The New Orbit of the Spacecraft after Jupiter Encounter

Larry Bogan

space velocity with respect to the Sun The final step in describing the path of the spacecraft is to determine its orbit after leaving the influence of Jupiter. The velocity of the spacecraft relative to Jupiter is the same as when it entered the sphere of influence but now is in a more forward direction by 53o. When this velocity is transformed to the Sun centered system, the velocity of Jupiter adds to the component of the spacecraft in the forward direction. As you can see in the diagram to the right, the velocity of the spacecraft has increase relative to the Sun to 16.17 km/s from the 9.36 km/s before its encounter with Jupiter . This corresponds to a three-fold increase in kinetic energy of the craft. The energy per mass of the orbit itself has changed from -126.7 to -39.8 (km/s)2. The fact that the energy of the orbit is still negative means the orbit is elliptical and the craft is still bound to the Sun. (A zero energy orbit is parabolic while a positive energy orbit is hyperbolic both which allow the craft to escape from the Sun's gravity)

The size, shape and orientation of the new orbit is determined using the same relationship for all elliptical orbits. The steps are as follows:

Plot of the Orbits of the Spacecraft

Since the spacecraft will cross the orbit of Saturn, if the timing were right, the craft could get a boost from Saturn to increase its energy even more and make it to Uranus, Neptune or possibly escape the Sun's gravity all together.

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by Larry Bogan - Feb 2000