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According to the SpaceX website (http://www.spacex.com/falcon-heavy) the falcon Heavy can carry 16.8 tons to Trans Mars Injection (TMI) and 26.7 tons to Geostationary Transfer Orbit (GTO). How much can it carry to Trans-Lunar Injection (TLI)?

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    $\begingroup$ It can carry atleast 28,000kg according to ArsTechnica $\endgroup$ – faroukcharkas Mar 22 '18 at 15:02
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    $\begingroup$ Item of interest: Apollo Command and Service Module weighed 28,800kg en.wikipedia.org/wiki/Apollo_Command/Service_Module $\endgroup$ – ORcoder Mar 22 '18 at 22:01
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    $\begingroup$ The lunar module comes in at 16,400kg, so Falcon Heavy would not be able to launch the whole Apollo stack to the moon (45,200kg). I wonder if a hypothetical Falcon Superheavy (4 side boosters) could plausibly manage... $\endgroup$ – ORcoder Mar 22 '18 at 22:04
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    $\begingroup$ @ORcoderI'll bet an Apollo-like replica made with 21st century materials would be a heck of a lot lighter, and so I've asked How much lighter could a modern, working replica of an Apollo payload and crew be at launch? $\endgroup$ – uhoh Mar 22 '18 at 23:32
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    $\begingroup$ The "crew around the moon" mission Ars was referring to was a free return trajectory in a Dragon 2 I believe $\endgroup$ – ORcoder Mar 23 '18 at 0:22
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One can use the NASA Performance Vehicle Estimator to get a decent idea of this, although it does have errors now with the Falcon Heavy. It does not have a TLI option, but it does have a negative C3.

To calculate the C3 required, one must know the delta V from LEO to Escape Velocity and to TLI. The escape velocity is requires a delta v of 3.22 km/s, the TLI for Apollo was between 3.08-3.25 km/s. Bottom line is, the delta v is roughly equivalent to escape velocity, so let's just use that. The mass is 6,000 kg with the recoverable Falcon Heavy, and 12,000 kg for the expendable.

enter image description here

Of course, we know these are wrong, because the Falcon Heavy can carry 16.8 tonnes to Mars, and that isn't quite there. The required C3 for Mars is about 8.1 km^2/s^2, so the plot shows about 10,300 kg or so. The amount to GTO is about 13,500 kg according to the plot (C3=-4.1 km^2/s^s).

All of this taken in to account, and trusting SpaceX's numbers, let's say about 2/3rds of the way between the two measurements, as that is where it falls on the C3 curve. Thus it should be about 23.4 tons, give or take.

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  • $\begingroup$ You know that still might be able to carry Orion haha. Maybe with the service module finishing the last bit of the injection burn. $\endgroup$ – ORcoder Mar 24 '18 at 3:07
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We can bound the payload capacity from the top and the bottom using the GTO and TMI numbers.
Suppose we are already in low Earth orbit.
GTO delta-v requirements: 2.5 km/s
TLI delta-v requirements: 3.05 to 3.25 km/s
TMI delta-v requirements: 3.8 km/s

Falcon Heavy GTO payload: 26,700 kg
Falcon Heavy TLI payload: ???
Falcon Heavy TMI payload: 16,800 kg

Therefore we know the TLI payload of Falcon Heavy is at least 16,800kg, but no more than 26,700kg. It is probably around 21,000kg*, but due to the nonlinear nature of rocket delta-v, that could be off by a couple tons.

*This value is between the results of a logarithmic fit of the delta-v/payload data for 3.25 km/s TLI and 3.05 km/s TLI

Sources:
https://en.wikipedia.org/wiki/Trans-lunar_injection#history https://en.wikipedia.org/wiki/Delta-v#Around_the_solar_system https://en.wikipedia.org/wiki/Falcon_Heavy#Capabilities

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  • $\begingroup$ Why does the delta v for tli vary? $\endgroup$ – Steve Linton Mar 23 '18 at 22:35
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    $\begingroup$ Wilipedia says that is how much the Saturn V injections varied on their TLI page. Perhaps it's the difference between a most efficient hohmann trajectory versus a free return trajectory? $\endgroup$ – ORcoder Mar 23 '18 at 22:47

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