B Third Cosmic Velocity: Will Voyagers Leave Solar System?

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The Voyager probes are currently traveling at 38,000 mph, which is below the third cosmic velocity of 42 km/s needed to escape the Sun's gravity well at Earth's orbit distance. Voyager 2 is traveling even slower, raising questions about whether these probes will leave the solar system or remain in elongated orbits. The escape velocity varies based on their position in the gravity well, and at their current location, it is significantly lower than 42 km/s. A simulation demonstrates that many spacecraft, including the Voyagers, are on escape trajectories, despite their current velocities. Ultimately, the discussion highlights the complexities of gravitational dynamics affecting the Voyagers' future paths.
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The cosmic velocities are dependent on position in the gravity well. The 42 km/s is the escape velocity in the Sun's gravity well at the distance of Earth's orbit. It's much lower where the Voyagers are currently.

There's a nice graph of Voyager 2's velocity vs escape velocity on its Wikipedia page:
512px-Voyager_2_velocity_vs_distance_from_sun.svg.png

The spikes are flyby manoeuvres.
 

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