Orbiter missions with no (or little) fuel usage for deceleration, Target planet capturing the spacecraft w/o extensive fuel usage |
Orbiter missions with no (or little) fuel usage for deceleration, Target planet capturing the spacecraft w/o extensive fuel usage |
Sep 1 2015, 05:18 AM
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Newbie Group: Members Posts: 11 Joined: 6-July 15 From: Russia, Saint Petersburg Member No.: 7559 |
I was involved in a casual conversation recently about the exploration of bodies in Solar System, in particular about fly-by approach vs. orbiter approach. In particular, I was saying that the main challenge with orbiter missions is that either you have to decelerate once you reach your target (requires tons of fuel on board), or you have to travel along the trajectory that would take an unreasonable amount of time to reach the target. As an example of the latter, I said that you could launch a spacecraft into a trajectory that would be a part of an elliptical orbit around the Sun with the perihelion around Earth and the aphelion around the destination. That way, when the spacecraft reaches its target, its speed relative to the planet will be slow enough for it to be "picked up" by the planet's gravity, and it will start orbiting the planet.
The other person in the conversation pointed out that it's been shown that when two bodies pass each other and influence each other gravitationally, it's not possible for them to start orbiting each other (or, in the case of one object being much more massive than the other (planet vs. spacecraft), simply "one orbiting another"). He said that either the more massive object will simply alter the trajectory of the passing smaller object, but not capture it, or the smaller object will crash into the bigger one. And this is something that, to me, "intuitively" shouldn't be right, but I don't have enough expertise to prove that it's wrong. My counter-arguments are: - Some of the natural satellites in the Solar System are believed to be captured by the planet as they were passing by (true, these are mainly hypotheses, but people wouldn't make such hypotheses if this wouldn't be possible?). - If the object is passing by the planet at the speed less than what is required to enter the orbit, then it will crash down onto the planet. If the object is passing at the speed greater than the escape velocity, then it will continue flying without being captured by the planet. Surely if the object's speed is between these two values, it has to start orbiting the planet? (Not necessarily in a perfect circular orbit of course). As further proof for the second point, I calculated the elliptical orbit with the perihelion at Earth (1 AU) and aphelion at Uranus (19.2 AU). Sure, it would take 16 years to get to Uranus, but the required takeoff speed would be 41.1 km/s (relative to Earth, that would be 11.3 km/s, so just barely above Earth's escape velocity, so we're good here), and the spacecraft's speed when it arrives to Uranus would be 2.1 km/s relative to Sun, and -4.6 km/s relative to Uranus. This 4.6 km/s speed happens to be the speed of a circular orbit at 266000 km from the center of Uranus. So, in my understanding, we can launch the spacecraft from Earth at 11.3 km/s into the elliptical orbit, and then some 16 years later it will pass by Uranus and be captured by it. If we make some small course corrections along the way so that it passes 266000 km from Uranus, it will even be a circular orbit. ... but, like I said, maybe I'm missing something that won't allow the spacecraft to be captured by the planet's gravity? My whole point was that in this scenario you don't have to use fuel for anything else other than takeoff. Of course, some course corrections would be inevitable, but at least you won't have to try to decelerate from New Horizons-like speeds. |
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Sep 1 2015, 01:43 PM
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Member Group: Members Posts: 128 Joined: 10-December 06 From: Atlanta Member No.: 1472 |
You cannot have capture in a pure two-body problem. This is simply a result of the conservation of energy. Using the usual conventions, the total energy (i.e. the sum of kinetic and potential energy) in a bound state is negative, but for two bodies that start from infinity with non-zero velocities, the total energy is positive.
In your example, the relative velocity between the s/c and Uranus is calculated assuming no gravitational pull on the s/c by Uranus. In fact, as s/c gets closer to Uranus, its velocity increases such that in the closest approach, it is above the orbital velocity a that distance. Now, the situation is different in a three-body problem. Here, one body can be ejected and carries away the extra kinetic energy and allows the two other bodies to bind. |
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