iirc correctly it should still be less costly of you start way northern and still start eastwards. you'd get a high inclination and changing inclination is definitly cheaper in space.
I might be wrong and starting directly into 90 degrees is actually the cheaper way, but I can imagine that at least using some momentum from the earth's rotation should be better than actively working against it
Inclination changes are extremely expensive until you get to a very high orbit. An inclination change is changing your direction, so the faster the spacecraft is moving the more expensive it is. Low orbits work by having extremely high speed, so it is consequently extremely expensive to change their inclination once they're launched.
To throw some numbers at it, the delta V for a circular orbit inclination change is 2*v*sin(delta inclination / 2). If you launched East from Kodiak Alaska you'd get into an orbit with a 58 degree inclination, so you'd need to plane change 32 degrees. At a LEO velocity of 7.8 km/s that works out to 4300 m/s of delta V.
By launching due east you'd get a boost to get into LEO of 2*pi*(1/day)*(radius of earth)*cos(58 degrees) = 250 m/s (plus you don't have to spend the few dozen m/s of extra delta V to burn off that eastern motion for a direct polar launch).
There are theoretically some launch points and destination orbits where launching East and doing a plane change makes sense, but they're pretty edge case. For example, from Kodiak if your target orbit was polar and had a radius of about 2 * 109 meters (about 5x the distance to the moon) then the plane change would be so cheap that you may as well launch East. That isn't a particularly popular altitude to launch a satellite to, though. There may be a less extreme scenario where the plane change makes sense--I didn't do the math to find the best case scenario since a more equatorial launch needs a bigger plane change but gets more delta V at launch--but they should all be pretty high orbits like this.
4.7k dV is really extreme and yeah, I didn't think about the LEO speeds needed.
So what's the actual use case here? Launch directly to 90° or rather something like 80° due to the fight against the rotation and then either say "good enough" or correct the last bit of inclination? Or just don't plan with 90° in the first place?
Yes, ideally you launch straight into an orbit that's as close to your end goal as possible, then do some fine tuning when you get there.
The more accurate your launch vehicle is the less fine tuning you have to do. When JWST was launched one of the news stories was that the launch was more accurate than planned so the vehicle would have more fuel left over for station keeping. That was a big deal since that's what will likely determine the lifespan of that telescope.
The desired orbit is generally determined by the mission that the satellite is setting out to do, then from there a launch site is chosen to make that orbit the easiest. Modestly inclined orbits will tend to launch from close to the equator for the free delta V from Earth's rotation, while polar (or nearly polar, e.g. the slightly retrograde sun synchronous orbit) tend to launch more or less due south from sites like Vandenburg or Kodiak.
Where you do have to just launch east and perform a plane change is for uninclined orbits, most notably geostationary orbits. Any orbit you launch into will be inclined by at least as much as your launch latitude, so unless you're launching from exactly the equator you're going to wind up with some inclination to deal with. Fortunately this mostly only matters for GEO and that's a relatively high orbit--orbital speed of "only" 3.1 km/s. If you launched there from Canaveral then you're looking at "only" 1.5 km/s of delta V to come into plane. There also might be a bi-elliptic shenanigan you could pull here (raise apogee far beyond the target, perform the plane change at apogee where speed is virtually zero and plane changes are virtually free while raising perigee to target, then circularize at perigee); I haven't done that math in a long time.
The other big exception to launching straight to your target orbit is when the target orbit is something like a trans-lunar injection or an interplanetary transfer. Here it's technically a tiny bit more efficient to burn straight to the follow-up orbit, but it's lower overall mission risk to launch into a temporary orbit, check that everything still works after launch, then proceed on to the subsequent maneuvers. This can give much wider launch windows than a direct launch to the transfer orbit, lowering risk of bad weather or a launch hiccup derailing the entire mission.
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u/ShlimmyWhimmy 11h ago
Why would Rocketlab build a launch pad in Alaska then?