Mothership flyby rendezvous versus slowing to orbit

[Tyko]

I'm trying to wrap my head around flyby rendezvous - like the one portrayed in the Martian - where a small, light lander accelerates to rendezvous with a big heavy mothership on a flyby encounter. I'm going to lay out my thoughts so far, but would appreciate it if the more knowledgeable orbital mechanics people would help me out.

Three options (there are many variations in between, but these three seem to capture the spectrum of possibilities)

1. Option 1) Mothership doesn't slow down, Lander accelerates to meet it, achieves rendezvous, Mothership continues on its path
2. Option 2) Mothership decelerates into a highly eccentric orbit, Lander achieves rendezvous, Mothership accelerates, breaks orbit on its outbound path
3. Option 3) Mothership decelerates into a circular orbit, Lander achieves rendezvous, Mothership accelerates, breaks orbit on its outbound path

So, what are the tradeoffs? Here's where I need some help

• DeltaV Budget - no difference - It seems like all three options would involve the same or close to the same DV expenditure. Whether the Mothership burns to slow/accelerate or the Lander does all the acceleration, I'm thinking that the DV budget is the same.
• Fuel expenditure - is higher in 2 and MUCH higher in 3 because you're changing velocity on the much heavier Mothership.
• Risk Level - Option 1 is the riskiest, while option 3 is the least risky because with 1 you only have one shot. If you miss the rendezvous, you don't have a second chance until the Mothership swings by for another encounter potentially years later. With 2 or 3, the Mothership will be returning fairly quickly, so you'll have multiple chances to achieve rendezvous.

Thanks for responding!

Edited August 3, 2016 by tjt

[suicidejunkie]

DV budget varies notably in terms of which vehicle pays it.  In the first case, you have an amazing lander capable of returning a corpse to Earth.  In the last case, you have a much more reasonable lander which can make orbit.

It should also be noted that the mothership can afford a high efficiency, low TWR engine burn, while the lander needs a short, high TWR burn to get off the ground.

Not all of that DV budget is equal!

[SchweinAero]

With option 1, it's true that you don't have to accelerate the heavy mothership that much - but you also have to pack an extra escape's worth of Delta-V into a high-TWR vehicle carrying all your landing and research equipment.

I'm not sure how that balances out for your total mass. It might be worth the hassle on small non-atmospheric bodies but not others.

[Tyko]

14 minutes ago, suicidejunkie said:

DV budget varies notably in terms of which vehicle pays it.  In the first case, you have an amazing lander capable of returning a corpse to Earth.  In the last case, you have a much more reasonable lander which can make orbit.

It should also be noted that the mothership can afford a high efficiency, low TWR engine burn, while the lander needs a short, high TWR burn to get off the ground.

Not all of that DV budget is equal!

Thanks for the reply! Understood that different vehicles pay for it...the part I'm trying to work out is whether or not there's really a difference in the total DV paid or whether it's a matter of which vessel pays for it. That's why I separated the point about DV from the point about fuel expenditure. I'm trying to figure out conceptually what's going on.

Edited August 3, 2016 by tjt

[something]

Well, in order to rendez-vous your two vessels need to match velocities, hence v_Mothership = v_Lander.

For your lander to achieve orbit it needs to spend a certain amount of dv - let's call that dv_Orbit. Since it spends that amount of dv in every scenario, we can neglect it. I will also neglect effects such as aerobraking. So, assume the lander already was in orbit, having a certain velocity v_Orbit. At the same time your mothership has a certain velocity as well, let's call that v_Mothership.

Now either you accelerate your lander from v_Orbit to v_Mothership spending the difference as dv, or you let your mothership slow down to orbital velocity which let's you spend the same amount of dv. Obviously you can also let the lander accelerate a bit and let the mothership slow down a bit - the difference in velocity which needs to be covered always stays the same.

 

Since your mothership is much more massive than the lander, the required energy to change its velocity is much higher and consequently you need much more fuel to change the speed of the mothership. And that was the point in the film "The Martian": Since the "Hermes" didn't have enough fuel to both, slow down and get back to Earth, they needed the Ascend Vehicle to cover the required amount of dV, which let to Matt Damon's epic performance as "Iron Man"...ooops I think I just spoilered the entire film But I guess you already saw it ...

 

[Corona688]

It's almost surely more efficient to accelerate the smaller, lighter craft than the bigger, heavier one.  If the mothership was already in a wide, slow orbit, where little amounts of DV can make big changes in the orbit, there might be some benefit.  But you say 'flyby', meaning, already at escape velocity.

Option 3 is a waste compared to option 2.  Think it through:  It's a choice between a little craft breaking orbit once, vs a giant craft spending double that amount of dv -- enough to make orbit AND enough to leave.

There's a third question however -- distance.  The lander doesn't just have to be at the right velocity, it also has to be in the right place.  You can't just leap 1km sideways to meet it without serious acceleration then serious deceleration, and if the mothership's not in orbit, a miss will leave you behind.

For that, minute changes in the mothership's trajectory could definitely be helpful.  A little change in dv some hours/days/as long as possible in advance can make a huge difference in the lander being the right speed in the right place.

Edited August 3, 2016 by Corona688

[Tyko]

16 minutes ago, something said:

Now either you accelerate your lander from v_Orbit to v_Mothership spending the difference as dv, or you let your mothership slow down to orbital velocity which let's you spend the same amount of dv. Obviously you can also let the lander accelerate a bit and let the mothership slow down a bit - the difference in velocity which needs to be covered always stays the same.

Thanks, this totally makes sense

5 minutes ago, Corona688 said:

It's almost surely more efficient to accelerate the smaller, lighter craft than the bigger, heavier one.  If it was in a wide orbit, maybe, where little changes in DV can make or break an encounter, there might be some benefit, but you say 'flyby', meaning it's already at escape velocity.

Option 3 is a waste compared to option 2.  Think it through:  It's a choice between a little craft breaking orbit once, vs a giant craft spending double that amount of dv -- enough to orbit AND enough to leave.

I think the trade-off though is the "Risk" part. If the Lander doesn't have supplies to wait (possibly years) for another encounter with the Mothership on flyby, then having the Mothership drop into at least an eccentric orbit gives the Lander a possibility of a second encounter.

I've gotten competent at rendezvous between two craft in similar orbits. I can usually get an encounter within one orbital rotation. In the case of a flyby I don't have the luxury of similar orbits or a full rotation to play with. I have to nail it on one try.

[Corona688]

2 minutes ago, tjt said:

Thanks, this totally makes sense

I think the trade-off though is the "Risk" part. If the Lander doesn't have supplies to wait (possibly years) for another encounter with the Mothership on flyby, then having the Mothership drop into at least an eccentric orbit gives the Lander a possibility of a second encounter.

I've gotten competent at rendezvous between two craft in similar orbits. I can usually get an encounter within one orbital rotation. In the case of a flyby I don't have the luxury of similar orbits or a full rotation to play with. I have to nail it on one try.

If it's a life or death situation, screw efficiency.  Let the mothership take as much of the burden as it can.  That'd be option 1.5 -- a very close flyby.  If you miss, the mothership can meet you halfway.

Also, if there's atmosphere, the mothership could conceivably aerobrake, an option not open to the lander.

Edited August 3, 2016 by Corona688

[theJesuit]

A 'real world' example/ scenario in KSP is to capture an asteroid that is flying through Kerbin's SOI.  Large potatoe and small lander to rendezvous.  Once the lander is in orbit how much fuel does it need?

[Corona688]

What do you mean by 'capture'?  Just land, or actually brake it into Kerbin orbit?

[Kermanzooming]

33 minutes ago, theJesuit said:

A 'real world' example/ scenario in KSP is to capture an asteroid that is flying through Kerbin's SOI.  Large potatoe and small lander to rendezvous.  Once the lander is in orbit how much fuel does it need?

From my experience with a class B asteroid (approx 20 tons), not much; around 650 m/s for making it orbit Kerbin. And something like 5.2 Km/s to make it from a polar orbit to an equatorial orbit.

[jlcarneiro]

2 hours ago, something said:

[...]

Since your mothership is much more massive than the lander, the required energy to change its velocity is much higher and consequently you need much more fuel to change the speed of the mothership. And that was the point in the film "The Martian": Since the "Hermes" didn't have enough fuel to both, slow down and get back to Earth, they needed the Ascend Vehicle to cover the required amount of dV, which let to Matt Damon's epic performance as "Iron Man"...ooops I think I just spoilered the entire film But I guess you already saw it ...

Oh, bad @something! No cookie for you!

[Tyko]

Going one step further...short of running a lot of formulas, how would I set up a flyby rendezvous?

I'm thinking I could get the Lander in an orbit with it's PE exactly matching the PE of the Mothership. Then I'd just time warp until the Mothership is a bit further than one Lander orbital period away from the joint PE and adjust the Lander's final orbit so it's back at the PE at the same time the Mothership arrives.

It all seems pretty iffy though...

[Corona688]

You can create nodes several orbits ahead in the orbit planner, you know.  If you right-click on a node it collapses into two buttons, + or -.  Each time you click +, that puts it another orbit ahead into the future.  Keep clicking + until you see the intercept.  Now you can hover your mouse over those lines and know exactly where your mothership will be, when.

You can take this further.  Make two nodes -- one 20 minutes ahead, and another in its 'after' line.  Advance the second node X orbits ahead with the + button until you see the intercept again.  You can adjust the T-20m node, and see the results, X orbits later!  A tiny burn in 20 minutes can have huge effects 3 hours later.  It can put you very, very close for minimal delta-V.  Get it close enough and it should show you relative velocities, too.

Matching the position does not match the speed, of course.  Brute force is still necessary there.

Edited August 3, 2016 by Corona688

[polytechnique]

30 minutes ago, tjt said:

Going one step further...short of running a lot of formulas, how would I set up a flyby rendezvous?

I'm thinking I could get the Lander in an orbit with it's PE exactly matching the PE of the Mothership. Then I'd just time warp until the Mothership is a bit further than one Lander orbital period away from the joint PE and adjust the Lander's final orbit so it's back at the PE at the same time the Mothership arrives.

It all seems pretty iffy though...

Well, it'd require a good bit of time and patience (and a lot of practice~). More or less, similar to encountering an asteroid - launch into orbit, match inclination and then burn to get a close approach. The actual mission is more... complicated than that, but that's the basic outline.

[pandaman]

I can see the conversation at NASA now...

'Ok,  we need to rendezvous and dock with the mother ship as it flys by'

'But we'll only get one shot at that!'

'It's our only option, it HAS to work'

'Hmmmm...  I'll need some practice, ... I'll go and fire up KSP'

[cfds]

1 hour ago, pandaman said:

I can see the conversation at NASA now...

'Ok,  we need to rendezvous and dock with the mother ship as it flys by'

'But we'll only get one shot at that!'

'It's our only option, it HAS to work'

'Hmmmm...  I'll need some practice, ... I'll go and fire up KSP'

Nope, NASA is strictly an 'Orbiter' shop: http://xkcd.org/1244/

[Scarecrow]

If you simplify the scenario and assume that both vehicles are of equal mass and therefore use the same amount of fuel for any given change of speed, consider the following.

In scenario 1 the lander has to accelerate all the way up to the speed that the mothership is doing.

In scenarios 2 and 3 the lander only has to accelerate up to the speed the mothership is doing in orbit and the mothership itself then accelerates back up to it's original speed.  It would appear that the overall dV cost is the same as scenario 1.  However, this isn't allowing for the dV cost of slowing the mothership down to orbital velocity in the first place, which would be higher for scenario 3 than for 2.

[magnemoe]

All dV costs are not equal, 1 would require more fuel on the lander than 3, with 1 you could drop the mothership outside of life support and more living space.
However if you want to land on Tylo 3 is best as you don't need an so heavy lander, the mothership with the efficient LV-N engines and low TWR goes into low tylo orbit, the small lander land and return to it.
 

[KerikBalm]

Option #1: Landers carriers all the fuel needed to get to escape velocity down to the surface, and then back up again... a waste. Apollo style is much more efficient.

If this were unmanned, why have a mothership at all? it seems like a direct return with just a rendevous thrown in. The mothership in the case essentially becomes an aldrin cycler. - The stuff you need for long duration manned flight like food stores, water/waste recycling, habitation space, etc... that you can do away with for short durations... you don't need to take it with you at all times.

Option #2: Fairly similar, most caputre burns to highly eccentric orbits are quite small.... oberth and all that

Look at eve... thats only an 80 m/s capture burn... Jool is only 160 m/s

So for a small dV penalty, you gain a lot of flexibility on launch windows for the lander.

Option #3: What they did with the apollo program... but the command module was probably not a mothership in the sense your talking about

This is also inefficient because you take the mass of fuel you need to get from an eliptical to an escape trajectory down to a circular orbit, and then back up to an eliptical orbit... but thats not much because the difference between highly eliptical, and escape/retrun trajectory is quite small.

So it basically comes down to what you have on your mothership that adds mass that you can do away with on your lander, and how many parts you want to break your ship into/how many rendevous you are willing to do.

Let me propose option #4)

* Your "mothership" is an aldrin cycler... it basically only has to do course corrections, and ion drives are sufficient for that (so very high Isp)

* Your lander first captures into a highly eliptical orbit - it detaches a fuel/propellant tank that will be used later

* Your lander circularizes into low orbit - it detaches another fuel/propellant tank that will be used later

* Your lander lands (probably stages), and ascends again, it docks with the fuel tank left in low orbit which contains the fuel needed to reach a highly eliptical orbit (discarding the tank once the fuel is transfered... or discarding the tanks used during ascent and using that tank left in orbit)

* Your lander proceeds to a highly eliptical orbit, and docks with the fuel tank left in that highly eliptical orbit.

* Your lander then burns to meet up with the aldrin "cycler"

Because of the added complexity of the intercepts and dockings, and the low dV budget needed to go from highly eliptical to escape, its probably best to skip the step of leaving fuel in a highly eliptical orbit... you either leave your mothership there with the long term life support equipment, or you turn your mothership into an aldrin cycler.

Basically, combine Option #1 or Option #2 (they aren't so different), with a reduced "mothership" for option 3... ie "apollo style"

And if your going to do this a lot, you have long term life support on the ground that you don't move. Life support in low orbit that you don't move, and life support in an aldrin cycler orbit that you just barely move to do course corrections.

[magnemoe]

27 minutes ago, KerikBalm said:

Option #1: Landers carriers all the fuel needed to get to escape velocity down to the surface, and then back up again... a waste. Apollo style is much more efficient.

If this were unmanned, why have a mothership at all? it seems like a direct return with just a rendevous thrown in. The mothership in the case essentially becomes an aldrin cycler. - The stuff you need for long duration manned flight like food stores, water/waste recycling, habitation space, etc... that you can do away with for short durations... you don't need to take it with you at all times.

Option #2: Fairly similar, most caputre burns to highly eccentric orbits are quite small.... oberth and all that

 

Look at eve... thats only an 80 m/s capture burn... Jool is only 160 m/s

So for a small dV penalty, you gain a lot of flexibility on launch windows for the lander.

Option #3: What they did with the apollo program... but the command module was probably not a mothership in the sense your talking about

This is also inefficient because you take the mass of fuel you need to get from an eliptical to an escape trajectory down to a circular orbit, and then back up to an eliptical orbit... but thats not much because the difference between highly eliptical, and escape/retrun trajectory is quite small.

So it basically comes down to what you have on your mothership that adds mass that you can do away with on your lander, and how many parts you want to break your ship into/how many rendevous you are willing to do.

Let me propose option #4)

* Your "mothership" is an aldrin cycler... it basically only has to do course corrections, and ion drives are sufficient for that (so very high Isp)

* Your lander first captures into a highly eliptical orbit - it detaches a fuel/propellant tank that will be used later

* Your lander circularizes into low orbit - it detaches another fuel/propellant tank that will be used later

* Your lander lands (probably stages), and ascends again, it docks with the fuel tank left in low orbit which contains the fuel needed to reach a highly eliptical orbit (discarding the tank once the fuel is transfered... or discarding the tanks used during ascent and using that tank left in orbit)

* Your lander proceeds to a highly eliptical orbit, and docks with the fuel tank left in that highly eliptical orbit.

* Your lander then burns to meet up with the aldrin "cycler"

Because of the added complexity of the intercepts and dockings, and the low dV budget needed to go from highly eliptical to escape, its probably best to skip the step of leaving fuel in a highly eliptical orbit... you either leave your mothership there with the long term life support equipment, or you turn your mothership into an aldrin cycler.

Basically, combine Option #1 or Option #2 (they aren't so different), with a reduced "mothership" for option 3... ie "apollo style"

And if your going to do this a lot, you have long term life support on the ground that you don't move. Life support in low orbit that you don't move, and life support in an aldrin cycler orbit that you just barely move to do course corrections.

For an unmanned lander it might still make sense to have an return ship, typical on an Mars sample return, return module stays in orbit while lander lands, accent rocket docks and transfer samples to return module who is responsible for returning to earth and land. 
Who higher dV required to take of who better is option 3. 

Would anybody think of something except 3 for an Tylo or Eve mission? Yes you could do an 2 / 3 version where mothership stays in an eliptical orbit and you use spare fuel on lander to match orbit as well as possible with motherhsip minimizing the dV requirements for mothership.
Note that an more advanced version of this involves an extra stage with an fuel tank left in orbit or an tug from mothership. 

Cyclers are pretty unpractical in KSP but make plenty of sense in real world. 

[suicidejunkie]

On Wednesday, August 03, 2016 at 2:05 PM, tjt said:

Thanks for the reply! Understood that different vehicles pay for it...the part I'm trying to work out is whether or not there's really a difference in the total DV paid or whether it's a matter of which vessel pays for it. That's why I separated the point about DV from the point about fuel expenditure. I'm trying to figure out conceptually what's going on.

To put in other words what has been noted by quite a few people in the thread; DV loses its practical meaning when you spread across multiple ships.

Saying that one ship will take up more or less of the DV burden changes the summed amount of DV needed, and could increase or decrease any of the actually summable physical properties like fuel or mass or time required.

You can use it as a yes/no for whether an option is even possible given a specific design, or get an idea of how monstrous your lander will be, but those are all for one vehicle of the pair.

[Tyko]

56 minutes ago, suicidejunkie said:

To put in other words what has been noted by quite a few people in the thread; DV loses its practical meaning when you spread across multiple ships.

Saying that one ship will take up more or less of the DV burden changes the summed amount of DV needed, and could increase or decrease any of the actually summable physical properties like fuel or mass or time required.

You can use it as a yes/no for whether an option is even possible given a specific design, or get an idea of how monstrous your lander will be, but those are all for one vehicle of the pair.

I'm not sure that's true and that's what I'm trying to understand. I agree that fuel/time/mass change, but DeltaV shouldn't. I thought that you could have a multi-ship DV budget.

Here's an image to help explain the multi-ship DV as I'm picturing it (but could be totally wrong about). The Lander and Mothership can dock in two places - either A or B in the image below. Let's assume that it would take 2000m/s for the Lander to change orbit at B to meet the Mothership at A.

• Docking at A would require Lander to: burn 2000m/s at B. Mothership then continues on its path.
• To Dock at B Mothership would have to: burn at A to drop to the lower orbit, rendezvous at B and then burn again at A to return to her previous course.

Question: How much DV would it cost the Mothership at each burn to dock at B. (The Lander will undock after rendezvous, so won't contribute to the mass of the Mothership)

Thanks for helping me understand this!

Edited August 4, 2016 by tjt

[magnemoe]

9 minutes ago, tjt said:

I'm not sure that's true and that's what I'm trying to understand. I agree that fuel/time/mass change, but DeltaV shouldn't. I thought that you could have a multi-ship DV budget.

Here's an image to help explain the multi-ship DV as I'm picturing it (but could be totally wrong about). The Lander and Mothership can dock in two places - either A or B in the image below. Let's assume that it would take 2000m/s for the Lander to change orbit at B to meet the Mothership at A.

• Docking at A would require Lander to: burn 2000m/s at B. Mothership then continues on its path.
• To Dock at B Mothership would have to: burn at A to drop to the lower orbit, rendezvous at B and then burn again at A to return to her previous course.

Question: How much DV would it cost the Mothership at each burn to dock at B. (The Lander will undock after rendezvous, so won't contribute to the mass of the Mothership)

Thanks for helping me understand this!

Well as other say getting into an elliptical orbit around Duna, Eve or Jool is cheap. It should also make the return easier as you can adjust orbit and ejection too return to Kerbin nicely.
Note that on return you will drop the return pod, think Orion and probably pick up the replacement crew, resupplies and an new lander. 
This makes more sense in RL than in KSP, An cycler could easy give you artificial gravity, decent living space and radiation shielding it could also do space related science like ISS does while underway. 

In KSP an high profile interplanetary ships is an MK2 landing can or cupola bridge, 2-3 hitchhikers and an science lab, some large solar panels and batteries, as we don't have 3 bodies physic we would need more adjustment burns at flyby, 
This can easy be expensive as you have to fly all fuel up to the cycler. 
 

[AmpsterMan]

While the "total" delta-v budget may seem to be the same, the actual details of the missions differ. A mothership that spends all it's time in orbit can have much more efficient engines (LV-N) so it has a larger payload fraction than a liquid rocket engine. This means that for comparable masses, an LV-N rocket will have more delta-v than a conventional rocket, or for comparable total delta-v, it will have less mass.

Now consider that a circular orbit, equatorial orbit, eliminates four out of the six different parameters you need to match in order to dock with the vehicle... you only need two pieces of information to dock with a vehicle: it's velocity, and it's position along the orbit. Therefore it behooves one, if only for the sake of simplicity, to take your third option whenever possible. Just send more fuel up, or even cooler, have a little sub ship that attaches to asteroids, mines them, and then returns the fuel to you.