High School Third Cosmic Velocity: Will Voyagers Leave Solar System?

[fresh_42]

The voyager probes have currently a speed of $38,000\text{ mph }$ which is roughly $17\text{ km/s }$. Now the third cosmic velocity is $42 \text{ km/s }$ which is far more, and Voyager 2 is even slower.

So will they actually leave the solar system, or will they simply orbit in quite big ellipsis?

 

[Bandersnatch]

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:

The spikes are flyby manoeuvres.

 

[tony873004]

Here is a pannable simulation that will run in your browser. It shows all the hyperbolic spacecraft . If you let it run a while, you will see that everything is on an escape trajectory. Don't increase time step past 8192.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1511746688216_hyperbolic.html