A method in a receiver apparatus configured to receive positioning signals from Global Navigation Satellite System (GNSS) satellites , comprising: positioning the receiver apparatus at a time value by, for each of a plurality of GNSS satellites: using an algebraic solution of the Kepler differential equation of motion of the GNSS satellite in a gravitational field of the Earth to determine a position of the GNSS satellite at the time value, wherein the Kepler differential equation of motion is expressed using geometric algebra and the gravitational field accounts for the uneven, non-axially symmetric distribution of the attracting mass of the Earth and using positioning signals received at the receiver apparatus at the time value from the GNSS satellite, wherein the Kepler differential equation of motion of the GNSS satellite in a gravitational field of the Earth, expressed using geometric algebra, is 2 d 2 ds 2 U − EU = U r _ f _ where r is a vector distance of the satellite from an origin E is a constant, the Kepler Energy U is the second mapped variable and is a quaternion defined by r = U + σ 1 U σ 1 is a unit vector s is the first mapped variable and is defined by d ds = r d dt and f is a force that accounts for the uneven, non-axial symmetric distribution of the attracting mass of the Earth and is expressed using geometric algebra in terms of U. positioning the receiver apparatus at a time value by, for each of a plurality of GNSS satellites: using an algebraic solution of the Kepler differential equation of motion of the GNSS satellite in a gravitational field of the Earth to determine a position of the GNSS satellite at the time value, wherein the Kepler differential equation of motion is expressed using geometric algebra and the gravitational field accounts for the uneven, non-axially symmetric distribution of the attracting mass of the Earth and using positioning signals received at the receiver apparatus at the time value from the GNSS satellite, using an algebraic solution of the Kepler differential equation of motion of the GNSS satellite in a gravitational field of the Earth to determine a position of the GNSS satellite at the time value, wherein the Kepler differential equation of motion is expressed using geometric algebra and the gravitational field accounts for the uneven, non-axially symmetric distribution of the attracting mass of the Earth and using positioning signals received at the receiver apparatus at the time value from the GNSS satellite, wherein the Kepler differential equation of motion of the GNSS satellite in a gravitational field of the Earth, expressed using geometric algebra, is 2 d 2 ds 2 U − EU = U r _ f _ where r is a vector distance of the satellite from an origin E is a constant, the Kepler Energy U is the second mapped variable and is a quaternion defined by r = U + σ 1 U σ 1 is a unit vector s is the first mapped variable and is defined by d ds = r d dt and f is a force that accounts for the uneven, non-axial symmetric distribution of the attracting mass of the Earth and is expressed using geometric algebra in terms of U. r is a vector distance of the satellite from an origin E is a constant, the Kepler Energy U is the second mapped variable and is a quaternion defined by r = U + σ 1 U σ 1 is a unit vector s is the first mapped variable and is defined by d ds = r d dt and f is a force that accounts for the uneven, non-axial symmetric distribution of the attracting mass of the Earth and is expressed using geometric algebra in terms of U. <EOS>