Law: semimajor axis of a planet (#866)

* Move law of semiminor axis to radial motion folder

* Create law and test for semimajor axis

* Fix description

symplyphysics/laws/gravity/radial_motion/semimajor_axis_via_kepler_constant_and_total_energy.py

@@ -0,0 +1,77 @@
+r"""
+Semimajor axis via Kepler's constant and total energy
+=====================================================
+
+The semi-major axis of an orbiting planet depends on the Kepler's constant of
+the star---planet system and the total energy of the planet per unit of its mass.
+
+**Notes:**
+
+#. Works for both elliptical (:math:`\varepsilon < 0`) and hyperbolical
+   (:math:`\varepsilon > 0`) orbits.
+"""
+
+from sympy import Eq, pi
+from symplyphysics import (
+    units,
+    Quantity,
+    Symbol,
+    validate_input,
+    validate_output,
+)
+
+semimajor_axis = Symbol("semimajor_axis", units.length)
+"""
+The semi-major axis of the planet's orbit.
+
+Symbol:
+    a
+"""
+
+kepler_constant = Symbol("kepler_constant", units.length**3 / units.time**2)
+r"""
+The Kepler's constant, whose value is determined by the mass of the orbited star.
+
+Symbol:
+    K
+
+Latex:
+    :math:`\mathfrak{K}`
+"""
+
+total_energy_per_unit_mass = Symbol("total_energy_per_unit_mass", units.energy / units.mass)
+r"""
+The total energy of the planet per unit of its :attr:`~symplyphysics.symbols.basic.mass`.
+Can be negative or positive.
+
+Symbol:
+    epsilon
+
+Latex:
+    :math:`\varepsilon`
+"""
+
+law = Eq(semimajor_axis, 2 * pi**2 * kepler_constant / abs(total_energy_per_unit_mass))
+r"""
+a = 2 * pi^2 * K / abs(epsilon)
+
+Latex:
+    .. math::
+        a = \frac{2 \pi^2 \mathfrak{K}}{|\varepsilon|}
+"""
+
+
+@validate_input(
+    kepler_constant_=kepler_constant,
+    total_energy_per_unit_mass_=total_energy_per_unit_mass,
+)
+@validate_output(semimajor_axis)
+def calculate_semimajor_axis(
+    kepler_constant_: Quantity,
+    total_energy_per_unit_mass_: Quantity,
+) -> Quantity:
+    result = law.rhs.subs({
+        kepler_constant: kepler_constant_,
+        total_energy_per_unit_mass: total_energy_per_unit_mass_,
+    })
+    return Quantity(result)

test/gravity/radial_motion/semimajor_axis_via_kepler_constant_and_total_energy_test.py

@@ -0,0 +1,39 @@
+from collections import namedtuple
+from pytest import fixture, raises
+from symplyphysics import (
+    assert_equal,
+    errors,
+    units,
+    Quantity,
+)
+from symplyphysics.laws.gravity.radial_motion import semimajor_axis_via_kepler_constant_and_total_energy as law
+
+Args = namedtuple("Args", "k e")
+
+
+@fixture(name="test_args")
+def test_args_fixture() -> Args:
+    k = Quantity(7.5e-6 * units.astronomical_unit**3 / units.day**2)
+    e = Quantity(-4.4e8 * units.joule / units.kilogram)
+    return Args(k=k, e=e)
+
+
+def test_law(test_args: Args) -> None:
+    result = law.calculate_semimajor_axis(test_args.k, test_args.e)
+    assert_equal(result, 1.0 * units.astronomical_unit, tolerance=9e-3)
+
+
+def test_bad_kepler_constant(test_args: Args) -> None:
+    kb = Quantity(units.coulomb)
+    with raises(errors.UnitsError):
+        law.calculate_semimajor_axis(kb, test_args.e)
+    with raises(TypeError):
+        law.calculate_semimajor_axis(100, test_args.e)
+
+
+def test_bad_energy_per_mass(test_args: Args) -> None:
+    eb = Quantity(units.coulomb)
+    with raises(errors.UnitsError):
+        law.calculate_semimajor_axis(test_args.k, eb)
+    with raises(TypeError):
+        law.calculate_semimajor_axis(test_args.k, 100)

test/gravity/semiminor_axis_of_elliptical_orbit_via_orbit_parameters_test.py → test/gravity/radial_motion/semiminor_axis_of_elliptical_orbit_via_orbit_parameters_test.py

@@ -6,7 +6,7 @@
     units,
     Quantity,
 )
-from symplyphysics.laws.gravity import semiminor_axis_of_elliptical_orbit_via_orbit_parameters as law
+from symplyphysics.laws.gravity.radial_motion import semiminor_axis_of_elliptical_orbit_via_orbit_parameters as law
 
 Args = namedtuple("Args", "s a m")