Pre-launch instrumentation staging disconnected prematurely resulting in loss of all booster data measurement.Sustainer and vernier engine shutdown occurred prematurely during flight.Range Safety destroyed vehicle at 303 seconds.

To convert earth-centered inertial cartesian coordinates (e.g., J2000) to geodetic latitude and longitude, I know that the rotation, precession and nutation of the earth since the epoch must be accounted for. Rotation seems easy enough, but I've yet to find an accessible (i.e., assuming enough physics and math to understand, but not assuming any previous knowledge of astronomy) resource about calculating precession and nutation matrices.1. Does anyone know of a good (preferably online) description of how to calculate the precession and nutation matrices, given an arbitrary epoch? Included examples would be even better to verify my results. I know the calculation gets pretty hairy, so even an approximation is fine for my purposes.

2. If I neglect precession and nutation, what is the ballpark error in the resulting geodetic calculations? (I assume it depends on the epoch.)

Basic orbital mechanics question:Is it possible to put a satellite in a geostationary orbit over a pole, or in a sort of halo orbit that stays within, let's say, 25 degrees latitude of a (rotational) pole?

If a mission is described as having a positive C3 (say 1.5km^{2}/s^{2}), is there an easy way to equate that to a delta-V, over and above the delta-V necessary to achieve escape velocity?

So a C3 of 1.5km^{2}/s^{2}, equates to V-inf of sqrt (2 * 1.5) = 1.73 km/s.

Would it be an over-simplification to say that an EDS would need to burn to escape velocity + 1.73 km/s to achieve that C3?

Constellation assumes that TLI will take advantage of the lowest delta-V opportunities. I've seen contradictory comments that these opportunities occur either once or twice per month. Which is correct?

Quote from: MP99 on 01/07/2010 04:41 PMConstellation assumes that TLI will take advantage of the lowest delta-V opportunities. I've seen contradictory comments that these opportunities occur either once or twice per month. Which is correct?Who cares. Either is more frequent than actual launch rates will be.

Quote from: OV-106 on 01/07/2010 04:47 PMQuote from: MP99 on 01/07/2010 04:41 PMConstellation assumes that TLI will take advantage of the lowest delta-V opportunities. I've seen contradictory comments that these opportunities occur either once or twice per month. Which is correct?Who cares. Either is more frequent than actual launch rates will be. MP99, it varies depending on if you're launching from the surface or from LEO. If you're launching from LEO, you get daily opportunities, because you can pick your launch time such that when your assembly is ready to depart LEO, your stack's orbital plane intersects the point where the moon will be when your stack arrives in its vicinity. Once you're in LEO though, you've got a plane, and planes precess at a rate that gives you launch windows on the order of 2-3 times per month. Depends a lot on inclination and altitude. So, if you're doing an EOR mission (say one with a depot for instance), you only get 2-3 good departure dates per month. But OV-106 is right. Having launch window frequency being a real issue would be a nice problem to have. If it ever becomes a problem (say with a depot-based architecture), you always have the option of putting up 1-2 more depots in additional orbital planes. Then you can send missions every 2-3 days....but we're a *long* way from that being important.~Jon

Quote from: jongoff on 01/07/2010 05:08 PMQuote from: OV-106 on 01/07/2010 04:47 PMQuote from: MP99 on 01/07/2010 04:41 PMConstellation assumes that TLI will take advantage of the lowest delta-V opportunities. I've seen contradictory comments that these opportunities occur either once or twice per month. Which is correct?Who cares. Either is more frequent than actual launch rates will be. MP99, it varies depending on if you're launching from the surface or from LEO. If you're launching from LEO, you get daily opportunities, because you can pick your launch time such that when your assembly is ready to depart LEO, your stack's orbital plane intersects the point where the moon will be when your stack arrives in its vicinity. Once you're in LEO though, you've got a plane, and planes precess at a rate that gives you launch windows on the order of 2-3 times per month. Depends a lot on inclination and altitude. So, if you're doing an EOR mission (say one with a depot for instance), you only get 2-3 good departure dates per month. But OV-106 is right. Having launch window frequency being a real issue would be a nice problem to have. If it ever becomes a problem (say with a depot-based architecture), you always have the option of putting up 1-2 more depots in additional orbital planes. Then you can send missions every 2-3 days....but we're a *long* way from that being important.~JonI'm thinking of CxP modified for dual launch.If the lander launches to take advantage of a minimum delta-V window (max payload), could the crew launch a few days later, even though it's not optimal?How much extra delta-V would be required? How does it vary as the month progresses?cheers, Martin

Let's see how well (or not) this amateur can do...To relate delta-v to energy you can't just say 0.5 * delta_v ^2 = delta-E. The efficiency of the burn depends strongly on your current velocity.

If we idealise things and consider only infinitely short, impulsive burns then we obtain instantaneous changes in velocity while positions remain unchanged. In real life situations with finite duration burns of significant thrust we get small changes to position and potentially large changes to velocity. If positions remain unchanged, then potential energy remains unchanged too. Kinetic energy does change of course. The total change in energy due to an impulsive burn therefore consists entirely of a change in kinetic energy. And since kinetic energy is quadratic in velocity, the increase in energy for a given delta-v increases linearly with the starting velocity. The faster you go already, the more benefit you get from your burn. This is the famous Oberth effect. For true orbits (i.e. not suborbital trajectories) this means the most efficient place to increase your energy is at perigee. On suborbital trajectories you can hardly expect to be able to execute a subterranean perigee burn...Of course there's more to it than just energy. To begin with velocity is a vector. You may also want to change the orientation of your orbital plane and the orientation of your major axis within that plane. It's no use flying in the wrong direction with the right speed!You typically need more than one burn to get into the desired orbit. In theory you could get into a sea level Earth orbit with a single impulsive burn that raises your perigee from the center to the surface of the Earth. In practice your burn cannot be impulsive and even if it could be you would burn up in the atmosphere and smash into mountains and other obstacles. To get into circular LEO you would need at least two impulsive burns: one burn to raise either apogee or perigee to the desired altitude, and once at the new apogee another circularisation burn to raise the new perigee to the desired altitude. In the real world you need to raise your current apogee by enough to escape the effects of drag and heating and to give your engines enough time to raise your perigee.All in all you'd need more delta-v than you'd expect from just comparing energies.

C3/2 = E = (v^2/2) - µ/r