Question about orbital mechanics.

[bdewoody]

OK, I understand that a space probe such as the Voyagers uses a planetary gravitational tug as it passes by a planet to change direction and gain velocity. My question is why doesn't the probe lose the additionl speed it gained on the way in on the way out? Doesn't the pull of say Jupiter slow a probe down after it's closest approach as it departs the planet? Why isn't the loss of speed the same as the gain it achieved as it approached?

 

[a_lost_packet_]

Just a guess - Conservation of momentum?

 

[EarthlingX]

Wiki : Gravity assist

In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver or swing-by is the use of the relative movement and gravity of a planet or other celestial body to alter the path and speed of a spacecraft, typically in order to save propellant, time, and expense. Gravity assistance can be used to accelerate, decelerate and/or re-direct the path of a spacecraft.
The "assist" is provided by the motion (orbital angular momentum) of the gravitating body as it pulls on the spacecraft.[1] The technique was first proposed as a mid-course manoeuvre in 1961, and used by interplanetary probes from Mariner 10 onwards, including Voyagers' notable fly-bys of Jupiter and Saturn.

[youtube]http://www.youtube.com/watch?v=I3F88w3LkiI[/youtube]


demonstrations.wolfram.com : Gravitational Slingshot Effect (with downloadable version)

[youtube]http://www.youtube.com/watch?v=Bh7wGA_p-BQ[/youtube]
In astronautical mechanics, the gravitational slingshot maneuver, which NASA calls a "gravity assist", exploits the gravitational attraction of a planet to alter the speed and trajectory of an interplanetary spacecraft. A spacecraft can thereby be accelerated by a near planetary flyby to enable considerable savings of fuel in missions to the outer planets, such as Jupiter and Saturn. At first sight, this might seem like a cosmic something-for-nothing scam. But the physics depends straightforwardly on conservation of momentum and energy and the huge planet-to-spacecraft mass ratio, which leaves the planetary orbit essentially undisturbed.
This Demonstration considers a hypothetical slingshot maneuver around the planet Jupiter (orange sphere with radius ≈ 143,000 km), which moves at an average speed of 13.1 km/sec in its orbit around the Sun. A spacecraft, with initial speed , which has a negligible mass and size compared to the planet, follows a hyperbolic path in Jupiter's frame of reference. In the Sun's frame of reference, however, the hyperbolic path is tilted and moves with velocity , which provides a terrific boost to the spacecraft after it crosses the orbit of the planet. The graphic shown is highly schematic, with both space and time scales significantly distorted. Refer to the references for more accurate formulas when you plan your next space mission.

 

[James_Bull]

OK, I understand that a space probe such as the Voyagers uses a planetary gravitational tug as it passes by a planet to change direction and gain velocity. My question is why doesn't the probe lose the additionl speed it gained on the way in on the way out? Doesn't the pull of say Jupiter slow a probe down after it's closest approach as it departs the planet? Why isn't the loss of speed the same as the gain it achieved as it approached?

Because it has accelerated to a higher speed so is influenced much less by gravity (for a shorter time) as it departs. I think...

 

[SpeedFreek]

My question is why doesn't the probe lose the additionl speed it gained on the way in on the way out? Doesn't the pull of say Jupiter slow a probe down after it's closest approach as it departs the planet? Why isn't the loss of speed the same as the gain it achieved as it approached?

The planet loses the energy that is gained by the space-probe. James' answer above is as good as any at explaining why.

If you are in an elliptical orbit, you accelerate as you approach periapsis (the closest point in the orbit) and decelerate as you approach apoapsis (the furthest point in the orbit). The speed gained on approach is the same as the speed lost on departure. The same can be said from the view of the planet - the planet loses energy to you as you approach and gains that energy back as you recede, but the effect is immeasurably small.

But if you change your angle of attack so that the acceleration on approach exceeds the escape velocity of the body in question, you have changed your elliptical path into a parabolic path and you will escape the gravity of the body, taking some energy from that body in the process.

 

[MeteorWayne]

The explanation above is small print explains it well, including this:

"But the physics depends straightforwardly on conservation of momentum and energy and the huge planet-to-spacecraft mass ratio, which leaves the planetary orbit essentially undisturbed."