 = cos(2*b*t) and C2 = sin(2*b*t)
+ * b = 2 * pi / P
+ */
+ const double t = (this->simulator_is_past_initialization()) ? this->get_time() : 0.0;
+
+ const double angular_frequency = 2. * dealii::numbers::PI / P;
+ const double C1 = std::cos( 2. * angular_frequency * t);
+ const double C2 = std::sin( 2. * angular_frequency * t);
+
+ const Tensor<1,dim> dTstar_gradient ({1./3. * p[0], 1./3. * p[1], -2./3. * p[2]});
+
+ const Tensor<1,dim> dT0_gradient ({C1 *p[0] - C2 *p[1], -C1 *p[1] - C2 *p[0], 0});
+
+ const double G = aspect::constants::big_g;
+ const double T_factor = 3. * G * M_p / ( 2. * a_s * a_s * a_s );
+
+ const Tensor<1,dim> tidal_gravity = T_factor *
+ (dTstar_gradient + dT0_gradient);
+
+ RadialConstant radialconstant;
+ return radialconstant.gravity_vector(p) + tidal_gravity;
+ }
+
+
+ template
+ void
+ RadialWithTidalPotential::declare_parameters (ParameterHandler &prm)
+ {
+ RadialLinear::declare_parameters(prm);
+ prm.enter_subsection("Gravity model");
+ {
+ prm.enter_subsection("Radial with tidal potential");
+ {
+ prm.declare_entry ("Mass of perturbing body", "1.898e27",
+ Patterns::Double (),
+ "Mass of body that perturbs gravity of modeled body. "
+ "The default value is chosen for modeling Europa, therefore, it is the mass of Jupiter. "
+ "Units is $kg$.");
+ prm.declare_entry ("Semimajor axis of orbit", "670900000",
+ Patterns::Double (),
+ "The length of the semimajor axis of the orbit that cause the tidal perturbation. "
+ "For example, tidal perturbation on Europa happens by Europa orbiting Jupiter, "
+ "and that on Earth, if Moon is in consideration, happens by Moon orbiting Earth. "
+ "The default value is for the semimajor axis of Europa's orbit. "
+ "Units is $m$.");
+ prm.declare_entry ("Period of nonsynchronous rotation", "10000",
+ Patterns::Double (),
+ "Period of nonsynchronous rotation (NSR). "
+ "This works for the modeled body having decoupled rotation between interior layers. "
+ "The default value is the period of NSR on Europa's icy shell. "
+ "Units is $year$ when 'Use years instead of seconds' is true, "
+ "and $second$ when 'Use years instead of seconds' is false. ");
+ }
+ prm.leave_subsection ();
+ }
+ prm.leave_subsection ();
+ }
+
+
+ template
+ void
+ RadialWithTidalPotential::parse_parameters (ParameterHandler &prm)
+ {
+ AssertThrow (dim==3, ExcMessage ("The 'radial with tidal potential' gravity model "
+ "can only be used in 3D."));
+
+ prm.enter_subsection("Gravity model");
+ {
+ prm.enter_subsection("Radial with tidal potential");
+ {
+ M_p = prm.get_double ("Mass of perturbing body");
+ a_s = prm.get_double ("Semimajor axis of orbit");
+ const double time_scale = this->get_parameters().convert_to_years ? constants::year_in_seconds : 1.0;
+ P = prm.get_double ("Period of nonsynchronous rotation") * time_scale;
+ }
+ prm.leave_subsection ();
+ }
+ prm.leave_subsection ();
+ }
+ }
+}
+
+// explicit instantiations
+namespace aspect
+{
+ namespace GravityModel
+ {
+ ASPECT_REGISTER_GRAVITY_MODEL(RadialWithTidalPotential,
+ "radial with tidal potential",
+ "A gravity model that is the sum of the `radial constant' model "
+ "(which is radial, pointing inward if the gravity "
+ "is positive), "
+ "and a term that results from a tidal potential and that "
+ "leads to a gravity field that varies with latitude and longitude."
+ "The magnitude of gravity for the radial constant part is read from the "
+ "input file in a section `Gravity model/Radial constant'; the "
+ "parameters that describe the tidal potential contribution are read "
+ "from a section `Gravity model/Radial with tidal potential'.")
+ }
+}
diff --git a/tests/gravity_tidal_potential.prm b/tests/gravity_tidal_potential.prm
new file mode 100644
index 00000000000..0e3f47b936c
--- /dev/null
+++ b/tests/gravity_tidal_potential.prm
@@ -0,0 +1,99 @@
+# This parameter file tests the gravity model plugin for a case where the
+# tidal potential by flattening and non-synchronnous rotation changes gravity with position and time.
+#
+# The equation implemented in this heating model is from Tobie et al. (2025) (https://doi.org/10.1007/s11214-025-01136-y),
+# which is defined as:
+# g = - magnitude - gradient ( - tidal potential ).
+# potential = 3 G M_p R_s^2 / 2 a_s^3 r^2 (Tstar + T0)
+# Tstar = 1/6 *(1-3*cos(theta)^2) and T0=1/2sin(theta)^2*cos(2*lambda + 2*b*t),
+# where G: gravitational constant, M_p: mass of planet, R_s: radius of satellite, a_s: semimajor axis of satellite's orbit, b = angular rate of nonsynchronous rotation.
+# r, theta and lambda are radial distance, polar angle and azimuthal angle, respectively.
+#
+# Model shows the Europa's icy shell without conduction in simpler model.
+# Visualization 'gravity' shows gravity distribution.
+
+set Dimension = 3
+set Use years instead of seconds = true
+set End time = 1e4
+
+set Output directory = gravity_tidal_potential
+
+set Maximum first time step = 1e3
+set CFL number = 0.8
+set Maximum time step = 1e3
+
+
+set Pressure normalization = surface
+set Surface pressure = 0
+
+
+subsection Geometry model
+ set Model name = spherical shell
+ subsection Spherical shell
+ set Outer radius = 1560800
+ set Inner radius = 1460800
+ set Opening angle = 360
+ end
+end
+
+
+subsection Initial temperature model
+ set Model name = function
+ subsection Function
+ set Coordinate system = spherical
+ set Variable names = r, phi,theta
+ set Function expression = 100
+ end
+end
+
+
+subsection Boundary velocity model
+ set Zero velocity boundary indicators = top, bottom
+end
+
+
+subsection Gravity model
+ set Model name = radial with tidal potential
+ subsection Radial constant
+ set Magnitude = 1.3
+ end
+ subsection Radial with tidal potential
+ end
+end
+
+
+subsection Material model
+ set Model name = simpler
+ subsection Simpler model
+ set Reference density = 917
+ set Reference specific heat = 2110
+ set Reference temperature = 100
+ set Thermal conductivity = 0 #1.93
+ set Thermal expansion coefficient = 0 #1.6e-4
+ set Viscosity = 1e20
+ end
+end
+
+
+subsection Formulation
+ set Formulation = Boussinesq approximation
+end
+
+
+subsection Mesh refinement
+ set Initial global refinement = 0
+ set Initial adaptive refinement = 0
+ set Time steps between mesh refinement = 0
+end
+
+
+subsection Postprocess
+ set List of postprocessors = velocity statistics, temperature statistics, visualization, basic statistics, \
+ pressure statistics, material statistics
+
+ subsection Visualization
+ set Time between graphical output = 1e3
+ set Output format = vtu
+ set List of output variables = material properties, strain rate, shear stress, stress, nonadiabatic pressure, gravity
+ end
+end
diff --git a/tests/gravity_tidal_potential/screen-output b/tests/gravity_tidal_potential/screen-output
new file mode 100644
index 00000000000..cc8652dedb8
--- /dev/null
+++ b/tests/gravity_tidal_potential/screen-output
@@ -0,0 +1,129 @@
+
+Number of active cells: 96 (on 1 levels)
+Number of degrees of freedom: 4,030 (2,910+150+970)
+
+*** Timestep 0: t=0 years, dt=0 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 38+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.04e-05 m/year, 7.18e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00000
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00209 Pa, 1.045e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 1: t=1000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.53e-05 m/year, 8.53e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00001
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.018e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 2: t=2000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.24e-05 m/year, 8.31e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00002
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 8.955e+05 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 3: t=3000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 47+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.24e-05 m/year, 8.31e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00003
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 8.955e+05 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 4: t=4000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.53e-05 m/year, 8.53e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00004
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.018e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 5: t=5000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.04e-05 m/year, 7.18e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00005
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.045e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 6: t=6000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 29+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.53e-05 m/year, 8.53e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00006
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.018e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 7: t=7000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.24e-05 m/year, 8.31e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00007
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 8.955e+05 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 8: t=8000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.24e-05 m/year, 8.31e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00008
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 8.955e+05 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 9: t=9000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.53e-05 m/year, 8.53e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00009
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.018e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+*** Timestep 10: t=10000 years, dt=1000 years
+ Solving temperature system... 0 iterations.
+ Solving Stokes system (GMG)... 50+0 iterations.
+
+ Postprocessing:
+ RMS, max velocity: 2.04e-05 m/year, 7.18e-05 m/year
+ Temperature min/avg/max: 100 K, 100 K, 100 K
+ Writing graphical output: output-gravity_tidal_potential/solution/solution-00010
+ Pressure min/avg/max: -5.226e+05 Pa, 0.00225 Pa, 1.045e+06 Pa
+ Average density / Average viscosity / Total mass: 917 kg/m^3, 1e+20 Pa s, 2.631e+21 kg
+
+Termination requested by criterion: end time
+
+
+
diff --git a/tests/gravity_tidal_potential/statistics b/tests/gravity_tidal_potential/statistics
new file mode 100644
index 00000000000..1340acc34a5
--- /dev/null
+++ b/tests/gravity_tidal_potential/statistics
@@ -0,0 +1,33 @@
+# 1: Time step number
+# 2: Time (years)
+# 3: Time step size (years)
+# 4: Number of mesh cells
+# 5: Number of Stokes degrees of freedom
+# 6: Number of temperature degrees of freedom
+# 7: Iterations for temperature solver
+# 8: Iterations for Stokes solver
+# 9: Velocity iterations in Stokes preconditioner
+# 10: Schur complement iterations in Stokes preconditioner
+# 11: RMS velocity (m/year)
+# 12: Max. velocity (m/year)
+# 13: Minimal temperature (K)
+# 14: Average temperature (K)
+# 15: Maximal temperature (K)
+# 16: Visualization file name
+# 17: Minimal pressure (Pa)
+# 18: Average pressure (Pa)
+# 19: Maximal pressure (Pa)
+# 20: Average density (kg/m^3)
+# 21: Average viscosity (Pa s)
+# 22: Total mass (kg)
+ 0 0.000000000000e+00 0.000000000000e+00 96 3060 970 0 38 39 39 2.04002849e-05 7.18187163e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00000 -5.22625857e+05 2.09015736e-03 1.04524968e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 1 1.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.53157545e-05 8.53402100e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00001 -5.22625788e+05 2.24999227e-03 1.01845606e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 2 2.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.24054782e-05 8.30686057e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00002 -5.22625788e+05 2.24991582e-03 8.95531001e+05 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 3 3.000000000000e+03 1.000000000000e+03 96 3060 970 0 47 48 48 2.24054780e-05 8.30686165e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00003 -5.22625787e+05 2.24969716e-03 8.95530999e+05 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 4 4.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.53157551e-05 8.53401992e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00004 -5.22625788e+05 2.25002031e-03 1.01845608e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 5 5.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.04002862e-05 7.18187350e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00005 -5.22625787e+05 2.24982528e-03 1.04524980e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 6 6.000000000000e+03 1.000000000000e+03 96 3060 970 0 29 30 30 2.53157554e-05 8.53402043e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00006 -5.22625787e+05 2.25015373e-03 1.01845607e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 7 7.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.24054782e-05 8.30686059e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00007 -5.22625788e+05 2.25002696e-03 8.95531001e+05 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 8 8.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.24054786e-05 8.30686277e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00008 -5.22625788e+05 2.24991928e-03 8.95530999e+05 9.17000000e+02 1.00000000e+20 2.63118556e+21
+ 9 9.000000000000e+03 1.000000000000e+03 96 3060 970 0 50 51 51 2.53157551e-05 8.53401992e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00009 -5.22625788e+05 2.25004559e-03 1.01845608e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21
+10 1.000000000000e+04 1.000000000000e+03 96 3060 970 0 50 51 51 2.04002862e-05 7.18187350e-05 1.00000000e+02 9.99999535e+01 1.00000000e+02 output-gravity_tidal_potential/solution/solution-00010 -5.22625787e+05 2.25020422e-03 1.04524980e+06 9.17000000e+02 1.00000000e+20 2.63118556e+21