Is Voyager leaving the Solar System?
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 3.2
Adapted from IOAA 2011 (Katowice), theory problem 3. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
On 9 March 2011 the Voyager probe was 116.406 au from the Sun and moving at 17.062 km/s. Is it on an elliptical, a parabolic or a hyperbolic orbit? What is the apparent magnitude of the Sun as seen from Voyager? Take the Sun's apparent magnitude from Earth as −26.74.
- The escape speed at 1 au is
- Voyager moves at 17.062 km/s, more than four times the escape speed, so by (3.6) its orbit is a hyperbola. Its energy is about
- By the inverse-square law and (4.2), the Sun seen from
- The Sun's apparent magnitude from Voyager is
AnswerVoyager is on a hyperbolic orbit and will leave the Solar System. The Sun shines on it at magnitude −16.41, still about 30 times as bright as the full Moon seems from Earth.
This problem also appears among the olympiad problems of Section 3.2, Energy and the vis-viva equation, which teaches the ideas it uses. Equation and figure numbers refer to the course.