
Math & Physics Mathematical and physical problems of space flight and astronomy. 

Thread Tools 
05232016, 02:31 AM  #16 
Mathematician

OK, one more stab at the Mars moons proposal. We have discussed before the surprising speed that New Horizons was able to pass the orbit of Mars due to its high departure speed:
Math needed for 5week flight from Earth to Mars. http://orbiterforum.com/showthread....3&postcount=78 The transit time of New Horizons to pass Mars' orbit was 78 days for a LEO departure deltav of 8.4 km/s. But as discussed in that post, the Mars capture deltav would be close to 12 km/s, prohibitive when added to the departure deltav. So instead I'm thinking of other ways of being captured at Mars such as aerocapture: https://en.wikipedia.org/wiki/Aerocapture This allows the spacecraft to be captured into Mars orbit with minimal propellant burn. So using a limiting LEO departure deltav of 8.4 km/s as with New Horizons and assuming the departure takes place in the time frame of the last quarter of this year to the first quarter of next year, what would be the travel time then? Bob Clark 
05232016, 05:13 AM  #17 
Orbinaut

This is doable. But I'm travelling without computer for a couple of weeks. Will get back to this upon my return to HK.
Last edited by Keithth G; 03052017 at 11:47 PM. 
05232016, 04:03 PM  #19 
Orbinaut

Quote:
Quote:
OTOH, MSL, I believe didn't bother with establishing orbit at all. It came in from the transfer orbit directly to atmospheric entry. Last edited by Shifty; 05232016 at 04:13 PM. 
Thanked by: 
05232016, 05:14 PM  #20 
Mathematician

Quote:
Aerocapture is a more difficult proposition. It would require the spacecraft to plunge deep into Mars atmosphere, skimming the tree tops so to speak. That has not been tried yet. Since this is only a test flight anyway this may be a good chance to test it. Bob Clark 
05232016, 05:23 PM  #21 
Orbinaut

According to Wikipedia atleast, the MSL entered the Martian atmosphere at 5.8 km/s and experienced a peak deceleration of 15g.
Last edited by Keithth G; 03052017 at 11:46 PM. 
06062016, 04:22 AM  #22 
Orbinaut

I've now had a chance to run the problem through PyKEP:
For possible transfer times of less than 500 days, the best day to leave is 11 October, 2016; the transfer time to Mars is 273 days; the departure dV is 8.4 km/s; and (at a 50 km periapsis altitude at Mars) the periapsis velocity would be 10.2 km/s. Last edited by Keithth G; 03052017 at 11:44 PM. 
04092017, 04:57 PM  #23 
Mathematician

Quote:
So my proposed mission is still possible for this first FH launch, to do a fast flight to Mars, ca. 35 day duration, to demonstrate its feasibility for a fast manned mission. The deltav needed for such a fast flight to Mars in 2018, a particularly close opposition, was discussed here: Math needed for 5week flight from Earth to Mars. http://orbiterforum.com/showthread....6&postcount=17 It's about 10 km/s. The updated specifications for the Falcon Heavy with the upgraded Merlin engines are on the SpaceX Falcon Heavy page. I estimate we could get 2 to 3 metric tons as payload to Mars for the fast trip depending on whether we used for the inspace stage the small cryogenic Ariane 5 upper stage leaving from Trans Mars Insertion, or the larger Centaur leaving from geosynchronous transfer orbit. We still have the problem of slowing down when the use such fast flight speeds which result in fast arrival speeds at Mars. Some preliminary calculations suggest it might work by plunging deep into the Martian atmosphere, skimming the treetops so to speak. Bob Clark Last edited by RGClark; 04122017 at 01:33 PM. 
04202017, 07:37 PM  #24 
Mathematician

Actually, while the Red Dragon mission on the Falcon Heavy is set for 2018, SpaceX plans for two prior FH test flights for the latter part of this year.
Elon has discussed testing recovery of the upper stage on these missions which will reduce payload. He has also discussed putting a "fun" payload on one of them, like his cheese wheel on the first Dragon test flight. Still, if low cost inspace stages could be used for a flight to the Martian moons perhaps Elon could be convinced to make one or both of these first FH flights be to the moons of Mars. Note that key to Elon's plan for manned flights to Mars is getting the fuel for the return trip from Mars. Taking the fuel from the Martian moons would have advantages such as low gravity for getting the fuel to an orbiting propellant depot. Then these first flights to the Martian moons could serve as scout missions for water ice deposits. Plus, it could resolve the mystery of Phobos' origin, whose low density led to much speculation about it. In the table provided by Keithth G in post #14, the launch dates from Sept. to Dec. 2017 have travel times to Mars in the range of 270 days. But being outside the optimal launch windows, they have large deltav requirements. So my plan to test short flight times by high departure speeds wouldn't be very useful for these flights. That would have to be reserved for the optimal departure windows. In the blog post "Low Cost Europa Lander Missions", I discussed some small inspace stages for a possible Europa mission. Two stages discussed were the storable propellant stage Delta K and the Integrated Apogee Boost Subsystem (IABS) stage. The Delta K has a 6 mT propellant load, 0.95 mT dry mass, and 319 s Isp. The Integrated Apogee Boost Subsystem (IABS) stage is a small kickstage used to put geosynchronous satellites in their final orbits. It has a 1.6 mT gross mass and .3 mT dry mass, for a 1.3 mT propellant mass, with a 312 s Isp. Then for a small 1.5 mT robotic rover it could get this to: 319*9.81ln(1 + 6/(.95 + 1.6 +1.5)) +312*9.81ln(1 + 1.3/(.3 + 1.5)) = 4,500 m/s. The latest specs on the Falcon Heavy give it a 16.8 mT payload to Mars transfer insertion. This is about a 3,800 m/s deltav. The Dec. 23, 2017 departure according to Keithth G's table takes 4,836.1 m/s for Earth departure and 2,451.5 m/s to match Phobos orbit at Mars, for a total of 7,287.6 m/s. Then to land on Phobos requires an additional 500 m/s, so all together 7,787.6 m/s, call it 7,800 m/s. Then since the Falcon Heavy will already provide 3,800 m/s for Earth departure, only 4,000 m/s would have to be provided by our two inspace stages, which is within their capability with a 1.5 mT payload. This 1.5 mT payload that could be landed on Phobos is so large we might even be able to include a solid rocket stage to return a sample from Phobos to Earth. In regards to the cost, NASA wants a mission to Phobos so they may be willing to pay for the cost of the inspace stages. Bob Clark Last edited by RGClark; 04202017 at 07:40 PM. 
04222017, 04:56 PM  #25 
Mathematician

Quote:
So how do you find the deltaV needed to make the Mars transfer injection assuming the spacecraft is already in LEO? Bob Clark 
04232017, 04:03 AM  #26 
Orbinaut

Quote:
where is the hyperbolic excess velocity (departure deltaV from trajectory planner). is the local escape velocity, aka the escape velocity for the parking orbit altitude. where is the gravitational constant, is the planet's mass, is the planet's radius and is the altitude of the parking orbit. is the parking orbit velocity. Same applies for arrival. If you want to simply calculate the periapsis velocity and not the orbit insertion/injection dV, then don't use the term. Source: ORBITAL MECHANICS Last edited by dgatsoulis; 04232017 at 04:20 AM. 
Thanked by: 
04232017, 01:20 PM  #27 
Mathematician

Quote:
Bob Clark 
05072017, 01:59 PM  #28 
Mathematician

Some suggestions for the test flights of the Falcon heavy:
Test flights of the Falcon Heavy for missions to the moons of Earth and Mars, Page 1. http://exoscientist.blogspot.com/201...heavyfor.html Bob Clark 
05192017, 06:05 PM  #29 
Hop David

Quote:
Here's a screen capture for arrival to a Deimos orbit: You can see insertion to this orbit takes about a 2 km/s periapsis burn. Here's a capture orbit with Deimos at apoapsis A 1 km/s periapsis burn plus about a .7 apoapsis circuralize burn gives about 1.7 km/s Quote:
The user can vary shape of transfer ellipse by inputing aphelion and aphelion. For example the typical Hohmann would have a 1 A.U. perihelion and a 1.52 A.U. aphelion. Here's a screen capture when transfer orbit has a .9 A.U. perihelion and a 3 A.U. aphelion: Underlined are numbers of interest: departure V infinity, arrival V infinity, and time of flight. Off to the right on this spreadsheet the user can input the Mars orbit you wish to insert into and it will give the delta V. 
Thanked by: 
05202017, 03:04 AM  #30 
Mathematician

Quote:
Bob Clark 

Thread Tools  


Quick Links  Need Help? 