Foundations — Pork chop plots — Δv vs launch - arrival date

3.2.27 · D1 · Physics › Orbital Mechanics & Astrodynamics › Pork chop plots — Δv vs launch - arrival date

Uss map pe ek bhi contour padhne se pehle, hume parent note mein aane waale har symbol pe poora command hona chahiye. Neeche, har idea usse pehle waale idea pe build hota hai — kuch borrow nahi, kuch assume nahi. Ek samajhdaar 12 saal ka baccha line one se shuru kar sakta hai.

0 — Vector kya hota hai, aur chhoti arrow ka matlab kya hai?

Yahan sab kuch solar system mein hai, jo ek 3-D space hai. Yeh kehne ke liye ki koi cheez kahan hai ya kitni tezi se move karti hai, ek number kaafi nahi — direction bhi chahiye.

Ek vector ki length vertical bars se likhi jaati hai: $|\vec{v}|$ matlab "arrow $\vec{v}$ ki length". Agar $\vec{v}$ 3 units right aur 4 units upar point kare, toh right triangle se, $|\vec{v}|=\sqrt{3^2+4^2}=5$. (Length hamesha arrow ke sideways aur upward parts se bane box ka diagonal hota hai — yeh sirf Pythagoras hai.)

1 — Vectors subtract karna: "kisi cheez ke relative velocity"

Parent note mein baar baar ${\vec{v}}_1-{\vec{V}}_E$ jaisi cheezein likhi hain. Hume exactly pata hona chahiye ki do arrows subtract karne ka matlab kya hai aur, sabse important, yeh kaise dikhta hai.

Yeh single picture parent ki ek "common mistake" already khatam kar deta hai: cost kabhi raw speed ${\vec{v}}_1$ nahi hoti, yeh difference ${\vec{v}}_1-{\vec{V}}_E$ hai.

2 — Dono planets aur transfer ke symbols

Ab hum parent ke use kiye har arrow ko naam de sakte hain.

Poori trip yeh hai: ${\vec{r}}_1$ pe ${\vec{v}}_1$ pe shuru karo, curved path pe coast karo, ${\vec{r}}_2$ pe ${\vec{v}}_2$ pe pahuncho.

3 — Time of flight (TOF) aur $\Delta t$

4 — $\Delta v$ kya hai? (show ka star)

Parent ki ek cell ke liye total cost hai $\Delta v_{tot}=\Delta v_{dep}+\Delta v_{arr}$ — jo tum Earth chodne ke liye jalate ho plus jo tum target pe arrive/capture karne ke liye jalate ho.

5 — Gravitational parameter $\mu$ aur do "escape" speeds

$\mu$ se bane do speeds har jagah aate hain:

6 — Hyperbolic excess speed $v_{\infty }$ aur $C_3$

Yeh sabse subtle symbol hai, isliye hum ise ek picture ke saath build karte hain.

7 — Perigee speed aur departure burn formula

Parent ka boxed formula upar ki sab cheezein bundle karta hai. Aao ise symbol by symbol padhein.

Arrival burn $\Delta v_{arr}$ ka ek jaisa hi shape hai, bas target ke ${\mu }_T$, uski capture radius $r_a$, aur $v_{\infty ,arr}$ ke saath.

8 — Synodic period $T_{syn}$: kyun windows repeat hote hain

Yeh sab topic ko kaise feed karta hai

Related deep tools jo aage milenge: Hohmann Transfer (sabse sasta, sabse slow case), Patched Conic Approximation (kyun hum Earth-escape aur Sun-transfer alag alag treat kar sakte hain), aur Tsiolkovsky Rocket Equation ($\Delta v$ ko fuel mein convert karna).

Equipment checklist

Right side cover karo; kya tum har ek ka jawaab reveal karne se pehle de sakte ho?