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Page 13 of the July 2018 issue states the solar system’s escape velocity is 1,381,308 mph. The Voyager satellites are not going that speed but appear headed out of the solar system. Should we expect them to return?

Mark Lampe 
St. Louis, Missouri


Voyagerpath
Launched in 1977, Voyager 1 (blue) has exited the solar system, with Voyager 2 (red) to follow. To leave the solar system, the Voyagers only needed to reach the escape velocity at the last planet from which a gravity assist was received: Saturn and Neptune, respectively.
Astronomy: Roen Kelly
Both Voyagers are on one-way tickets out of the solar system. But, as you note, neither is traveling anywhere near 1,381,308 mph (2,223,000 km/h). The apparent inconsistency arises because escape velocity depends on where you start your journey.

A handy formula for calculating escape velocity is ν esc = √2GM/R where v esc is the escape velocity, G is the gravitational constant, M is the mass of the object you’re leaving, and R is the distance from the center of that object. The diagram and Fast Fact in the July issue assumed you were escaping from the object’s surface, so R is simply the radius.

If you’re trying to leave the solar system from Earth’s orbit, however, R is about 93,000,000 miles (150,000,000 km; the distance of Earth from the Sun) and not 432,000 miles (695,500 km; the Sun’s radius, as used in the figure), so the escape velocity is only about 94,000 mph (151,300 km/h). Further, for an interplanetary spacecraft, its escape velocity from the solar system is the escape velocity at the last planet it received a gravity assist from. Take Voyager 1 as an example: It encountered Saturn in November 1980, when the ringed planet was about 890 million miles (1.4 billion km) from the Sun. The escape velocity was thus 30,400 mph (49,000 km/h), well below the probe’s exit velocity of 49,000 mph (79,000 km/h). Today, the distant spacecraft is still traveling at 38,000 mph (61,000 km/h) and leaving the solar system at nearly five times the escape velocity of 7,900 mph (12,700 km/h).

Richard Talcott  
Senior Editor  

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