A question about the delta V needed to reach Mercury?

[dunwich]

Normally to reach Mercury , you need a lot of fuel to bridge the Δv.

However, Dr Chen-wan L. Yen desginend an orbit with a lot of flyby's reducing the need for fuel (using gravity assists).

How much delta v is needed in actual propellant for a mission to Mercury (compared to let's say Mars) and using Dr Chen-wan L. Yen route.

(Yes I know it will take roughly 7 years for the probe to arrive that isn't the question).

thank you for your response

[1]

Without knowing anything about the proposed trajectory, there's little meaningful answer to be had.

What has your own research turned up? Or, why not ask this 'Dr Chen-wan L. Yen' directly?

BepiColombo appears to have a similar transit time and uses multiple gravity assists, and ESA claims BP launched with a hyperbolic excess velocity (roughly the dV needed beyond Earth escape) of 3.475 km/s. So that's probably your best rough estimate of comparable performance.

[dunwich]

It seemed like a question with a clear answer.

I assumed that 3.475 km/s is better than 3.6 km/s to reach Mars, which would mean it is cheaper to send mass to Mercury than to Mars; it just takes a lot of time. This was the opposite of what I had learned, so it seems difficult to believe.

To my understanding both MESSENGER and bepi (really the Mercury Cruise System) are using the same trajectory... that takes less energy to reach then to go to mars... only to mercury just want to make that clear. 

[1]

Well, no. Low energy transfers to Mars can require excess velocities below 3 km/s, though arrival velocities may be quite high.   For a meaningful comparison, you really need to define what you mean by "to mars" and "to mercury". Trajectories at the discussed excess velocities exist that will at least get you to an orbit, even if it's one that's very highly elliptical. So what then?

BC also has onboard propulsion, both chemical and electrical, for orbital / trajectory maneuvering, so that would need to be considered in addition to the initial kick from the launch vehicle. But Mars has an atmosphere. So maybe your spacecraft can aerobrake and get some of that orbital insertion performance for free.

This is why, in the absence of specific trajectories or mission profiles, direct comparison between performance requirements does not have a clear answer.

[dunwich]

Okay perhaps a other way of looking at it,

I took MESSENGER over BEPI because it was launched using a Delta II 7925H-9.5 a rocket that has been used for mars mission.

MESSENGER mass 1107.9kg launched by the Delta II 7925H-9.5

VS mars
Mars Global Surveyor 1030.5kg launched by the Delta II 7925
D-239
2001 Mars Odyssey 725kg launched by the    Delta II 7925-9.5

specifickly the Delta II 7925H-9.5 was also used by spirit and opportunity, but the mass that reached orbit was only
    Rover: 185 kg (408 lb)
    Lander: 348 kg (767 lb)
    Backshell / Parachute: 209 kg (461 lb)
    Heat Shield: 78 kg (172 lb)
    Cruise Stage: 193 kg (425 lb)
    Propellant: 50 kg (110 lb)
    Instruments: 5 kg (11 lb)[38]

Total mass is 1,063 kg (2,344 lb).

First off the MESSENGER probe appears to be the most massive one despite going to Mercury but the 2001 Mars Odyssey  seems to be missing 25% of it's mass. So it's probably not as simply.

[leovinus]

Gravity-assist was developed in 1960s. If you want to go old school and start at the beginning then maybe try
http://www.gravityassist.com/IAF2/Ref.%202-82.pdf
which discusses Mercury trajectories. The site itself is a treasure trove on the topic.

Also search NTRS for "mercury trajectory"
Trajectory analysis of an Earth-Venus- Mercury mission in 1973
https://ntrs.nasa.gov/citations/19670008498

Hope that helps

[deltaV]

a hyperbolic excess velocity (roughly the dV needed beyond Earth escape)

That parenthetical is wrong because of the Oberth effect.

[1]

a hyperbolic excess velocity (roughly the dV needed beyond Earth escape)

That parenthetical is wrong because of the Oberth effect.

I think you read that comment as 'dv applied after the escape burn' rather than 'dv applied in addition to the escape burn'. Rereading the line though, I can see how my wording can be misinterpreted. I originally wanted to avoid discussing C3 and keep things in terms of 'simple' velocities, but I'm not sure I succeeded in making things any clearer now. May rephrase that later.

But yes. Since Earth escape is usually performed via chemical propulsion. I would expect both Mercury-bound and Mars-bound missions to take advantage of Oberth as feasible.

[DeimosDream]

I'm not familiar with Dr Chen-wan L. Yen, but..

If for this thought exercise we simplify the solar system down to circular orbits, going from Venus (108.2e6 km) to Mercury (57.9e6 km) requires departing Venus at 5.78 km/s.

For gravitational flybys velocity relative to the flyby planet doesn't change, so Venus flyby(s) on the way to Mercury would need to occur at 5.78+ km/s (C3@venus=33.4km2/s2).

Earth (149.6e6 km) ->Venus (108.2e6 km) is only 2.7 km/s at Venus by hoffman, so a probe is going to have to overshoot Venus. Running a bunch of number in excel says we need to hit a perigee of 100.3e6 km when launching from Earth, which takes an Earth launch of 3.1 km/s or 9.6 km2/s2 C3.

The same circular orbit simplification says Earth->Mars is 2.94 km/s, so a Mercury flyby by way of a Venus gravity assist takes only a slightly faster launch than a direct Mars flyby. (Although Mercury orbit is much harder).