Thrust value for space mission from Earth's orbit to Venus' orbit

Question

If I had to take a spacecraft from Earth's orbit (400km above earth) to an orbit around Venus (6151km X 50,000km elliptical orbit), how much thrust will I need. Delta V is 5km/s using hohmann transfer? Also can you share any papers of previous Venus missions that may have thrust values?

from comment:

I considered an elliptical orbit around sun with 2a = (dist b/w sun & venus) + (dist b/w sun & earth), then I calculated hyperbolic excess speed around earth to get into this trajectory, which was 11.14 km/s. But initally in a 400km above earth my speed is 7.67km/s. So my delta v1 is 11.14 - 7.67 = 3.47km/s.

Now, I did similar calculations near venus & got delta v as 1.13km/s. So total delta v is 4.6km/s. I just said 5km/s considering some buffer for corrections and to change orbits around venus. Now, I need thrust value so I can design engines for a 2 stage rocket.

Basically I need thrust to weight ratios for further calculations. But I'm not able to find values. Even if I did they were varying a lot so I don't know how to go about this

Answer 1

A couple of considerations

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I replicated your hyperbolic Hohmann calculation for Earth, and got 3.46 km/s. Close to your value.

But for the Venus part, the numbers seem off. Assuming a helocentric transfer orbit with apsis at the semi-major axis of Venus and Earth, and a circular orbit for venus, the relative velocity should be 2.71km/s, working out to a hyperbolic velocity of 10.63km/s at 6151km pericythe. Considering the pericythe velocity of a 6151km x 50,000km venus orbit is 9.70km/s, that's a delta-v requirement of only 0.93km/s.

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The entire 3.46 km/s manoeuvre in Earth orbit is not required to be performed in a single burn. Doing a partial burn, you are still in an elliptical Earth orbit, and can wait some hours or days to get pack to perigee for the next part. A relatively short time compared to the interplanetary transfer. The "marginal" burn is a mere 0.28km/s on top of the escape velocity at the end, putting you into a non-looping hyperbolic escape trajectory. On the Venus side, the similar marginal single burn for capture is 0.35km/s. The rest can be done in increments.

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A rule of thumb for escape trajectory burn times is to consider the radial acceleration in a rotating frame of reference:

$$a_{radial} = \omega^2r - \frac{\mu}{r^2}$$

While this is instantaneous of course, it's usable for upper bound calculations since the radial acceleration will only get lower as the distance grows.

At tangential escape velocity at 400km altitude, that's 8.7m/s² in a rotating reference frame. When looking at short periods of time, the altitude thus grows quadratically. Less than 15km for 1 minute, 60km for 2 minutes, 240km for 4 minutes. (Again, this is an upper bound. The actual altitude grows somewhat slower, so consider this an additional safety margin). From this, Steve Linton's estimate of a couple of minutes seems very reasonable. To get how much extra cost this adds, try doing your hyperbolic calculation for say 500km.

Getting the marginal cost of 0.28km/s done in a couple of minutes gives you acceleration requirements in the 1 - 5 m/s² range. As this marginal burn split up into parts is somewhat inconvenient, aiming for around a G of acceleration seems applicable.

Answer 2

To a first approximation, thrust doesn't matter. If it takes 3 minutes instead of 2 to apply the delta-V to go from Earth orbit to a Venus transfer, it makes no odds.

Beyond that first approximation, there are differences mostly in the direction that lower thrust increases the total impulse (delta-V essentially) that is needed. The main one is the Oberth effect which means, in this context, that you want to do all your accelerating as close as you can to Earth or to Venus. If your thrust is very low, your orbit will have risen noticeably before the maneuver is completed.

If your thrust is extremely low (for instance an ion engine) then entirely other trajectories are needed -- the Hohmann transfer assumes that you can apply the delta-V without doing very much of an orbit around the Sun.

Answer 3

Concerning thrust values in previous Venus missions here are some examples.
A lot of first Russian probes in "Venera" ("Venus") series was launched by the R-7 family launcher with "Block-L" upper stage, which accelerated probes to Venus direction. It had the thrust of 65.41 kN, gross mass of 5,100 kg (11,200 lb), unfuelled mass 1,080 kg (2,380 lb) and the specific impulse of 340 s.

The next generation of Veneras had upper stage "Block-DM" with thrust of 83.61 kN, empty weight of 3,420 kg (russian wiki)/2,140 kg (english wiki), propellant mass 15,050/15,220 kg and the specific impulse of 361/363.5 s.

"Mariners" had used "Agena-D" upper stage with the thrust of 71 kN.

But all or these are departure stages.

And here is the map of Delta-V, broadly known in the Internet. Source (Although, it seems I saw it here in SpaceExploration-SE.)