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For an object of mass the energy required to escape the Earth's gravitational field is GMm / r, a function of the object's mass (where r is radius of the Earth, nominally 6,371 kilometres (3,959 mi), G is the gravitational constant, and M is the mass of the Earth, M = 5.9736 × 10 24 kg).
Entering a Hohmann transfer orbit from Earth to Jupiter from low Earth orbit requires a delta-v of 6.3 km/s, [170] which is comparable to the 9.7 km/s delta-v needed to reach low Earth orbit. [171] Gravity assists through planetary flybys can be used to reduce the energy required to reach Jupiter.
^ Surface gravity derived from the mass m, the gravitational constant G and the radius r: Gm/r 2. ^ Escape velocity derived from the mass m, the gravitational constant G and the radius r: √ (2Gm)/r. ^ Orbital speed is calculated using the mean orbital radius and the orbital period, assuming a circular orbit. ^ Assuming a density of 2.0
where the product G M sun is the heliocentric gravitational parameter. The initial speed required to escape the Sun from its surface is 618 km/s (1,380,000 mph), [20] and drops down to 42.1 km/s (94,000 mph) at Earth's distance from the Sun (1 AU), and 4.21 km/s (9,400 mph) at a distance of 100 AU. [21] [22]
Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative ...
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.
As Jupiter is very massive, the side of Io nearest to Jupiter has a slightly larger gravitational pull than the opposite side. This difference in gravitational forces cause distortion of Io’s shape. Differently from the Earth’s only moon, Jupiter has two other large moons (Europa and Ganymede) that are in an orbital resonance with it.
Jupiter's gravity accelerated the approaching spacecraft to around 210,000 km/h (130,000 mph). [38] On July 5, 2016, between 03:18 and 03:53 UTC Earth-received time , an insertion burn lasting 2,102 seconds decelerated Juno by 542 m/s (1,780 ft/s) [ 39 ] and changed its trajectory from a hyperbolic flyby to an elliptical , polar orbit with a ...