View Full Version : Slingshot Spaceflight

harkeppler

2010-May-06, 10:51 PM

As well known, flyby at any planet increase or decrease the velocity of an interplanetary probe. Voyager spaceprobes so got some extra velocity to leave the system.

But where is the maximum velocity which can be gotten if the flyby planet is a large object like a star and the flyby distance is very small?

01101001

2010-May-06, 11:39 PM

But where is the maximum velocity [...]

Velocity with respect to what?

neilzero

2010-May-07, 03:23 AM

Relative to what is rarely mentioned in popular astronomy articles, so I'm not sure about a maximum speed. A black hole without significant accretion disk should provide large speeds, assuming your craft is strong enough to not be torn apart by the tidal forces that occur on close approach to the event horizon. For simplicity, the speed (with respect to the black hole) might be 0.1 c several years after the sling shot maneuver around the black hole. It was faster shortly after the sling shot maneuver, but deceleration occurs as the craft climbs out of the gravity well of the black hole. Possibly the deceleration is 39,000 miles per hour for a one solar mass black hole, if there are any with that small a mass. I say possibly, as I suspect escape velocity from a gravitational body is at a specific starting point, which is likely different than the close approach distance. If 39,000 miles per hour is correct in this problem, then it is close to negligible compared to 0.1 c = 18,600 miles per second. Perhaps someone will clarify and reduce my confusion about escape velocity. In another thread, it was suggested that the maximum possible speed is the orbital speed of the speed boosting body, but I suspect that is wrong. If correct the black hole likely has an orbital speed about the same as our sun, if it is within a few light years of our Sun. Likely not that close now, but possible in a few centuries of converging with the black hole. Neil

Jens

2010-May-07, 03:35 AM

As well known, flyby at any planet increase or decrease the velocity of an interplanetary probe. Voyager spaceprobes so got some extra velocity to leave the system.

But where is the maximum velocity which can be gotten if the flyby planet is a large object like a star and the flyby distance is very small?

I don't know, but I think the main limiting factors are the size of the planet itself and the atmosphere. The closer you get to the center of mass, the more of a boost you will get, but obviously your craft will burn up in the atmosphere if it gets too close. So in fact there is a balance where at some point, the drag of the atmosphere beings to override the effect from the gravity assist. The Wikipedia article is pretty easy to understand, but I don't know the calculations. In any case, it will depend on the mass of the planet, its orbital speed, and how close you can get to it, I think.

grant hutchison

2010-May-07, 05:39 PM

Our slingshot spacecraft leaves the planet with the same speed it arrived with, in the planet's reference frame. So the speed we have to play with is just the relative speed of spacecraft and planet, when they are far apart. The very best we could achieve is to add that speed to the planet's orbital speed.

Our slingshot spacecraft is initially moving around the sun more slowly than the planet. The planet catches up with the spacecraft. The spacecraft falls into the planet's gravitational sphere of influence, describes a hyperbola around the planet (in the planet's frame of reference) and exits the planet's sphere of influence with the same relative speed but in a new direction. If the planet is massive, and the approach close, then this new direction is almost opposite to the direction of arrival. With increasing mass and reducing pericentre distance, we can get closer and closer to the ideal value. But the limit is always set by the relative velocities of spacecraft and planet.

As an example (taken from Roy's Orbital Motion), we can drop a spacecraft into a transfer orbit between Earth and Jupiter, so that it arrives travelling tangentially to Jupiter's orbit. Under these circumstances, Jupiter catches up to our spacecraft with a relative velocity of 1.19 AU/year. Jupiter's heliocentric velocity is 2.76 AU/yr. The best heliocentric slingshot velocity we could get from that encounter would be 2.76+1.19 = 3.95 AU/yr. In fact, we score a little less, because, even with a cloud-skimming closest approach, Jupiter rotates the spacecraft's orbital vector by only 160 degrees, so the vector sum is less than the ideal (and of course always will be, for all encounters).

Grant Hutchison

neilzero

2010-May-07, 08:02 PM

So the only advantages of a solar mass black hole is it orbits the mass center of our galaxy at higher speed than planets orbit their star, and we can likely get closer to the black holes center of mass than we could to a star of the same mass, if the accretion disk in minimal? Neil

grant hutchison

2010-May-07, 09:20 PM

So the only advantages of a solar mass black hole is it orbits the mass center of our galaxy at higher speed than planets orbit their star, and we can likely get closer to the black holes center of mass than we could to a star of the same mass, if the accretion disk in minimal? I refer you back to 01101001's question: "Velocity with respect to what?"

Your orbiting black hole may have a high orbital velocity around the galactic centre, but so, necessarily, do all the other stars in its vicinity. The relative velocity between stars is typically measured in tens of kilometres per second, which is the same order of magnitude as planetary velocities in our own solar system.

And if you've already achieved interstellar travel, it seems unlikely you'll need to fiddle around with slingshots to gain a few extra tens of kilometres per second.

Grant Hutchison

IsaacKuo

2010-May-07, 10:00 PM

Our slingshot spacecraft leaves the planet with the same speed it arrived with, in the planet's reference frame. So the speed we have to play with is just the relative speed of spacecraft and planet, when they are far apart. The very best we could achieve is to add that speed to the planet's orbital speed.

Of course, this is assuming an unpowered slingshot maneuver. If you have some sort of rocket thruster, you can do a powered slingshot and take advantage of the Oberth effect. With Jupiter, a mere 1km/s thrust at closest approach translates to a whopping 10km/s delta-v at infinity.

If you want to go really really fast, then the best way would be to first do a largely unpowered slingshot maneuver at Jupiter to go toward the Sun, and then do a powered slingshot around the Sun from as close to the Sun as you dare. If you can get close enough to the Sun for, say, a 200km/s escape velocity (max is 600km/s), then you could use a solar thermal rocket to boost yourself by 15km/s. That translates to a velocity of about 215km/s at closest approach, or 80km/s at infinity. If you can get close enough for a 400km/s escape velocity, then you Vinf would be 110km/s.

(The purpose of the Jupiter flyby is to alter your trajectory to go almost toward the Sun. It's the easiest way to do it--the alternative of trying to nullify your orbital speed with rockets and/or slingshots around other planets is just too hard.)

In fact, we score a little less, because, even with a cloud-skimming closest approach, Jupiter rotates the spacecraft's orbital vector by only 160 degrees, so the vector sum is less than the ideal (and of course always will be, for all encounters).

160 degrees is close enough. Compared to an "ideal" of 180 degrees, the loss is only 1.5%.

Hop_David

2010-May-07, 10:08 PM

As well known, flyby at any planet increase or decrease the velocity of an interplanetary probe. Voyager spaceprobes so got some extra velocity to leave the system.

But where is the maximum velocity which can be gotten if the flyby planet is a large object like a star and the flyby distance is very small?

With regard to the body you're slingshotting around, the incoming and outgoing arms of the hyperbola are the symmetrical. The speed at the outer reaches of either arm is the same.

There can be big direction changes, though. As the hyperbola's eccentricity approaches one, the direction change approaches an 180 degree turn around.

If you do a burn at the hyperbola's periapse, you can get a delta V change bigger than the burn. As seen from any frame of reference.

grant hutchison

2010-May-07, 10:34 PM

If you want to go really really fast, then the best way would be to first do a largely unpowered slingshot maneuver at Jupiter to go toward the Sun, and then do a powered slingshot around the Sun from as close to the Sun as you dare.Technically speaking, would that really be a "powered slingshot" around the Sun? We're not exploiting any prexisting heliocentric velocity asymmetry in that case. Seems like it would be more strictly accurate to call it just a "powered flyby".

Grant Hutchison

harkeppler

2010-May-07, 11:01 PM

Thanks to all!

I should more specific: the end velocity is normally thought to be seen in respect to a.) the sun of the system the probe is starting from, b.) the center of mass.

It does not matter, because that can be transformed.

I am looking fo a formula or a numerical aproach to get the velocity of a probe with respect to the flyby distance and the mass of the "planet" which is used. If the mass becomes larger, the velocity increase may reach some high values. The question is, if intersteller probes can be started out of a system with a normal star and a White Dwarf or Newtron Star for example by using flyby techniques.

How fast can a interstellar probe be?

There are some mathematical solutions, but here m(Planet, flyby) << m(sun) and I have a difficulty with the barycentric solution.

Any ideas?

IsaacKuo

2010-May-07, 11:15 PM

I am looking fo a formula or a numerical aproach to get the velocity of a probe with respect to the flyby distance and the mass of the "planet" which is used.

Roughly speaking, the velocity change that's possible is on the order of the "planet"'s escape velocity from closest approach. If you're doing an unpowered slingshot, then the velocity you can get is roughly the smaller of its escape velocity and twice its orbital velocity.

In the case of Jupiter, the limiting factor is its relatively low orbital velocity.

In the case of the inner planets, the limiting factor is the relatively low escape velocity.

You can think of an unpowered slingshot like hitting a baseball with a baseball bat. A big slow planet like Jupiter is like a really sturdy baseball bat that isn't moving very fast. A small fast planet like Earth is like a really flimsy baseball bat that's moving very fast.

The question is, if intersteller probes can be started out of a system with a normal star and a White Dwarf or Newtron Star for example by using flyby techniques.

How fast can a interstellar probe be?

Not very fast, unfortunately. Using a retrograde orbit, it's possible to get up to 3x the planet's orbital velocity. This is limited by the planet's escape velocity also. I have analyzed the nearest star systems, and the best that seems to be available is on the order of 100km/s. This is very very slow for interstellar travel, but it's a very good speed for exploiting a system's resources (using the "retrograde colony cluster" strategy, it's like getting oodles of free energy).

A seemingly promising possibility would be to do a powered slingshot around a neutron star or black hole. Unfortunately, this requires stupendous acceleration levels that would turn even an unmanned probe into mush. And the tidal forces are crazy also.

However, it may be possible to exploit a neutron star or black hole in some way which lets you cheaply create a relativistic plasma beam. If so, then that plasma beam could be used to accelerate a fast interstellar probe.

harkeppler

2010-May-07, 11:32 PM

Roughly speaking, the velocity change that's possible is on the order of the "planet"'s escape velocity from closest approach. If you're doing an unpowered slingshot, then the velocity you can get is roughly the smaller of its escape velocity and twice its orbital velocity.

In the case of Jupiter, the limiting factor is its relatively low orbital velocity.

In the case of the inner planets, the limiting factor is the relatively low escape velocity.

You can think of an unpowered slingshot like hitting a baseball with a baseball bat. A big slow planet like Jupiter is like a really sturdy baseball bat that isn't moving very fast. A small fast planet like Earth is like a really flimsy baseball bat that's moving very fast.

Not very fast, unfortunately. Using a retrograde orbit, it's possible to get up to 3x the planet's orbital velocity. This is limited by the planet's escape velocity also. I have analyzed the nearest star systems, and the best that seems to be available is on the order of 100km/s. This is very very slow for interstellar travel, but it's a very good speed for exploiting a system's resources (using the "retrograde colony cluster" strategy, it's like getting oodles of free energy).

A seemingly promising possibility would be to do a powered slingshot around a neutron star or black hole. Unfortunately, this requires stupendous acceleration levels that would turn even an unmanned probe into mush. And the tidal forces are crazy also.

That is interesting. Maybe a too-close flyby can be avoided.

I only thought if some people living in a binary system with a White Dwarf or so can so some interstellar spaceflight around 1.000 or 5.000 km/s.

It would be interesting if an alien civilization can send probes without a great investment in energy to the nearer star systems in, say, several hundred years.

If someone have a hint for useful literature I would thank You very much!

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