"Hohmann-Like" and Chemical / Electric Thrust Comparison

Question

Part of the work I have to do for my degree is to perform a "Hohmann-like" transfer between Earth and Mercury, of which I believe I have accomplished. I have attempted numerous times to confirm that it is "Hohmann-like" with the Professor with no reply, which I find rather vague and my worst nightmare is to get to the Mission Summery presentation and find out it is not in fact "Hohmann-like".

A conformation would be a great relief.

Secondly, I done the transfer with both chemical thrusters and electrical. I expected that the Delta V of the electrical thruster would be significantly lower but apparently this was not the case. Shown below:

  Chemical Maneuver Summary
    -----------------
    Impulsive Burn:     TCM
    Spacecraft:         DefaultSC
    Origin:             Earth
    Axes:               VNB
    Delta V Vector:
       Element 1:   -15.391902348528 km/s
       Element 2:   -0.0012308398803 km/s
       Element 3:   -4.4865567022084 km/s
Mass depletion from MainTank:  
   Delta V:        16.032462395518 km/s
   Isp:            300.00000000000 s
   Mass change:   -4398.9744517915 kg




Electrical       Maneuver Summary
Impulsive Burn:     TCM
Spacecraft:         DefaultSC
Origin:             Earth
Axes:               VNB
Delta V Vector:
   Element 1:   -8.7407066088320 km/s
   Element 2:   -0.0007028275620 km/s
   Element 3:   -6.8141580876057 km/s

Mass depletion from ElectricTank1:  
   Delta V:        11.082991606896 km/s
   Isp:            4200.0000000000 s
   Mass change:   -815.09870601026 kg

[I have gotten rid of a propagation sequence that I realised did nothing. This explains the difference in the image and the data]

This leaves me under the impression that I have done something wrong. What am I missing?

Thank you.

Mission sequence:

It must be quite frustrating to have a professor give you a problem and then not give you feedback. Hopefully one of the orbital-mechanical folks here will be able to help out. When you said you've used electrical thruster what jumps out immediately is that your electrical Isp is only 300 seconds, the same as your chemical thruster and that's a big problem. They have 10 times higher Isp or more, so use 1/10th the mass or less, and they have 1/1000 the thrust or less of a chemical rocket. The durations of the burns last for months or years rather than seconds or minutes. — uhoh, Dec 24 '21 at 22:15
So a transfer based on realistic electric propulsion will likely visibly less Hohmann, it will take much longer and if the engine is really weak or the spacecraft really heavy it will look more like a slow spiral inwards. For example here's a calculated low thrust (electric) trajectory from Earth to Mars taking 2.36 years. — uhoh, Dec 24 '21 at 22:20
The DAWN spacecraft had powerful electric propulsion; if you look at the gravity assist from Mars to the arrival at Vesta it's a full 360+ degree circle, not an ellipse. From the departure from Vesta to arrival at Ceres is still much bigger than 180 degrees; it looks a little more Hohmann-like but clearly not a transfer ellipse. DAWN's engine burned for a total of 5.9 years, whereas for Hohmann you only have short burns at the beginning and end. https://en.wikipedia.org/wiki/File:Dawn_trajectory_as_of_September_2009-en.svg — uhoh, Dec 24 '21 at 22:29
I have since changed the ISP to 4200 seconds and the Thrust force to 0.125 N. Apparently it only takes 20 days longer. I'm extremely confused as to why this is. My suspicion is that it is to do with my vary commands as I have no burn command in my chemical transfer. Perhaps it will only work with a single finite burn for the electrical transfer? And yes, the Prof is notoriously difficult to contact, its a well know thing among students. — Andrew Blair, Dec 24 '21 at 22:34
The only thing I know is that it MUST be Hohmann-like. The specification of what Hohmann-like is to the professor is unknown but the are running under the assumption it just must be hyperbolic. — Andrew Blair, Dec 24 '21 at 22:36
Okay that's GREAT! Please update the numbers in your question as soon as possible so that others don't just duplicate my comments. We'll get you to Mercury non-Hohmann style straightaway. Thanks! btw how much time before your presentation? Hours? Days? — uhoh, Dec 24 '21 at 22:41
I made the changes and also added my mission sequence. The presentation is on the 25th of January, so plenty of time. — Andrew Blair, Dec 24 '21 at 22:52
Okay that looks great! If you make more progress or get close to an answer yourself, please feel free to post a "partial answer" to your own question, and not modify your question much further. This set of corrections is helpful, but ultimately we want the answers to be in answer posts. — uhoh, Dec 24 '21 at 22:55
OK, thank you for the information, I'm new to StackExchange and am unfamiliar with the platform. I assume I just press the "Answer Your Question" box for a partial answer? In regards to the question, in your opinion, what figures should I be looking out for to call it "done". I feel happy to call the chemical version OK, but we were never actually taught anything about electrical propulsion and I'm dubious to settle for "It went where I wanted it", feels like a luck more than understanding. — Andrew Blair, Dec 24 '21 at 23:07
Hmm... well let's wait for others with more academic experience in orbital mechanics to chime in, we have several! I'm just an amateur hack at this and just wanted to help with question improvement. Yes for a partial answer push the answer button, and I usually just start with "This is a partial answer based on progress I've made since posting the question, further answers are most welcome and encouraged." or something in your own words. — uhoh, Dec 24 '21 at 23:11
OK cool. I'll do that now and include everything from both simulations for extra clarity. — Andrew Blair, Dec 24 '21 at 23:13

Andrew Blair · Answer 1 · 2021-12-24T23:47:27.527

1

//Partial Answer as advised//

Chemical Thrust Transfer

This section is my answer to the first part of my task. I believe this is correct. My only worry is that is might not qualify as "Hohmann-like", mostly because it seems like a vague specification and I am not sure about the difference between Hohmann and Hohmann-like.

    Chemical Maneuver Summary
    -----------------
    Impulsive Burn:     TCM
    Spacecraft:         DefaultSC
    Origin:             Earth
    Axes:               VNB
    Delta V Vector:
       Element 1:   -15.391902348528 km/s
       Element 2:   -0.0012308398803 km/s
       Element 3:   -4.4865567022084 km/s
Mass depletion from MainTank:  
   Delta V:        16.032462395518 km/s
   Isp:            300.00000000000 s
   Mass change:   -4398.9744517915 kg

Electrical Thrust Transfer

This is what I have arrived at for the transfer under electrical thrust. I have set the ISP to 4200 seconds and the constant thrust to 0.125 Newtons with a solar power system that have the shadow bodies of Earth, Moon and Venus.

 Manoeuvre Summary
    -----------------
    Impulsive Burn:     TCM
    Spacecraft:         DefaultSC
    Origin:             Earth
    Axes:               VNB
    Delta V Vector:
       Element 1:   -8.7407066088320 km/s
       Element 2:   -0.0007028275620 km/s
       Element 3:   -6.8141580876057 km/s
Mass depletion from ElectricTank1:  
   Delta V:        11.082991606896 km/s
   Isp:            4200.0000000000 s
   Mass change:   -815.09870601026 kg

The further assistance needed:

Do the transfers qualify as Hohmann-like?
Are the figures of the electrical thrust transfer as expected?
Why does GMAT not have a gravity profile for Mercury? Will this pose a problem when I sort out the orbit?

edited Dec 24 '21 at 23:47

answered Dec 24 '21 at 23:40

Andrew Blair

111
3

Welcome to space! If you have additional questions, do not ask them in your answer. Answer posts are for answers. Either edit your question to include this new information, or ask a new question. – Organic Marble Dec 25 '21 at 01:34
1

My apologies, I was asked to post a partial answer. – Andrew Blair Dec 25 '21 at 21:57
1

The chemical transfer doesn't look like a Hohmann transfer, the departure and arrival should be on opposite sides of the Sun. – djr Dec 28 '21 at 22:36
You should also calculate how long it takes to consume 815 kg of propellant with a thrust of 0.125 N and an Isp of 4200 s. – djr Dec 29 '21 at 11:40
@AndrewBlair how's it going? Any progress? – uhoh Jan 03 '22 at 22:05
1

Why don't you just look on Wikipedia and on this site for Hohmann transfers to Mercury ? – Cornelis Jan 04 '22 at 15:00
GMAT does model Mercury's gravity, you just need to add it as a point mass to your propagator. Also, your chemical transfer is not Hohmann-like because Mercury arrival does not happen anywhere near the transfer orbit's periapse. Finally, the difference between Hohmann and Hohmann-like is essentially that the former has impulses AT the transfer orbit's apsides, whereas the latter has impulses NEAR the transfer orbit's apsides. – Ravi Mathur Mar 31 '22 at 20:13

"Hohmann-Like" and Chemical / Electric Thrust Comparison

Electrical Maneuver Summary

1 Answers1