Help Needed with under pressure

[Axiom]

I'm stuck on under pressure, I seem to not have enough delta V to land on mercury properly as I usually crash at around 200m/s

I've tried hitting Mercury at its apoapsis so the transfer there is cheaper but I enter Mercury too fast and spend too much fuel trying to land and run out of fuel and crash

I've also tried hitting Mercury at it's periapsis, but that takes more fuel and I still crash at around 100m/s. I also need a powered flyby at venus so that isn't good

I've tried multiple Mercury assists but I think they are wasting fuel as unless you get it exactly right, you have to spend around 100m/s to encounter Mercury again

so what do I need to do?

 

[Axiom]

So turns out I just needed to chain 2 venus assists together (like Altaïr did) and it works like a charm

Starting position

Venus flyby 1:

Between the flyby's

Result of venus flyby 2: I needed this one to be a powered assist as it wasn't enough to reach mercury's periapsis on it's own

I used this to get a cheap encounter with mercury

Mercury flyby to get captured

Mercury orbit

Mercury landing

And the final landing (with 11% fuel left and all solar panels untouched)

Overall I think this went really well

 

[Orion]

Oh nice, I wasted fuel getting mercury encounters . At some point I'm going to be redoing all my submissions, as I did them when I was bad at the game.

 

[Axiom]

The problem I had with trying to do repeated mercury encounters was that it's really easy to miss mercury (like you could be 100km off the resonant orbit and not get the encounter) and when you do miss mercury you have to spend around 100m/s to get to mercury again (which is basically the savings from a mercury gravity assist due to it being so DAMN SMALL)

So is my submission ok?

 

[Altaïr]

The problem I had with trying to do repeated mercury encounters was that it's really easy to miss mercury (like you could be 100km off the resonant orbit and not get the encounter) and when you do miss mercury you have to spend around 100m/s to get to mercury again (which is basically the savings from a mercury gravity assist due to it being so DAMN SMALL)

Yeah, it's very painful. There's where the closest approach line really shines because it allows to plan encounters over several turns. This is basically the reason why I never could get rid of it, despite the fact that ANAIS is supposed to be a more evolved version of what was my original navigation mod.

The problem I had with trying to do repeated mercury encounters was that it's really easy to miss mercury (like you could be 100km off the resonant orbit and not get the encounter) and when you do miss mercury you have to spend around 100m/s to get to mercury again (which is basically the savings from a mercury gravity assist due to it being so DAMN SMALL)

So is my submission ok?

Check your badges

 

[Axiom]

Yeah, it's very painful. There's where the closest approach line really shines because it allows to plan encounters over several turns. This is basically the reason why I never could get rid of it, despite the fact that ANAIS is supposed to be a more evolved version of what was my original navigation mod.

Reason #584 why I really want mods on mobile (yes I know it's pretty much impossible)
I tried to be smart with resonant orbits, but the lack of a SMA readout made it very tedious and painful, and didn't quite work in the end as I was still a bit out

Check your badges

Thank you!

 

[Altaïr]

Reason #584 why I really want mods on mobile (yes I know it's pretty much impossible)

I'm offended that it only comes at such rank

 

[Axiom]

It's not in order

 

[Dahzito]

So turns out I just needed to chain 2 venus assists together (like Altaïr did) and it works like a charm

Starting position
View attachment 116749
Venus flyby 1:
View attachment 116750
Between the flyby's
View attachment 116751
Result of venus flyby 2: I needed this one to be a powered assist as it wasn't enough to reach mercury's periapsis on it's own

I used this to get a cheap encounter with mercury
View attachment 116753
Mercury flyby to get captured
View attachment 116754
Mercury orbit
View attachment 116755
Mercury landing
View attachment 116756 View attachment 116757
And the final landing (with 11% fuel left and all solar panels untouched)
View attachment 116758
Overall I think this went really well

Congrats on getting Team Hawk and I'm very impressed with this mission! (even that I already know that you're much better at these types of missions (I think))

 

[Axiom]

Congrats on getting Team Hawk and I'm very impressed with this mission! (even that I already know that you're much better at these types of missions (I think))

I honestly think I just got lucky here, like I was trying to land on mercury with only one venus assist (like most people did), and failed miserably (that's what this thread was for), so I looked at Altair's mission and tried the double venus assist thing and it worked! If I ever do a mercury return I'll definitely try doing the double venus assist route

I also helped encountering mercury at it's periapsis as you seem to enter mercury at a much slower speed (like when entering at apoapsis I was going like 2500m/s but with entering at the periapsis I was going at like 1500m/s)

Still don't get how people land on mercury with only one venus assist lol

Also Dahzito how would you know I'm good at these type of missions? I've barely been here for a month and a half

 

[Altaïr]

It's important to aim for the periapsis of Mercury yes, the ΔV cost will be much lower.
That's the calculation I made a while ago, for Mercury at periapsis, and Mercury at apoapsis (look directly at the result in the lower part):

There are around 500 m/s of difference in favor of Mercury at periapsis. In my calculation that's for a direct transfer, but it's not surprising that you find a similar difference between both possibilities.

The explanation relies in the Oberth effect: a burn performed while being close to a massive body will be more efficient. Mercury is lighter than Earth, so the Oberth effect is less efficient there, so it's a good idea to make sure that your insertion burn around Mercury is as cheap as possible.

 

[Axiom]

It's important to aim for the periapsis of Mercury yes, the ΔV cost will be much lower.
That's the calculation I made a while ago, for Mercury at periapsis, and Mercury at apoapsis (look directly at the result in the lower part):
View attachment 116792 View attachment 116793
There are around 500 m/s of difference in favor of Mercury at periapsis. In my calculation that's for a direct transfer, but it's not surprising that you find a similar difference between both possibilities.

The explanation relies in the Oberth effect: a burn performed while being close to a massive body will be more efficient. Mercury is lighter than Earth, so the Oberth effect is less efficient there, so it's a good idea to make sure that your insertion burn around Mercury is as cheap as possible.

Yeah, though one thing I noticed is that when doing my gravity assist off venus I didn't get a poweful enough kick to hit mecury's periapsis, is it possible to do it in one venus flyby?

 

[Altaïr]

Yeah, though one thing I noticed is that when doing my gravity assist off venus I didn't get a poweful enough kick to hit mecury's periapsis, is it possible to do it in one venus flyby?

Probably but it would cost more fuel.

 

[Astro826]

It's important to aim for the periapsis of Mercury yes, the ΔV cost will be much lower.
That's the calculation I made a while ago, for Mercury at periapsis, and Mercury at apoapsis (look directly at the result in the lower part):
View attachment 116792 View attachment 116793
There are around 500 m/s of difference in favor of Mercury at periapsis. In my calculation that's for a direct transfer, but it's not surprising that you find a similar difference between both possibilities.

The explanation relies in the Oberth effect: a burn performed while being close to a massive body will be more efficient. Mercury is lighter than Earth, so the Oberth effect is less efficient there, so it's a good idea to make sure that your insertion burn around Mercury is as cheap as possible.

Even if Mercury was as massive as Earth, it would likely be better to encounter it at periapsis. Given Mercury's elliptical orbit, it greatly decreases the flyby velocity when the fastest point(periapsis) of the rocket's orbit matches with the fastest point of Mercury's orbit, instead of meeting Mercury when it is moving slowest(apoapsis)

 

[Altaïr]

Even if Mercury was as massive as Earth, it would likely be better to encounter it at periapsis. Given Mercury's elliptical orbit, it greatly decreases the flyby velocity when the fastest point(periapsis) of the rocket's orbit matches with the fastest point of Mercury's orbit, instead of meeting Mercury when it is moving slowest(apoapsis)

It's not that simple, because in the mean time, the transfer from Earth is more expensive when you aim for Mercury at its periapsis.
I think you're right in the end, but I've made the calculation to check.

With Mercury at apoapsis:
ΔV(Earth) = 1016.3 m/s
ΔV(Mercury) = 1803.1 m/s

Total ΔV = 2819.4 m/s

With Mercury at periapsis:
ΔV(Earth) = 1408.1 m/s
ΔV(Mercury) = 1240.9 m/s

Total ΔV = 2649.0 m/s

Aiming for Mercury (where Mercury is replaced by Earth) at periapsis is still cheaper, but by 170.4 m/s. The difference is not as massive, but still significant though. I think it's due to the Oberth effect of the Sun itself, since it's a bit more effective when Mercury is closer to the Sun.

 

[Axiom]

I also noticed when going for the mercury at it's apoapsis you are going much faster, so I think aiming for the periapsis makes it so your orbital velocities are more similar

Edit: So I did the maths and here are the results:

Mercury at apohelion:
Mercury velocity: 8737m/s
Craft velocity: 11416m/s
Craft velocity relative to mercury (Craft velocity - Mercury Velocity): 2679m/s

Mercury at perihelion:
Mercury velocity: 13090m/s
Craft velocity: 14785m/s
Craft velocity relative to mercury: 1695m/s

So according to my calculations (which honestly have a pretty good chance to be wrong), you go at a slower speed relative to mercury when encountering at the perihelion compared to the apohelion.

I would expect similar effects for a transfer at venus level aswell

 

[Altaïr]

So according to my calculations (which honestly have a pretty good chance to be wrong)

I confirm they are wrong, sorry

The speeds you found are too high. For the craft velocity, I calculated them in the screenshots I posted here, this is what I called "Vp". Then, there is "ΔVp" that is the speed difference between Mercury and the craft.
However your observation is right: both speeds are higher at the aphelion, but their difference is closer.

 

[Axiom]

Are you calculating delta v (so taking into account oberth effect) or just the difference in velocity? because I did the latter

Edit: nevermind

 

[Altaïr]

Are you calculating delta v (so taking into account oberth effect) or just the difference in velocity? because I did the latter

Calculating the difference in velocity DOES take into account the Oberth effect. The Oberth effect is just the fact that increasing the speed of an object which already travels at high speed has an higher impact on its kinetic energy.

It's not specifically an astrodynamics effect by the way, it can be experimented in a constant gravity environment with simple physics. Here is an example:

Two objects are thrown upwards with the same velocity and from the same altitude, so they have the same energy. On this drawing, since object 2 is higher than object 1, it's slower in comparison. This is generally expressed with the law of conservation of mechanical energy: the sum of kinetic energy and the potential energy remains constant:
E = K + P = 1/2×m×v² + m×g×h = constant

As both objects have the same energy:
1/2×m×V1² + m×g×h1 = 1/2×m×V2² + m×g×h2

Object 1 has more speed but less altitude in comparison with object 2.

Now what if you increase instantly both objects's speed by 1 m/s. Now their energy is:
E1 = 1/2×m×(V1+1m/s)² + m×g×h1
E2 = 1/2×m×(V2+1m/s)² + m×g×h2

Both speeds increased by the same value, but since V1 > V2, it's easy to notice that V1² increased more than V2², so now the object 1 has more energy than object 2.

And that's it. Oberth effect is just that. On the solar system scale gravity is variable, so the formula for potential energy differs slightly, but the law of energy conservation still applies, and the same experience would give a similar result. When you calculate changes in velocities with the usual formulas you already take into account the Oberth effect, there's no additional treatment to apply.

 

[Axiom]

Oh so that's why the oberth effect exists! Thanks for the explanation

I confirm they are wrong, sorry

Anyways where did I go wrong with my orbit calculations?
So I have the mass of the sun in sfs to be 4.967*10^27 kg
And the Earth's apoapis and periapsis to be 7.48*10^9m (because Earth's orbit eccentricity is 0 according to the planet files i think)
And Mercury's apoapsis and periapsis to be 3.474*10^9m and 2.316*10^9 respectively
and I use the vis-viva equation which is this:

where v is the orbital velocity, G is the gravitational constant, M is the mass of the sun. r is the distance between the 2 bodies centre of mass (approximated as just being the distance to the sun as it is many orders of magnitude larger than everything else in this equation) and a is the semi-major axis of the orbit.

With mercury at apo:
r for both mercury and the craft would be 3.474*10^9m
a for mercury would be 2.895*10^9m and a for the craft would be 5.477*10^9m
and I get v for mercury to be 8737m/s and v for the craft to be 11416m/s

With mercury at peri:
r for both mercury and the craft would be 2.316*10^9m
a for mercury would (still) be 2.895*10^9m and a for the craft would be 4.898*10^9m
and I get v for mercury to be 13090m/s and v for the craft to be 14785m/s

So what did I do wrong? this is my first real attempt at orbital maths

Edit: if you're wondering how I got the suns mass to be what I have here is how I did it
F = GM1M2/r^2
where G is the gravitational constant, M1 is the mass of body 1 (in this case the sun) and M2 is the mass of body 2 and r is the radius of the sun. You can rearrange it to get this equation:

M1 = (F/M2)*r^2/G which can be simplified in our case to M1 = A*r^2/G where A is the acceleration at the bodies surface
And plugging in 274m/s^2 for A and 3.4785*10^7m for r I get 4.967*10^27kg

 

[Altaïr]

Oh so that's why the oberth effect exists! Thanks for the explanation

Anyways where did I go wrong with my orbit calculations?
So I have the mass of the sun in sfs to be 4.967*10^27 kg
And the Earth's apoapis and periapsis to be 7.48*10^9m (because Earth's orbit eccentricity is 0 according to the planet files i think)
And Mercury's apoapsis and periapsis to be 3.474*10^9m and 2.316*10^9 respectively
and I use the vis-viva equation which is this:
View attachment 116947
where v is the orbital velocity, G is the gravitational constant, M is the mass of the sun. r is the distance between the 2 bodies centre of mass (approximated as just being the distance to the sun as it is many orders of magnitude larger than everything else in this equation) and a is the semi-major axis of the orbit.

With mercury at apo:
r for both mercury and the craft would be 3.474*10^9m
a for mercury would be 2.895*10^9m and a for the craft would be 5.477*10^9m
and I get v for mercury to be 8737m/s and v for the craft to be 11416m/s

With mercury at peri:
r for both mercury and the craft would be 2.316*10^9m
a for mercury would (still) be 2.895*10^9m and a for the craft would be 4.898*10^9m
and I get v for mercury to be 13090m/s and v for the craft to be 14785m/s

So what did I do wrong? this is my first real attempt at orbital maths

Edit: if you're wondering how I got the suns mass to be what I have here is how I did it
F = GM1M2/r^2
where G is the gravitational constant, M1 is the mass of body 1 (in this case the sun) and M2 is the mass of body 2 and r is the radius of the sun. You can rearrange it to get this equation:

M1 = (F/M2)*r^2/G which can be simplified in our case to M1 = A*r^2/G where A is the acceleration at the bodies surface
And plugging in 274m/s^2 for A and 3.4785*10^7m for r I get 4.967*10^27kg

Let's see...

For the Sun mass the calculation seems correct, except that for the radius I have 34.817,000 kilometers for the radius. In practice however you don't calculate the mass but the product GM, since those 2 variables will always come together. This is called the gravitational parameter and is usually noted µ ("mu"): µ = GM.
With your notations, µ is equal to A*r^2 indeed.
For the Sun: µ = 2.99419.10^17 m^3/s²

Therefore, the vis-viva equation is simply written v² = µ*(2/r - 1/a)

I checked the orbital parameters of Earth, Mercury and your craft, they seem good too.

For Mercury at apohelion

I find V(Mercury) = 8303.7 m/s, and V(craft) = 10849.4 m/s, so the speed difference is 2545.7 m/s.

For Mercury at perihelion

I find V(Mercury) = 12455.5 m/s, and V(craft) = 14051.2 m/s, so the speed difference is 1595.7 m/s.

Your speed values are above mine. You slightly overestimated the mass of the Sun, but not by much, it would only explain a little difference. Are you sure you applied the vis-viva equation correctly?

 

[Axiom]

I think I probably screwed up a calculation somewhere, as doing it again gives your values

 

[Altaïr]

I think I probably screwed up a calculation somewhere, as doing it again gives your values

It happens... ... often
I've invited you to a discussion I made a while ago, I think you will like it