Moonwards

kim holder

17:23

@Hohmannfan alright, so if i want to put the acceleration of something tossed off the top of a tether like Hop designed, and put it in the baby spreadsheet i've been building, what formula do i need to use?

Hohmannfan

When you have released yourself from the top of the tether, you are in freefall, so the acceleration is 0.

kim holder

he has included the concept that there is an upper tether on each one, that extends outwards from the central body.

so that imparts an acceleration in the same way that extending the foot down allows less acceleration to reach it

Hohmannfan

So you mean the acceleration at the top of the tether when connected to it?

kim holder

yeah. my memories of learning this in physics in high school are completely gone.

if you can point me in the right direction i can look it up, but i don't really know what i'm looking for

and maybe i'm not aware of what i'm getting into. he seems to use it to calculate the apolune of things released from the upper end of a lunar tether, and how things would be tossed between the cislunar system.

Hohmannfan

No, he is not using the acceleration for that, that just requires the velocity.

kim holder

17:38

acceleration at the end is the square of the velocity at the balance point - the anchor?

Hohmannfan

No.

kim holder

the remainder when you subtract... something

Hohmannfan

Ah, m_Moon is the Moon's mass times the gravitational constant.

Basically, you just subtract the acceleration due to gravity

kim holder

so, mu

i don't understand the use of the word balance

$v_balance$

Hohmannfan

Balance where the tether is exactly in orbital velocity.

r = radius at the top of the tether.

kim holder

17:47

oooh

Hohmannfan

v = velocity at the end of the tether

That is only if r > r_balance. Otherwise, obviously A = r

kim holder

so i'm looking at the velocity at the end of the tether in excess of the velocity it would normally have orbiting at that altitude

Hohmannfan

Not exactly, v_balance is the orbital velocity at the tether's balance point

kim holder

okay - that's what i was trying to say at first - i was trying to say the formula in english and stopped when i wasn't sure if i was saying it right

so it was an incomplete sentence

this is interesting, i guess it is a simplified formula? my brain can't see how you can take the velocity at a different point and combine it with different radii and some gravity and get acceleration.

i'll try using the formula and see if i get it right :P

Hohmannfan

kim holder

17:56

oh - cool

Hohmannfan

For reference:

kim holder

oh right, the velocity is a ratio tied to radius...

Hohmannfan

Interesting point: If r_end is more than 1.26 times larger than r_balance, you are above escape velocity.

kim holder

and the acceleration at the end can be gotten from the rest because, like you said, it is the left over acceleration once you figure out how much of the acceleration of gravity has been removed at that altitude

@Hohmannfan oh - that is indeed very interesting

that works inside the hill sphere of the moon?

Hohmannfan

Why not?

kim holder

18:07

i dunno... it would be a different ratio for Earth?

Hohmannfan

No, it is the same ratio, regardless of location.

kim holder

huh. wow.

that i will really need to chew on to see why it would always be the same

Hohmannfan

kim holder

i need to star this somewhere so i can go back and check through it... maybe i'll create a bookmark

Hohmannfan

GeoGebra-GIMP-LaTeX is a powerful combination to create diagrams on the fly.

kim holder

18:18

geogebra is one of the things i really want to get to.... at some point i'll suddenly be able to start doing all that stuff

kim holder

19:20

docs.google.com/spreadsheets/d/…

@Hoh i seem to have formatted the formula for apoapsis wrong in field O6, but i can't see the mistake

Hohmannfan

Just wait a few minutes, then I can take a look at it

kim holder

sure. thanks for all the help :)

also i need to go buy veggies so i'm gone for 20 min

Hohmannfan

My deadline :)

kim holder

19:51

ok i'm back. i just didn't want you to think i'm not paying absolute attention. :]

Hohmannfan

I have not found the error yet.

kim holder

well, the number changed at least

Hohmannfan

I have not fixed THE error, just some other things.

kim holder

you seem to be optimizing...

Hohmannfan

It is entirely my error. Here is the corrected formula:

I started with v=sqrt(m*(2/r-1/(A+r))) instead of v=sqrt(m*(2/r-2/(A+r))) when I created the equation

But there is still something fishy in that spreadsheet

kim holder

20:02

oh look, copying and pasting that into the search bar got me the results i needed to find a good page on the physics

@Hohmannfan what's wrong?

Hohmannfan

Gahrrr!! I deleted the wrong part of the latex formula!

Now your spreadsheet works too

kim holder

:D

Hohmannfan

Negative apoapsis just means you are past escape velocity.

kim holder

oh, that's cool

i didn't compare the speed at the tip with the orbital velocity at the tip...

Hohmannfan

You have the edits I made to the spreadsheet, right?

kim holder

20:09

yeah, actually i think i'll work from now on on the google drive version

Hohmannfan

If so, anybody following that link can make whatever edits they want, you should protect it.

kim holder

if the past is any indication, the chances that someone would find it and do something bad to it are very low

maybe i'd rather download it occasionally to have a backup

Hohmannfan

You are a mod, so can you delete the images with the error in them?

kim holder

i am pretty keen to give anyone who stumbles on to this and knows something the chance to contribute

@Hohmannfan :) sure. we don't want to spread disinformation

i'm going to continue on with the timeline while you mess with that. better for me to look it over once you are done.

Hohmannfan

Spreadsheets are kind of fun, the time since last time I worked with one is too long.

Now it is good.

kim holder

20:23

yeah, i have to take a good look at it to follow what you've done... :)

i don't have an emoticon that expresses 'raised eyebrows'...

you have added some good formatting conventions

Hohmannfan

Time to update this one:

kim holder

:) i'm fond of that one

Hohmannfan

I was home last weekend. My brother got his first HTML lesson.

kim holder

:D the youngest?

or the middle one? there are three, right?

Hohmannfan

Yes, he is my youngest sibling.

three, counting me

kim holder

20:34

it is a great advantage to learn young in that way. my path was very different.

does he like the idea of coding? (since that is sort of a minimal introduction)

Hohmannfan

yes, he has played around with spreadsheet formulas for a while.

But he is still a little young. (Not too long to learn, that is not a thing).

HTML is forgiving to spelling errors, that is not the case with JS. So no JS before he is eight. Some general things about algorithms are perfect though.

kim holder

yeah, i can see that... are there exercises out there aimed at someone his age?

or do you find things he can make?

Hohmannfan

There is no need to hurry, I did not do my first spreadsheet calculations before I was 13, so there is hope ever for old people like me.

kim holder

20:49

man, i worry that my brain will get too creaky before i properly turn my attention to learning enough physics and math to properly do this project, so i hear you :)

and chemistry...

i am thinking about things to add to the spreadsheet down the road. for the sake of the timeline i wanted to have a sense of what the layout of the tethers should be.

it looks like if the upper tether around the moon reached to 8000 km above the surface, the speed it would toss something towards the Earth would be enough to support even human travel

Hohmannfan

Sure, a sling from a tether is no different from a regular hohmann transfer.

kim holder

Hop's system concentrates on servicing and delivering satellites.

from the moon end of that system, that tether could toss something to any of the tethers he has set up

i still don't picture trajectories well. i keep thinking you need a lot of extra velocity when you leave the moon in order to do it in a short enough period of time

instead of thinking about how fast you will be going when you reach the earth if you do it that way

Hohmannfan

21:05

I added a "velocity at infinity cell"

kim holder

oh - awesome :)

this really helps because i can think over time about the formulas, and the way it is all set up helps it sink in how it is all related.

and i like how this resource for this has shaped up: physicsclassroom.com/class/circles/Lesson-4/…

Hohmannfan

A v_inf of 1030 m/s is needed to do a Hohmann transfer towards the Earth.

kim holder

so this would be less than an ideal transfer

ah - there we go :)

Hohmannfan

You can do a faster transfer with a higher v_inf

Transfer times for non-Hohmann transfers are a pain to calculate though, so I am not going to write a cell for that.

kim holder

the 3 days it usually takes should be fine

Hohmannfan

21:13

It is probably going to be close to the ideal Hohmann transfer anyway, it is not worth it to hit the atmosphere harder than you have to.

kim holder

yeah - still having no feel for this, i'd thought the 716 m/s from an 8000 km release altitude would just be added onto the speed when it reaches the atmosphere, and thought about that

Hohmannfan

NOPE

kim holder

i'd like to install KSP again, but i don't want to mess with all the ship building and all that. i want to use it to get a sense of how orbits work.

the vectors - i don't get that yet

Hohmannfan

The best way to learn orbits in my opinion: Paper and desk calculator.

kim holder

really? i really struggle to picture the movement in my head, that would take that away.

ok - so the release speed of about 1 km/s counteracts the forward motion of the moon in its orbit?

Hohmannfan

21:18

Yes.

kim holder

because that is the thing - i have only just started to imagine that, instead of imagining heading straight towards the earth

when i think about it, i know it is wrong, but it is just the picture that happens in my head. and i'm all about those pictures.

Hohmannfan

I just looked up the orbital velocity of the Moon, and it is about 1020 m/s, so the v_inf needed is actually about 930 m/s

kim holder

um... why would that be?

are you trying to set up the right angle of approach when it gets to earth?

get an ellipse of the right shape?

Hohmannfan

An ellipse that touches the top of the atmoshphere

kim holder

oh, nice. yeah. maybe i should stop other things for a bit and go through a few geogebra tutorials.

Hohmannfan

21:26

kim holder

but i feel a need to finish the timeline and post it on the website main page.

Hohmannfan

In low Moon orbit, the escape velocity is about 2430 m/s

as v_escape² + v_inf² = v²

where v is the velocity we must have,

then for a required v_inf of 930 m/s

kim holder

that is pretty neat, a totally abstract right triangle.

Hohmannfan

, the velocity in low Moon orbit required is sqrt(2430² + 930²)= 2600 m/s

Yep, a totally abstract right triangle out of nowhere.

Hop talks about the v_inf triangle even in his first post

kim holder

so, the escape velocity is a quantity easy to find for any body. but how do you get one of the other 2 sides?

oh - you got it from the ellipse that was used to get the best speed at that point?

Hohmannfan

21:41

Yes, the difference between the ellipse and lunar orbit.

kim holder

ooohhh

Hohmannfan

Generally, you have one of two scenarios: "Ok, I am going this fast now, how fast am I going to go when I have escaped?" >> you have your initial velocity. Alternatively "Ok, I have to move that fast after the escape to make the next transfer (this case), what should my initial velocity be?" >> you have the v_inf.

kim holder

i should probably turn my attention back to finishing the timeline.

Hohmannfan

Example case:
Say you for some crazy reason want to go to Mars.
Going to Mars means following a Hohmann transfer.
The Hohmann transfer is an ellipse tangential the orbit of the Earth.
Calculate the difference between the velocity of the Earth's orbit, and the velocity of the elliptical orbit at the tangent point.
That is your v_inf.

kim holder

so, it really helps that i can specify the tether with the set up in the spreadsheet now

@Hohmannfan ok, so if you have an accurate map of where the planets are on the best date, then you can approximate that

otherwise, i don't know how you get the ellipse

Hohmannfan

21:50

Usually, you almost always launch close to a Hohmann transfer, so the ellipse is the same each time.

kim holder

really, it would have the same shape even though the distances and gravitational forces are different?

Hohmannfan

The orbits of the Moon, Earth and Mars are pretty circular, so there is not a lot that changes.

As for sending spacecraft to Mars, you wait for the orbits to line up for a Hohmann transfer.

That part, at least, is something you can get a good feeling about from playing things like KSP.

kim holder

the ellipse you showed dealt with velocity, not shape really

Hohmannfan

I can post a new one for this type of situation.

In stead of touching the atmosphere of the Earth and the orbit of the Moon, it is touching the orbit of Earth and the orbit of Mars.

kim holder

22:09

alright, but you have to be using something to get the velocities involved. I have seen the formula for getting the velocity at a point on an ellipse when you have the period for an orbit, but i don't see how you are getting the velocity without knowing that.

the ellipse up there that 930 m/s came from i didn't think through.

it goes through every possible angle to the orbit of the moon at different points along its length

Hohmannfan

You just need the periapsis and apoapsis of the ellipse.

If you are calculating the velocity at periapsis, then r = P

and in the apoapsis, r = A

I do not need to have a clue about the period of the ellipse, just the apoapse and periapse.

kim holder

but there are two different gravitational forces at the different foci of the ellipse

Hohmannfan

? wut?

kim holder

wait... the place where the apoapsis needs to be is the thing, the speed it would be going at that point is irrelevant to establishing the velocity here...?

Hohmannfan

Still ?wut?

kim holder

22:21

the ellipse between the moon and earth, you placed the apoapsis where it needed to be so the ship would just touch the atmosphere, right?

so the speed it is going at that point is determined largely by the acceleration due to the gravity of earth

but the speed it is going when it leaves the moon is not determined by that, it comes later.

Hohmannfan

Yes, we know exactly how fast an object is moving at apoapsis in that orbit (^equation above).

We also know how fast the Moon moves.

The difference between the two numbers is the v_inf

As we then know both the v_inf and, presumable, the escape velocity in the lunar orbit we start in, we can calculate the required velocity (the hypotenuse in the triangle).

The difference between the required velocity and the velocity we are actually moving at is the Delta-v

This process, by the way, of gluing orbits around the Earth together with orbits around the Moon is the patched conics approach.

kim holder

i can run through it in the case of the tether that was set up, using the average distance of the moon from earth

i can even set it up in the spreadsheet, and if it's wrong you can fix it later :P

because i'd like to do that in the opposite direction too

though it is much more ambitious - i have put it on the timeline as the last piece in the transport system, so there is time for things to be developed and organized so it is reasonable

Hohmannfan

The existing spreadsheet should have most of what is required, just tweak the altitudes of the tether balance point and the tether tip until the "velocity at infinity" cell reaches 930 m/s

kim holder

wouldn't it be good to have it as a separate formula as well, to help determine the release point that is best for different destination points, like GEO or EML1?

btw - i wish to note there has now been an anonymous gopher, anonymous beaver, and anonymous llama on the spreadsheet page.

and an anonymous grizzly. presumably all you.

Hohmannfan

22:50

kim holder

realtimeboard.com/app/board/o9J_k0mgZNg=

Hohmannfan

I wonder if stack exchange enforces a maximum number of image uploads. Surely, I must be close to that limit now.

kim holder

oh, i don't think so. uhoh would break it all the time. :)

it is a pretty sweet system...

with the tether, that is

i should set up a series of graphics like that, for the system in stages

Hohmannfan

23:28

Multi-threaded chat :)

kim holder

:]]]

i love it. it keeps it so focused.

Hohmannfan

Do you have this one?

kim holder

no, i didn't. that one is really detailed. thanks.

Hohmannfan

Too bad I have forgotten where I stole it.

kim holder

23:49

my husband is tired and hungry :) he has asked me to take a break so we can eat. He likes that little bit of being looked after.

Hohmannfan

Go and it :) I must go to bed now anyway.

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