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Meithan
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It was impressive to see how slowly the rocket climbs at first. I wonder what's the TWR at liftoff of that thing? I looked up the numbers. MAVEN weighs about 2500 kg, while the Atlas V 401 launch rocket weighs about 334,500 kg and its first stage produces about 3,827 kN of thrust at sea level. That computes to a thrust-to-weight ratio at liftoff of 1.16. Makes sense.
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It's nice to see things work out I computed a few more numbers that might be interesting. The escape speed at 250 km altitude is very close to the usually quoted 11 km/s. After launch, MOM's perigee speed was 9.9 km/s, so it needed an extra about 1.1 km/s at perigee to reach Earth escape speed. After the orbit raising burns, its current perigee velocity is now 10.8 km/s. It now just needs a small kick of around 180 m/s to escape Earth's gravity. Of course, it'll need to apply more in order to leave on a Mars interception course. Notice that we're achieving escape speed from perigee. Now consider this. As I said, escape velocity at 250 km/s is about 11 km/s. At the initial apogee altitude of 23,563 km, escape velocity is about 5.2 km/s -- considerably lower. Isn't it easier to escape at apogee? Why don't we burn at apogee instead? The reason is that while escape velocity is indeed lower at apogee, the spacecraft's velocity is also considerably smaller. It turns out that the difference between the escape speed and the craft's orbital speed is in fact greater at apogee than at perigee. Let me show it with numbers: Departing from initial 250 km x 23,563 km orbit: Escape speed at perigee: 11.0 km/s Orbital speed at perigee: 9.9 km/s Delta-v to escape at perigee: 1.1 km/s Escape speed at apogee: 5.2 km/s Orbital speed at apogee: 2.2 km/s Delta-v to escape at apogee: 3.0 km/s The required delta-v for escape is almost three times larger at apogee! So it's much more efficient to burn for escape at perigee, where we're moving fast. And what does that remind us of? Yup, our friend the good ol' Oberth effect. The mechanical energy of the spacecraft is the same at any point of its orbit, and the energy for escape is also a unique value (namely, zero). That means that escaping Earth from a given initial orbit requires a fixed amount of extra energy, regardless of where we do the burn. But the Oberth effect says that we get more kinetic energy out of every kg of spent fuel when we're moving faster. So we don't need to spend as much fuel to gain that extra energy if we burn at perigee. And that's equivalent to a lower delta-v requirement.
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Actually, mass flow rate of the engine is simply related to the specific impulse and the thrust, , and we know those numbers. If we assume constant Isp, and consider it's been burning for 2240.9s total, then it has burned through 324 kg of propellant so far. Since its initial mass was 1337 kg, that translates into a spent delta-v of 844.60 m/s, out of 3084 m/s total Another way to compute the delta-v, perhaps more precisely, is to compare the initial and final orbits after each maneuver. Since the burns occur near perigee, one can deduce the delta-v applied by looking at how much the apogee changed.
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I looked up MOM's and MAVEN's specifications and calculated their ÃŽâ€v, just for fun: Mars Orbiter Mission Full mass: 1337 kg Dry mass: 485 kg Main Engine: 440N LAM Engine Isp: 310 s ÃŽâ€v: 3084 m/s MAVEN Full mass: 2559 kg Dry mass: 903 kg Main Engine: 6 x 170N MR-107 Engine Isp: 230 s ÃŽâ€v: 2236 m/s MAVEN cheats because it's injected into a Mars transfer trajectory by the Centaur upper stage of the Atlas V rocket. Does anyone know the ÃŽâ€v that MOM has applied so far during the orbit raising maneuvers? I wonder how much of its ÃŽâ€v budget will be spent leaving Earth.
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And to think MAVEN doesn't carry a methane detector nor a color camera! (But to be fair, it carries a much more complex suite of instruments -- and it's also quite heavier, about 2.5 tons vs. MOM's 1.3 tons.)
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I just had a look and I have to say that's a great PR site! I loved the diagrams and explanations.
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That's MAVEN's High Gain Antenna. Here's a shot before the conical dome was installed. The dome protects the antenna and stabilizes its temperature. From NASA: "For optimal performance, it’s important for the high-gain antenna to maintain a consistent temperature while the spacecraft experiences large temperature swings from being exposed to the Sun or in the eclipse behind Mars. To maintain a consistent temperature range, a radome blanket covers the large antenna. Similar to the blanketing material that covers the spacecraft, the radome is made from very thin germanium-coated black Kapton film."
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Nice graphic. Assuming the perigee's still around 250 km altitude, that's a ~91 hour orbit, with an apogee about halfway to the Moon. I'm confident that the Dec 1 burn will be successful and then MOM will race MAVEN (assuming it launches successfully too -- only two days to go!) to Mars .
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Yeah that would be a simpler fix I guess.
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Yeah, I agree that the whole George Clooney's character being pulled away doesn't make physical sense. You could change it just a bit to make it physically correct. After their multiple collisions and attempts to slow themselves down, the characters manage to get a hold of each other (tethered to each other, for instance) but they're still drifting at a few meters per second. Bullock's character's legs gets entangled in the chute's ropes, but she's still not being held by them (they're still not taut). Clooney's character realizes that when they reach the end of the ropes, their combined mass will be too much and she won't be able to stop them both. So despite Bullock's character insistence, he detaches in order to save her.