Equations for navigating in space

[KAL 9000]

I know the rocket equation and Newton's gravity equation, but what other equations do you want to have for navigating in the solar system?

[Bill Phil]

Vis viva equation. Equation of the various conics. The orbital energy equation.There's a few more out there...

[Plusck]

This is a most excellent website that provides all of the nuts and bolts:  http://www.braeunig.us/space/index.htm

 

edit: oops, that's the index page for the site. Actual page with equations is http://www.braeunig.us/space/orbmech.htm

[YNM]

Don't forget angular momentum - else you don't know where you are in orbit, eccentricity. Also, many of the "less common" dV (inclination change, plane change etc.) relies on the different angular momentum.

[Bill Phil]

Some trig for plane changes. 

The keplerian elements.

[GoSlash27]

Vector addition for transfer burns crossing SoI boundaries.

DV= sqrt(Vxs^2+Vesc^2)-Vorb

I use this one constantly for mission planning.

Vxs is the DV required to set up an intercept, neglecting the current gravity well.

Vesc is the escape velocity from the current gravity well... which happens to be your orbital velocity times sqrt(2).

Vorb is your orbital velocity in the current gravity well.

This can be concatenated (chained) to calculate transfers from a moon about one planet to a moon about a completely different planet.

 

Also, gate orbits.

r=2GM/Vxs^2

Handy for figuring out the optimal transfer altitudes (not always LKO).

Best,
-Slashy

[OhioBob]

I believe there are three equations that form the bedrock of almost all the calculations we do around here.  All have already been mentioned in some form or another, but I'll summarize.

Tsiolkovsky rocket equation,

Δv = v_e LN(m_o / m_f)

Vis-viva equation,

v² = GM (2/r - 1/a)

Hyperbolic excess velocity,

v_∞² = v_bo² – v_esc²

Master those three equations and you'll be in good shape.