Real life transfer window basics?

[TheTripleAce3]

I know that transfer windows are when it is most efficient to get to one location from another, but what are the rules of thumb irl?

[YNM]

Ain't an RoT AFAIK. Calculation is necessary, or get a lookup table.

[TheTripleAce3]

4 minutes ago, YNM said:

Ain't an RoT AFAIK. Calculation is necessary, or get a lookup table.

Thanks for the reply. I'll keep looking for some simple charts before really digging into it.

[YNM]

Generally, the way you calculate it is :

- Calculate the average of the two planet distance to Sun

- Calculate  half the period of an orbit with that radius

- Compare with synodic period between the two planet to get the phase angle. whoops that was half-arsed.

EDIT : Last step should be :

- Determine position of origin planet at arrival

- Using synodic movement, determine the position of destination planet half-transfer-orbit-period before.

- The angle between the planets is the phase angle.

Edited April 21, 2018 by YNM

[Bill Phil]

Result of a real quick google search:

https://www.jpl.nasa.gov/edu/teach/activity/lets-go-to-mars-calculating-launch-windows/

It's not perfect, and is simplified. But it does help explain what's going on to an extent. 

[VaPaL]

There`s also this site http://www.braeunig.us/space/interpl.htm very good source for a lot of things! Also, it's made by a forum member @OhioBob  

 

EDIT: this site is more indepth, but I found its explanation very good and it has exercises to help you understand better

(my English seems "broken" today, everything seems off and weird, hope I'm making sence and it's just me )

Edited April 21, 2018 by VaPaL

[TheTripleAce3]

Thank you @YNM, @Bill Phil and @VaPaL, I'll be looking at those tomorrow, assuming something else doesn't come up in my schedule.

I've been trying to figure out why transfer windows seem so random and undefined but it's making more sense now after briefly skimming the sources you gave me. I'm a noob at space irl, so this is one thing I'll probably have the ost trouble with for a while.

[YNM]

4 hours ago, TheTripleAce3 said:

I've been trying to figure out why transfer windows seem so random and undefined

Actually, their periodicity should be equal to the synodic period of the two planets. The configuration is also connected with the synodic period, but is indeed slightly more convulted than a simple relationship.

Not to mention non-Hohmann interplanetary transfers.

[TheTripleAce3]

6 hours ago, YNM said:

Not to mention non-Hohmann interplanetary transfers.

Non-Hohmann transfers aren't that bad to understand as they mostly are GA routes.

[YNM]

54 minutes ago, TheTripleAce3 said:

GA routes.

... what ?

Why I think it's a bit hard is because of their limitless (unlimited) possibility. You need to figure out the constraints (so usually dV), then numerically work out all the possible combination. Look up porkchop plots. If you will to work them by hand... dunno XD

[TheTripleAce3]

I thought most non hohmann routes were done using Gravity Assists to make it almost as efficient as a Hohmann transfer.

[Zeiss Ikon]

For the simple case -- a Hohmann transfer between planets in adjacent orbits (Earth to Mars, Earth to Venus, etc.), you can eyeball the window, at least to the precision needed for an initial burn.  You need a chart of the planetary orbits, printed to scale (with accurate eccentricity) and the planetary positions marked accurately for a reference date.  The Hohmann ellipse will have a period exactly halfway between the departure and destination orbits, so you move the target planet forward in its orbit by that number of days, place an ellipse to touch both orbits with the departure contact on the departure date, then move both planets and the Hohmann orbit forward and back in time so that the target orbit contact occurs on the arrival date.

I know this method works, because we used the chart in the Field Guide to the Stars and Planets, along with the supplied ephemerides (for planetary periods accurate to fractional seconds) to calculate windows from Earth to Mars when I took high school physics in 1974.  I used a slide rule for the class; calculators were too expensive.

Edited April 21, 2018 by Zeiss Ikon

[TheTripleAce3]

@Zeiss Ikon

So a Hohmann transfer from Earth to Pluto would have a period of 124.5 years since Earth has a 1 yr orbit and Pluto has a 248 yr orbit?

[YNM]

2 hours ago, Zeiss Ikon said:

... printed to scale (with accurate eccentricity)...

Hmm...

2 hours ago, Zeiss Ikon said:

so you move the target planet forward in its orbit by that number of days, place an ellipse to touch both orbits with the departure contact on the departure date, then move both planets and the Hohmann orbit forward and back in time so that the target orbit contact occurs on the arrival date.

Yeah, that's for phase angle.

2 hours ago, Zeiss Ikon said:

I used a slide rule for the class; calculators were too expensive.

I wonder what people long ago did in my branch without computers and numerical methods... XD The drawing aspects seems fun though ! (well until I did them with any accuracy - then that's quite a hill...)

Edited April 21, 2018 by YNM

[Bill Phil]

3 hours ago, TheTripleAce3 said:

@Zeiss Ikon

So a Hohmann transfer from Earth to Pluto would have a period of 124.5 years since Earth has a 1 yr orbit and Pluto has a 248 yr orbit?

The square of the orbital period is proportional to the cube of the semi-major axis.

Doing a basic calculation and making some assumptions the orbital period of the transfer orbit is 91 years. Of course, doing the actual math would be more accurate.

[Zeiss Ikon]

2 hours ago, YNM said:

Hmm...

I wonder what people long ago did in my branch without computers and numerical methods... XD The drawing aspects seems fun though ! (well until I did them with any accuracy - then that's quite a hill...)

Yeah, it works a lot better if both orbits are drawn on the same center.  You can actually see and measure the eccentricity of Mars's orbit relative to Earth's on a quarto-sized book page (though that may be more due to the arguments of periapsis differing by around 120 degrees than due to the magnitude of the eccentricity of either one).  The orbits look circular to the eye, but they look like they're off center.  Get a caliper or finely divided scale and you can measure the eccentricities in that size and the space between orbits is off-center.

It's worth remembering that numeric methods greatly predate what we'd think of as modern computers; the earliest n-body orbit work was done with slide rules, mechanical calculators (or even Napier's Bones), and MUCH iteration.  For something as "simple" as calculating a transfer window, you don't need multivariate differential equations; the early iterations would be done with a slide rule and refinement to acceptable accuracy with either an early computer or a mechanical or electronic calculator (mechanical calculators with enough accuracy -- 10 digits or so, and at least the four basic functions -- came along in the same time frame with typewriters, late 19th century).  These methods worked well enough that Herschel was able to predict the location of Neptune from the perturbations in the observed orbit of Uranus -- in the mid-19th century!

Drawing accurate ellipses (without computer software) requires a special tool called a "trammel".  A draftsman's version of this can draw about as accurately as a draftsman's compass (call it .1 mm with a good instrument and skilled user), and is adjustable for semi-major, semi-minor, and orientation of the semi-major axis (IOW, it can draw any ellipse bigger than its base and small enough for the arms to reach).

Don't forget, too, that no one cared about m/s level of accuracy for transfer orbits until it became possible to actually launch spacecraft that could perform the transfer -- and by then, electronic computers existed (though a mainframe that filled a couple rooms had about the computing power of a modern graphing calculator  -- still capable of doing the work, just took a long time to produce a high precision result).

[YNM]

15 minutes ago, Zeiss Ikon said:

It's worth remembering that numeric methods greatly predate what we'd think of as modern computers...

Well, given what my lecturers said they passed through, I could say they're more or less true XD

But then, I haven't seen much about using calculations when it comes to even older times ie. Brunel - I think at such times they had those going-round methods of calculating like the greeks did - straightedges and a compass...

[Zeiss Ikon]

13 hours ago, YNM said:

Well, given what my lecturers said they passed through, I could say they're more or less true XD

But then, I haven't seen much about using calculations when it comes to even older times ie. Brunel - I think at such times they had those going-round methods of calculating like the greeks did - straightedges and a compass...

Well, this is the old classic method of integrating a "nasty" expression -- draw a graph on paper of known "weight" (mass per area), cut it out carefully, and weigh the cutout on the most precise scale you can find.

Then again, there was a mechanical device for numeric integration: the goniometer.  I have no idea, mechanically, how it worked, but it had a base and an arm, and it would measure the area when you traversed the edge of an irregular figure with its pointer.  You could use it, for instance, to measure the work done by a steam engine during one cycle by integrating over the pressure/displacement diagram (which, in turn, was drawn by a mechanical plotting device -- I saw the plotting device operate on a steam engine in the engineering lab at U of Idaho, back in 1979-1980 time frame).  Today, of course, you've had a pressure transducer and a shaft encoder, and a computer would spit out the work per cycle in real time as you vary the cutoff, throttle, and load.

But there were ways, as far back as the 18th century, to get from, say, a series of observations that yielded nothing more than a 3-D bearing from a point on Earth's surface for a series of observation times/dates, to plotting the orbit of a newly discovered object (this was done for comets before the first asteroid was discovered and named; the method was worked out by Kepler, refined by Newton).