Flight Question What Is The Minimum Altitude The Chapman Probe Can Aerobrake At On Jupiter?

Nicholander

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I'm using the Chapman outer, and I'm trying to get it to orbit Jupiter, but it can't do that all on it's own with the 2 km/s of delta-v it already has, so it needs to aerobrake. The arrival velocity will be about 7.406 km/s, if you're wondering. So, what is the minimum altitude I can aerobrake at on Jupiter?
 

Castor

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Aerobraking with the Chapman is highly unrealistic and defeats the purpose of flying it all the way out there. The 2 km/s of delta-v is sufficient to insert it into a high elliptical orbit around Jupiter.

If you must aerobrake, a radius of 71000 km around Jupiter will be about the minimum that you can go.
 

asbjos

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I don't know if you're using [ame="http://orbithangar.com/searchid.php?ID=6379"]my modules[/ame] for the Chapman Probes, but if you do, the aerodynamic stress-limit I made uses the same model as Orbiter uses for particle streams: [math]0.5 \cdot AtmDensity \cdot {v}^3[/math]
My limit is set to [math]1 \cdot 10^7[/math]. If you try to aerobrake in Jupiter (or any other atmosphere), you can use density- and velocity readings the Surface MFD gives you to find out when you are in trouble.

Escape velocity at Jupiter's "surface" is approximately 60 000 m/s, so if you have a model of the density in Jupiter's atmosphere as a function of altitude (I don't have any), you can find the minimal altitude you can go to while aerobraking.
 

Nicholander

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Aerobraking with the Chapman is highly unrealistic and defeats the purpose of flying it all the way out there. The 2 km/s of delta-v is sufficient to insert it into a high elliptical orbit around Jupiter.

If you must aerobrake, a radius of 71000 km around Jupiter will be about the minimum that you can go.
I know that, but I want to enter an orbit with an apoapsis a little above Callisto's orbit. Also, how is it highly unrealistic?

EDIT: I am using the Chapman Modules.
 

Castor

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I know that, but I want to enter an orbit with an apoapsis a little above Callisto's orbit.

I'm not sure, but I think Callisto's orbit is high enough to do that kind of a burn. Some adjusting might have to be done to intercept plan to get the timing right.

Also, how is it highly unrealistic?

The Chapman probes are built bare-bones, with little or no heat dissipating systems to cope with kind of a situation. In my personal opinion, I don't like the idea of such a flimsy structure hurtling through an atmosphere, but it's your choice to make.
 

Nicholander

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I think I got it, though the aerobraking did not do as nearly as much as I anticipated it too, still, it saved a bit of fuel (And thus a bit for delta-v). Also, asbjos, what units should I enter when trying to do that equation? kPa and m/s? (I'm assuming the "v" means velocity) Also, would that 1 x 10^7 equal to 10 million? Just curious, because I'm trying to figure out how to aerobrake in the Martian atmosphere to get an orbit so I can intercept the Martian moons.
 

asbjos

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Also, asbjos, what units should I enter when trying to do that equation?
Using my limit of [math]10^7 > 0.5 \cdot Density \cdot v^3[/math] and setting the velocity to escape velocity at Jupiter (60 000 m/s), you get that the density limit is approximately [math]10^{-7} > D[/math].
I don't know what model Orbiter uses for the atmosphere, but [math]Density = D_0 \cdot e ^ {-h / c}[/math] is often used in very simple models, where [math]h[/math] is the altitude, [math]D_0[/math] is density at the "surface" and the constant [math]c[/math] is the [ame="http://en.wikipedia.org/wiki/Scale_height"]scale height[/ame] of Jupiter's atmosphere.
I used Orbiter's value of [math]D_0=1.329 kg/m^3[/math], and found the scale height here to be [math]c=27000 m[/math].
Solving for the altitude gives us the altitude to be approximately [math]h > 445 km[/math].


(I'm assuming the "v" means velocity)
Yes, [math]v[/math] is the velocity. To find the limits of the probe, we use maximal velocity at minimum altitude, in other words the velocity at the perigee.


Also, would that 1 x 10^7 equal to 10 million?
Yes, [math]10^7[/math] is a 1 with 7 zeros, or 10 million (10 000 000).


Just curious, because I'm trying to figure out how to aerobrake in the Martian atmosphere to get an orbit so I can intercept the Martian moons.
In general, assuming that assumptions for velocity, scale height, surface density and atmosphere model is correct for Orbiter, the equation for every planet is
[math]h > -c \cdot \ln \frac{2\cdot 10^7}{D_0 \cdot v^3}[/math]where [math]h[/math] is PeA (surface altitude at perigee, and therefore minimal altitude allowed by the Chapman Modules), [math]c[/math] is the scale height which you will have to find on the internet for your specific planet, [math]\ln[/math] is the [ame="http://en.wikipedia.org/wiki/Natural_logarithm"]natural logarithm[/ame], [math]D_0[/math] is the surface density which can be found in your planet's config file or found manually by placing yourself on the surface and reading the DNP reading in Surface MFD and [math]v[/math] is your velocity (for example the escape velocity at the surface, as an approximation).

If you don't know your velocity at the surface, you can break the equation down even further, and use this:
[math]h > -c \cdot \ln \frac{2\cdot 10^7}{D_0 \cdot \sqrt{\frac{2 \cdot G \cdot M}{R}}^3}[/math]where [math]G[/math] is the [ame="http://en.wikipedia.org/wiki/Gravitational_constant"]gravitational constant [/ame] always at [math]6.67 \cdot 10^{-11}[/math], [math]M[/math] is the mass of your target planet and [math]R[/math] is the radius of your target planet.


I made a spreadsheet for experimenting and calculating your own altitudes. You can also set the velocity to something other than the escape velocity, to make it more realistic. To calculate and set input for yourself, press "File"-->"Download as" and open the downloaded file to get editing privileges.
https://docs.google.com/spreadsheets/d/1SWxHw1WSz_sXHTtK-of3zIAcWXoj1RCAtYcpbzCkS30/edit?usp=sharing
 
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Nicholander

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Oh, THANK YOU! That spreadsheet really helps. :thankyou:

---------- Post added at 11:54 PM ---------- Previous post was at 11:50 PM ----------

Also, just a little question, is there a way to figure out how much velocity I will lose when doing an aerobrake/aerocapture?
 

Kyle

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Have you tried AerobrakeMFD? That'll also be super helpful if you want to aerobrake using a Chapman probe.
 

Nicholander

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Yes, I've tried it, but there's a few problems with it:

1. It only gives you info when you're 20 kps away from your periapsis.

2. You can't see that info before you start your mission, so anything important after that aerobrake may or may not happen just because you didn't know how much that aerobrake would slow you down. (IE: You don't have enough fuel to do a direct orbital insertion for a planet/moon, and you don't know how much that aerobrake will slow you down. You assume that it will slow you down enough, and when you get there, it doesn't slow you down as much as you need, so you can't do your orbital insertion.)
 
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