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Why not have a craft go back and forth between inner and outer planets building up speed? Even if it took a hundred years, the final velocity would make traveling to another star time cost effective.

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    $\begingroup$ "the final velocity would make traveling to another star time cost effective." Even if such 'ping-pong gravity assists' managed to produce a velocity of .01 C, it would still take over 4 centuries to reach the nearest star. $\endgroup$ – Andrew Thompson Jun 4 '15 at 5:22
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    $\begingroup$ You'd have a very hard time getting up to .01 C. At even 1/10th that speed, .001 C or 300 KM/S you'd be flying past most planets in our solar system at a comparatively straight hyperbolic curve and the added velocity corresponds to the bend in the hyperbola. Find a very high gravity object orbiting close to a star and you might be able to flirt with .01 C but nowhere close to that in our solar system. $\endgroup$ – userLTK Jun 4 '15 at 6:51
  • $\begingroup$ Thanks! Yeah--I'm trying to beat the 80,000 years that it would take Voyager, which is what I meant by 'time cost effective'. Spending an extra hundred years building up speed will pay off if it saves a few thousand years in travel time. $\endgroup$ – Charlie Jun 4 '15 at 8:45
  • $\begingroup$ @Charlie, the goal of both Voyagers and Cassini wasn't maximizing velocity but maximizing planetary encounters. Flying out of the solar system was kind of an added bonus with the Voyagers, not the primary goal. If the primary goal is to move a craft as fast as possible away from the solar system, certainly a ship could go faster using gravity assists, but gravity assists would still be very slow, maybe 20,000 years instead of 80. There's probobly better methods. A laser driven ship or magnetic drive that accelerates through Jupiter's magnetosphere or a larger nuclear engine. $\endgroup$ – userLTK Jun 5 '15 at 0:42
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This isn't a complete answer, but there's practical limits to this approach. The planets likely wouldn't cooperate. http://en.wikipedia.org/wiki/Gravity_assist

The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example the Voyager missions which started in the late 1970s were made possible by the "Grand Tour" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.

Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the more boost it gets, because gravity falls off with the square of distance from a planet's center. If a spacecraft gets too far into the atmosphere, the energy lost to drag can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish aerobraking. There have also been theoretical proposals to use aerodynamic lift as the spacecraft flies through the atmosphere. This maneuver, called an aerogravity assist, could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.

In addition to this, the faster the spacecraft goes, the less of a push it gets from the planet and I'm not even sure back and forth gravity assists are even possible (well, maybe in a binary star system with 2 sets of orbiting planets).

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  • $\begingroup$ I guess I don't understand why the spacecraft could not just go back to visit the inner planets for additional speed. $\endgroup$ – Charlie Jun 4 '15 at 5:03
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    $\begingroup$ @Charlie they often do this. NASA's Juno probe flew all the way back to Earth from a heliocentric orbit just to use it's gravity to gain additional speed using the Oberth effect. The Cassini probe did just what you're saying, slingshotting past Venus twice to get to Saturn. $\endgroup$ – Vedant Chandra Jun 4 '15 at 8:38
  • $\begingroup$ Thank you. What is the limit in terms of the number of gravitational assists? How fast can we go? $\endgroup$ – Charlie Jun 4 '15 at 8:47
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    $\begingroup$ @Charlie As Loren Pechtel pointed out, you are ultimately limited by the solar escape velocity. For our system, that's about 42.1 km/s or 0.00014 C. This isn't necessarily the absolute upper limit, but you are unlikely to be able to achieve velocities significantly higher than this using gravity slingshots. $\endgroup$ – a CVn Jun 4 '15 at 14:17
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    $\begingroup$ I'm pretty sure that's not accurate. The principal of a gravity assist is that it can be the initial velocity of the ship plus up to twice the planet's orbital velocity. (which is 1.414 times the escape velocity at the planet). That's in a perfect situation, which is rarely the case. You can also combine a string of planet's gravity assists if they are aligned right and add velocity more than once. Source: askthephysicist.com/classical%20mechanics.html and physics.stackexchange.com/questions/61960/… $\endgroup$ – userLTK Jun 4 '15 at 14:42
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In addition to userLTKs answer pointing out the lack of availability of planets there's another even bigger problem: Once you exceed solar escape velocity you're heading out no matter what. You can grab one last helping at the gravity assist buffet if anything is in your path but you can't turn back for more.

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    $\begingroup$ The math gets a bit complicated. But I think you can go faster than escape velocity from the sun and still whip around Jupiter and come back towards the inner solar system - say a 150, 160 degree pass around, go towards the inner solar system and speed up because the orbital velocity around Jupiter is quite a bit faster than the escape velocity from the sun at that point. The problem is you're still limited by how much speed you could pick up and how many passes you could do before escape is inevitable. I think, two Neutron Stars orbiting massive star or black hole - his plan might work. $\endgroup$ – userLTK Jun 4 '15 at 6:32
  • $\begingroup$ @userLTK I considered a turn around Jupiter but I don't think it works--I believe such a turn towards the sun will rob you of velocity, not help you. I do agree that if you have sufficiently massive objects available you can bounce all you want but I'm not sure you would want to--Mr. Oberth will make even chemical rockets pretty powerful if you light them off while skimming a neutron star. $\endgroup$ – Loren Pechtel Jun 4 '15 at 22:07
  • $\begingroup$ You could be right. Certainly my math is rusty with this kind of thing. I think the optimal gain is 0 degrees, basically in the direction of the planet's orbital velocity (Parallel to the planet's orbit), with that in mind, any vector addition to that, less than 90% (a full 90 degrees would be back towards the sun or directly away from the sun), but less than that, towards the inner planets some added velocity should be possible (I think). There would still be limits within our solar-system as to what could be practically added. $\endgroup$ – userLTK Jun 5 '15 at 0:27

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