Delta-V

Delta-V of a particular rocketry operation is the accumulated instantaneous change in speed wrt an inertial frame: it does not represent the actual change in speed, necessarily. For instance, an object in low earth orbit (LEO) is moving at around 7700 m/s, the object on the ground is moving at around 400 m/s, but to get to low earth orbit you need a delta-V of between 9000 and 10000 m/s, depending on the delivery system.

Per the Tsiolkovsky equation, for a specific impulse (roughly equivalent to given rocket exhaust speed) the wet to dry weight ratio (ie fueled to depleted) changes exponentially with delta-V. e.g. if you double the delta-V, you can basically expect to square the wet to dry ratio.

Considering only conventional chemical rockets for now: different propellents will have different specific impulses. Among the affordable ones, H2/O2 has the highest specific impulse at about 4500 m/s but H2 leaks like a sieve so you can only use it for launch or in the very early part of a mission. (Methane/O2 is not bad on 3000 m/s, kero is okay at 2900 m/s, and there are advantages to using liquid fuels.) For rocketry stages that will be fired after months or years, you are going to want something that has a highish boiling point, without tiny molecules that can leak through solid steel, won’t ice up so much, and that will ignite spontaneously when the oxidiser and reducer are mixed: unsymmetrical dimethylhydrazine and nitrogen tetroxide are a popular pair.

A fly-by will require less total mission delta-V than an orbital mission, because an orbital mission will require a major orbital insertion burn at the target (though this can lowered if aerobraking is used.) A landing mission to an airless orb will take even more delta-V, one to a airy place could be less if you can rely solely on aerobraking. There are a lot of permutations.

Bottom line: for a given size of parcel to deliver to a solar system target, if you can reduce the amount of propulsive delta-V required, you can reduce the required LEO-mass (and hence choose a cheaper launcher), or alternatively you can stick to the same launcher and deliver a better parcel to the target. This is why reducing the total mission delta-V is good.

Transfer orbits

Your basic minimum energy transfer from one planet to another is a Hohmann transfer. This is a reasonable option for inner solar system targets.

A Hohmann throw to Mars takes about eight months.
To Venus, about five months.
Mercury, about three months.
Jupiter, 33 months.

Often, though, you want to get there faster, and you can spend a bit more delta-V, which means either a bigger launcher or a smaller parcel. But what you can’t do is say that you are happy to take longer and reduce the delta-V, if you’re using a direct transfer.

Fortunately, it is possible to get some free delta-V using “gravity assists” or gravitational slingshot.

Mariner 10 (launched 1973) was the first mission ever to use a GA, based on the orbital mechanics plans of Bepi Colombo, the Italian mathematician. It made a single pass of Venus to give a kick down to the first of a series of Mercury flybys. MESSENGER, thirty years later, used a single Earth flyby and two Venus flybys, then three Mercury flybys in order to drop enough speed to eventually go into Mercury orbital insertion. So far, then, all missions to Mercury have been “via” Venus, and the 2017 ESA mission (named BepiColombo) will also involve multiple Earth-Venus-Mercury flybys.

Venus flybys have also been used to save delta-V in going to Jupiter. It adds years to the target arrival delay but the delta-V saving greatly improves the mass of equipment that can get to target for a given launch hardware.

Also, every single thing that has been sent beyond Jupiter has used a Jupiter flyby.

-Pioneer 10 (Jupiter)
-Pioneer 11 (Jupiter, Saturn)
-Voyager 1 (Jupiter, Saturn)
-Voyager 2 (Jupiter, Saturn, Uranus, Neptune)
-Ulysses (which used a Jupiter flyby to reach a high orbit out of the ecliptic in order to view the sun’s pole)
-Galileo (Venus, Earth, Earth, Jupiter)
-Cassini (Venus, Venus, Earth, Jupiter, Saturn) which is the only probe so far to use inner solar system GA AND a Jupiter GA to reach another target)
-New Horizon (Jupiter, Pluto)
-Juno (upcoming) (Earth, Jupiter)

Cassini’s route may seem unduly circuitous: it took fully seven years to reach Saturn. But for a single Titan IV launch they managed to send the most massive and complicated interplanetary probe (and lander!) ever commissioned by NASA. It arrived at Saturn with a mass of 5.6 tonnes (including 3.1 tonnes of propellent for the orbit insertion burns: its mass was 2.5 tonnes after orbital insertion) and 13 separate science and imaging instruments. It would not have been possible to deliver such a craft without the multiple gravitational assists.

If you’re patient, and you can get your craft to Venus, then you can get it to Jupiter: if you can get it Jupiter, then you can get it anywhere.

N2O4 freezes below -11 degrees. in space for long periods would mean it would be frozen unless you had a heat source handy before firing. hydrazine might suffer the same problems assuming it wasn’t insulated and heated I guess , though the yanks used it in the lunar lander so the tanks might have been heated or insulated well.

this equation regarding delta V not totally sure how you’d adapt it for drag though I guess there would be something out there that could tell me

Project Orion doesn’t care about your puny Delta-V and payload restrictions.

Project Wookiemeister is still running

wookiemeister said:

Project Wookiemeister is still running

from what?

Spiny Norman said:

Project Orion doesn’t care about your puny Delta-V and payload restrictions.

I imagine when we send crewed missions to the outer solar system we’d need to use something like Project Orion

Short of jumping on the back of one, is it possible for us to send a probe on a comet like trajectory around the solar system? Or can that orbit only be started from further out? How fast do comets go compared to our usual slingshot-around-planets method? The comet that has the orbiter and lander on it now, is that expected to make it back out with the man made objects intact or is it a crash and burn mission?

furious said:

Short of jumping on the back of one, is it possible for us to send a probe on a comet like trajectory around the solar system?

Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

The comet that has the orbiter and lander on it now, is that expected to make it back out with the man made objects intact or is it a crash and burn mission?

It is near perihelion now and will survive.

dv said:

furious said:

Short of jumping on the back of one, is it possible for us to send a probe on a comet like trajectory around the solar system?

Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

The comet that has the orbiter and lander on it now, is that expected to make it back out with the man made objects intact or is it a crash and burn mission?

It is near perihelion now and will survive.

I wonder what sort of mission time frame they would consider for probes, if feasible I wonder if they’d send a probe to the Oort Cloud even though it may mean many, many decades of travel time.

• Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

But is it possible without hitching a ride?

• It is near perihelion now and will survive.

How long/far is it expected to go and continue to communicate with home?

furious said:

• Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

But is it possible without hitching a ride?

• It is near perihelion now and will survive.

How long/far is it expected to go and continue to communicate with home?

If the solar panels and stuff work… the next time it gets some light?

Cymek said:

dv said:

furious said:

Short of jumping on the back of one, is it possible for us to send a probe on a comet like trajectory around the solar system?

Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

The comet that has the orbiter and lander on it now, is that expected to make it back out with the man made objects intact or is it a crash and burn mission?

It is near perihelion now and will survive.

I wonder what sort of mission time frame they would consider for probes, if feasible I wonder if they’d send a probe to the Oort Cloud even though it may mean many, many decades of travel time.

It should be possible for them to engineer a probe to last 50 years at least. Voyager 2 is still partly functional after 38 years of operation. Given that there has been considerable development since then, and they weren’t even trying to make Voyager 2 last that long, they should be able to do much better.

On the other hand, it will take more than 50 years to get to the Oort cloud using normal technology. There has been some talk of a massive solar sail project to the Oort cloud.

furious said:

But is it possible without hitching a ride?

Yes

How long/far is it expected to go and continue to communicate with home?

The current mission profile ends in September 2016. There may be an extended mission depending on how things go.

The other thing is that the Oort Cloud does not have a high object density. You aren’t going to bump into bodies by accident.

I now see that I probably missed part of furious’s meaning so I’ll put some more information in:

Comets have a great range of orbits.

Some, such as the 67P/Churyumov–Gerasimenko currently being tracked by Rosetta, never leave the inner solar system. 67P/C-G has a period of about 6 years.

Some, such as Halley’s comet, have a perihelion in the inner solar system, and an aphelion within Pluto’s orbit. Halley has a period of about 75 years.

Some have hyperbolic, parabolic or near-parabolic orbits, and hence have either no period or an extremely long period. From the context I suspect these were what you meant. These are witnessed by humans only once: if we wanted to follow one we would not have very long between discovery and launch.
Comet Arend–Roland is an example of a comet that ain’t never coming back to the inner solar system. Comet West is a very long period comet: it’s aphelion is around 1 light years from the sun, and it has a period of about half a million years.
So as far as that goes, we already have five objects on a trajectory that is like one of these comets: Pioneer 10 and 11, Voyager 1 and 2, and New Horizons are all on hyperbolic paths out of here (though the Pioneers are no longer working).

dv said:

The other thing is that the Oort Cloud does not have a high object density. You aren’t going to bump into bodies by accident.

Not particularly ‘cloud-like’ then is it? Why’d they not just call it the Outer Belt?

Postpocelipse said:

dv said:

The other thing is that the Oort Cloud does not have a high object density. You aren’t going to bump into bodies by accident.

Not particularly ‘cloud-like’ then is it? Why’d they not just call it the Outer Belt?

Well I don’t know. Maybe they oort to rename it.

DGMW, there might be ten trillion objects in the Oort cloud. There’s a lot of little things there which I suppose makes it cloudlike. But the volume of it is around a thousand trillion cubic AU. One rock per hundred cubic AU is somewhat rarified.

i think some people think it is like the movies with a “swarm” of asteroids.

JudgeMental said:

i think some people think it is like the movies with a “swarm” of asteroids.

I thought it was cloud-like with little angels sleeping in folds of cloud…..

furious said:

• Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

But is it possible without hitching a ride?

There’s not much benefit in hitching a ride on a comet.

To reach a comet you need to match its trajectory, that is, you need to have the comet’s velocity (speed & direction of motion) when you reach the comet’s location. But if you can do that, you’re travelling along the comet’s orbit anyway, since the orbit of a body around the Sun is almost totally determined by the body’s location and velocity.

One of the terms in the equation of orbital motion of a two body system is the sum of the masses of the two bodies, but when calculating solar orbits we can (mostly) get away with treating the orbiting body’s mass as negligible since it’s (generally) so much tinier than the Sun’s.

There is a slight benefit in hitching a ride. Your craft doesn’t need to match the comet’s velocity exactly. It can crash into the comet, thereby losing or gaining a bit of kinetic energy. Or it can interact with the comet gravitationally & exchange a little bit of KE that way. However, the mass of a comet is pretty tiny compared to a planet and so its gravitational field is quite weak. So the gravitational effect of the comet on your craft’s trajectory will be very small and unless you’re close to the comet and your velocity is almost identical to the comet’s the effect would be barely noticeable.

OTOH, if you land on a comet you may be able to use some of the comet’s matter as reaction mass &/or fuel when you leave.

PM 2Ring said:

OTOH, if you land on a comet you may be able to use some of the comet’s matter as reaction mass &/or fuel when you leave.

Now you’re talking. But we are not at that stage yet.

dv said:

Delta-V …

Considering only conventional chemical rockets for now: different propellents will have different specific impulses. Among the affordable ones, H2/O2 has the highest specific impulse at about 4500 m/s …

Your basic minimum energy transfer from one planet to another is a Hohmann transfer. This is a reasonable option for inner solar system targets. …

Also, every single thing that has been sent beyond Jupiter has used a Jupiter flyby. …

If you’re patient, and you can get your craft to Venus, then you can get it to Jupiter: if you can get it Jupiter, then you can get it anywhere.

An excellent summary.

There are nice plots of Delta V on the web. They’re well worth looking at, for example when flying between A and B, flying via a Lagrangian point is usually a bad strategy. The Delta V plots I’ve seen are only for the inner solar system.

Yes, H2/O2 has the highest specific impulse. Nuclear is better, but even that has limitations. No fusion powerplant could get the spacecraft up to even low relativistic speeds.

At least one old edition of the Handbook of Chemistry and Physics had tables of Hohmann transfer ellipses. I’d like to get myself a copy once I remember which edition it was.

I once calculated how fast it is possible to get out of the solar system using multiple gravitational slingshots off Jupiter, Saturn, Uranus and Neptune. The limiting value was how close the spacecraft could get to Jupiter without encountering atmospheric drag. It turned out to be the same order of magnitude as a single gravitational slingshot off Jupiter (within a factor of two), not enough to greatly reduce the travel time to a nearby star.

PM 2Ring said:

furious said:

• Well yes, an indeed there is a probe that is on an exactly comet like trajectory now, because it is in orbit around a comet.

But is it possible without hitching a ride?

There’s not much benefit in hitching a ride on a comet. To reach a comet you need to match its trajectory …

No. We can easily do a lot better than that. My strategy from the old days was to put the spacecraft in the path of the comet (same position but NOT same velocity) and fire a harpoon at the comet, as you would harpoon a whale from a rowboat. Use the elasticity of the cord attached to the harpoon to change the spacecraft’s velocity to match that of the comet. Include some energy damping mechanism (similar to in a fishing reel) to stop the craft’s oscillations. In other words, use the energy of the comet rather than the energy of the spacecraft to get you out of the solar system.

In these notes, I have mentioned chemical rocketry with specific impulse in the range from 2800 to 4500 m/s.

There have been flight tests of solar sails, and there are all kinds of suggested methods including solar thermal, nuclear thermal, antimatter etc.

Ion thrusters, however, have been used successfully in real missions. Ion thrusters have specific impulse 10 times those of chemical rocketry.

However, their thrust to dry mass ratio is low, so if you wanted to use them to leave earth orbit, you would need to use a series of perigee burns.

But once beyond earth orbit, ion thrusters can provide great opportunity for high delta-v missions.

So far, ion thrusters have been used in the Japanese sample return mission Hayabusa, the ESA lunar mission SMART1, and two NASA missions, Deep Space 1 and Dawn.

Dawn has involved a Martian flyby (actually the first mission to use Mars for gravity assist), transfer and orbital insertion at Vesta, then escape from Vesta and transfer to Ceres and orbital insertion at Ceres. Such a mission profile would be difficult to achieve with chemical rocketry: you would need a very large launch vehicle for a modest probe. The delta-V achieved by Dawn, following the Mars throw, is an amazing 11000 m/s.

It would be easy to foresee the use of ion thruster technology in multitarget outer solar system missions.