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The moons of the trans-Neptunian objects (other than Charon) have not been included, because they appear to follow the normal situation for TNOs rather than the moons of Saturn and Uranus, and become solid at a larger size (900–1000 km diameter, rather than 400 km as for the moons of Saturn and Uranus).
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
The Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 consists of two probes, nicknamed "Tom" and "Jerry", in polar orbit around the Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth, and to track changes that occur over time ...
The acceleration of Solar System body number i is, according to Newton's laws: ¨ = ^ where is the mass of body j, is the distance between body i and body j, ^ is the unit vector from body i towards body j, and the vector summation is over all bodies in the Solar System, besides i itself.
t r is the elapsed time for an observer at radial coordinate r within the gravitational field; t is the elapsed time for an observer distant from the massive object (and therefore outside of the gravitational field); r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object);
As a rule of thumb, for a constant acceleration at 1 g (Earth gravity), the journey time, as measured on Earth, will be the distance in light years to the destination, plus 1 year. This rule of thumb will give answers that are slightly shorter than the exact calculated answer, but reasonably accurate.
To quantify the effects of the perturbations in this frame, one should consider the ratio of the perturbations to the main body gravity i.e. = | | | |. The perturbation g B − a A {\displaystyle g_{B}-a_{A}} is also known as the tidal forces due to body B {\displaystyle B} .
The surface gravity, g, of an astronomical object is the gravitational acceleration experienced at its surface at the equator, including the effects of rotation. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in order not to disturb the system, has negligible mass.