# What payload mass can different launchers send in Hohmann trajectories to different destinations?

It would be nice to get an overview of what the launchers are capable of in terms of actual space missions. I understand that this depends on many factors, but the Hohmann trajectory seems to be a common and major factor for many missions. Could this Hohmann part of the puzzle be summarized in a table with payload mass for different launchers and destinations?

Most interesting would be to compare these three launcher classes:

• SLS or Saturn V

• Falcon Heavy

• Atlas V551 or Ariane 5 or Proton

The smaller Falcon 9, Soyuz, Indian PSLV would also be of interest since even little PSLV actually has launched an orbiter to Mars.

Latitude of the launch site should not make a difference big enough to matter for an overview purpose, one could assume the equator. The eccentricity and inclination of the destination object is much more important and variable over time. But except for Mars and Mercury, I would think that at least the planets have low enough eccentricity for an average to work well.

Gravity assists, Oberth effect, continuous ion thrusting of course totally distorts the Hohmann geometry and all spacecraft to outer planets have and surely will use Jupiter for gravity assist. So that kind of leaves only Jupiter and Venus and the Moon! But those are very likely mission targets. Each launcher should have a pretty good specification as an X tons to Venus or Y tons to Jupiter or Z tons to the Moon vehicle. For Mars and asteroids the specific launch date seems to be too important. However, Mars will make a close opposition in 2035 which could be used as a benchmark for a crewed mission.

# To Mars

The Delta-V required to transfer from Low Earth Orbit to Low Mars Orbit is around 7 km/s (utilising the Oberth effect). So the payload being sent up to LEO must have this ∆V budget. Additionally your launcher needs about 8km/s to get up to LEO in the first place.

Your question is specifically about payload mass. You've given a multitude of different launchers and targets, and you can calculate each one's mass using the Tsiolkovsky Rocket Equation: $$\Delta V\ = v_e \ln \frac {m_0} {m_1}$$

You have the ∆V needed. So now experiment with different payload masses (adjusting the total starting mass accordingly). You can thus get an idea of how large your launcher needs to be to send a reasonably sized manned payload to Mars. Rinse and repeat for any other target you have in mind.

This answer performed the calculation for a manned mission to Mars and found:

I plugged the data provided by @PearsonArtPhoto into the rocket equation, with Isp=304 seconds (Merlin 1C in vacuum), and I get a launch mass of 262 tons to get a Dragon into Mars orbit. A Falcon 9v1.0 weighs 333 tons.

# Launcher Classes

Use these values to get started.

## Saturn V

The Saturn V remains the tallest, heaviest, and most powerful rocket ever brought to operational status and still holds records for the heaviest payload launched and largest payload capacity to low Earth orbit (LEO) of 118,000 kilograms (260,000 lb).

Launch Mass: 2,970,000 kilograms

Maximum Payload to orbit: 118,000 kilograms

## Falcon Heavy

Falcon Heavy (FH), is a spaceflight heavy lift launch vehicle being designed and manufactured by SpaceX. The Falcon Heavy is a variant of the Falcon 9 v1.1 launch vehicle and will consist of a standard Falcon 9 rocket core, with two additional strap-on boosters derived from the Falcon 9 first stage.

Launch Mass: 1,462,836 kilograms

Maximum Payload to orbit: 53,000 kilograms

## Atlas V-551

Atlas V is an active expendable launch system in the Atlas rocket family. Each Atlas V rocket uses an RD-180 engine burning kerosene and liquid oxygen to power its first stage and an American-built RL10 engine burning liquid hydrogen and liquid oxygen to power its Centaur upper stage.

Launch Mass: 334,500 kilograms

Maximum Payload to orbit: 18,814 kilograms

• One has to know fuel mass and structural mass in order to solve for payload mass. I found this table from 2009 but the payload mass fraction doesn't add up according to the definition of it below the table. Titan II in the first row has 0.962 fuel and 0.279 payload which adds up to -24.7% structural mass, not +3.5% as stated. Is it a reliable table? (From a homepage of a guy who is member of the National Opossom Society, so it's probably I who gets it wrong). – LocalFluff May 31 '15 at 8:43
• I can't verify that table, but it's not hard to find data on different launchers by simply Googling them. – Vedant Chandra May 31 '15 at 8:47
• I also wonder if the Hohmann trajectory is affected by the mode of insertion. User Hobbes here, to whom you made a link, has on his blog very clearly explained how valuable it is to use eccentric insertion orbits with minimal periapsis in order to advantage of Oberth and aerobraking. Could the trip from LEO to insertion, circular or not, be analyzed separately as I ask for? – LocalFluff May 31 '15 at 8:47
• This is probably more of a back-and-forth discussion we can have with more qualified people over in the Pod Bay. Let's move this there. chat.stackexchange.com/rooms/9682/the-pod-bay Do you want any more details on the answer? – Vedant Chandra May 31 '15 at 8:50