## Finite burn launching from Moon problem

Spacecraft, Thruster, Tank, Propagator, CoordinateSystem, etc.

### Finite burn launching from Moon problem

We are having a problem modeling a module launching from the Moon to a Earth-Moon L2 halo orbit. We found trajectories with impulsive burns and finite burns if we do not decrement the mass. But it fails on the first iteration when we decrement the mass. We have tried a wide range of parameters including ones from work done in the past with another program. I computed that the fuel needed for this particular launch would be somewhat less than 1400kg, and we have given it significantly more. We must have an error in our script and would appreciate some hints on how to correct it. The working and the failing versions of the script are attached. The only difference between them is that the fuel is allowed to go negative and the mass is decremented in the failing scripts.
Thanks for any hints!
Attachments
Target finite burn mass fixed.script
This works
Target finite burn mass dec.script
This fails
joandunham

Posts: 6
Joined: Sat Apr 19, 2014 3:52 pm

### Re: Finite burn launching from Moon problem

Hi, sorry for the delay in getting back to you.

Here's an answer from our team:

From the script:
Code: Select all
`GMAT Thruster1.C1 = 16000; GMAT Thruster1.K1 = 311; `

m_dot = Thrust / Isp = 16000 / 311 = 51.44 kg / sec (constant mass flow rate with the scripted coefficients)

Then the targeter starts with a 600 secong burn:
Vary 'VaryBurnDuration' DC1(BurnDuration = 600, ...

so 51.44 * 600 = 30,864 kg lost. Initial total mass (spacecraft + tank) is 4503 Kg. GMAT's "AllowNegativeFuelMass" on the tank allows negative tank masses. The total mass of a vehicle is still required to be positive, and 4503 - 30,864 < 0.0 (by a lot!)

Joel J. K. Parker
Flight dynamics engineer, GMAT team
http://gmatcentral.org
jjkparker

Posts: 617
Joined: Thu Jan 07, 2010 9:48 pm
Location: NASA Goddard Space Flight Center, Greenbelt, MD

### Re: Finite burn launching from Moon problem

GMAT Thruster1.C1 = 16000;
GMAT Thruster1.K1 = 311;

m_dot = Thrust / Isp = 16000 / 311 = 51.44 kg / sec (constant mass flow rate with the scripted coefficients)

I'm not sure this is correct.
K1 has units of seconds, and C1 is in units of Newtons. So the equation above actually gives units of (kg*m/s^3), which would be weight flow (N/s).

I think the equation you are looking for is I_sp=(Force_thrust/m_dot)*(1/g_0). I think g_0 in this case would be 9.8m/s^2, because it is acting as a conversion factor. Then solving for m_dot you get:
m_dot=(Force_thrust/I_sp)*(1/g_0) which has units of (kg/sec)

In this case,
m_dot = 16000 / (311*9.8) = 5.25 kg/sec
If BurnDuration = 600sec
Fuel Used = M_dot * BurnDuration = 5.25 *600 = 3149.81 kg

Since the initial mass is 4503 (tank plus spacecraft), the final mass should still have a positive value of 1,353.19 kg. So I am also not sure why GMAT is saying there is a negative mass if this is the case. I didn't look at the script though. My comments are based on the last post.
AsteroidX

Posts: 8
Joined: Sat Feb 06, 2016 6:33 pm

### Re: Finite burn launching from Moon problem

AsteroidX, good catch. You're absolutely right, Thruster.C1 has units of N, not kg.
Joel J. K. Parker
Flight dynamics engineer, GMAT team
http://gmatcentral.org
jjkparker

Posts: 617
Joined: Thu Jan 07, 2010 9:48 pm
Location: NASA Goddard Space Flight Center, Greenbelt, MD

### Re: Finite burn launching from Moon problem

jjkparker wrote:AsteroidX, good catch. You're absolutely right, Thruster.C1 has units of N, not kg.

I do have a question about g_0 though... I'm not sure when GMAT uses local gravity or 9.8. I would assume that you could only use 9.8 if GMAT was also using 9.8 as the conversion factor for variables that incorporate a g_0 conversion factor.

I don't know what parameters GMAT uses, but example parameters that would be effected by this are Required Thrust, Gross-Sensitive Mass, and the mass ratio.

Do you know if GMAT is using 9.8 as the conversion factor?
AsteroidX

Posts: 8
Joined: Sat Feb 06, 2016 6:33 pm

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