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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 Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun.
Uranus V Uranus I Uranus II Uranus III Uranus IV Neptune I Pluto I Symbol SVI SVIII UV UI UII UIII UIV NI PI Discovery year 1655 1671 1948 1851 1851 1787 1787 1846 1978 Mean distance from primary km 1,221,870 3,560,820 129,390 190,900 266,000 436,300 583,519 354,759 17,536 Mean radius: km :E: 2,576 0.404 735.60 0.115 235.8 0.037 578.9 0.091 584.7
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 ...
This means that the acceleration vector ¨ of any planet obeying Kepler's first and second law satisfies the inverse square law ¨ = ^ where = is a constant, and ^ is the unit vector pointing from the Sun towards the planet, and is the distance between the planet and the Sun.
Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.
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.