[Space, Spaceships] Total ΔV for Interplanetary Travel

[Phantasm]

How much difference is there if launching from Earth's surface as opposed to being launched from a facility already in orbit?

[Ulzgoroth]

Originally Posted by Phantasm

How much difference is there if launching from Earth's surface as opposed to being launched from a facility already in orbit?

Per Spaceships p37, going surface to escape costs planetary escape velocity, while going from low orbit to escape costs 30% of escape velocity.

[Anthony]

Originally Posted by DaltonS

When calculating the total ΔV for an interplanetary trip, do we have to add the ΔV for breaking planetary orbit (both from the origin and braking to the destination) to that of the interplanetary transfer orbit?

Realistically, the Oberth Effect means that the total ΔV is less than their sum; how much less depends on your thrust.

The limit case for infinite thrust is ΔV = sqrt( escape velocity ^ 2 + transfer velocity ^ 2 ) - orbital velocity, to either enter or leave orbit. For example, from low earth orbit (escape velocity = 11.2 km/sec, velocity = 7.92 km/s) to a Mars transfer orbit (2.9 km/s) requires sqrt( 11.2^2 + 2.9^2) - 7.92 = 3.65 km/s, which is barely more than the 3.28 km/s required to break orbit.

Launch direct from ground saves the fuel required to circularize your orbit.

[DaltonS]

Originally Posted by Anthony

Realistically, the Oberth Effect means that the total ΔV is less than their sum; how much less depends on your thrust.

The limit case for infinite thrust is ΔV = sqrt( escape velocity ^ 2 + transfer velocity ^ 2 ) - orbital velocity, to either enter or leave orbit. For example, from low earth orbit (escape velocity = 11.2 km/sec, velocity = 7.92 km/s) to a Mars transfer orbit (2.9 km/s) requires sqrt( 11.2^2 + 2.9^2) - 7.92 = 3.65 km/s, which is barely more than the 3.28 km/s required to break orbit.

Okay, let's translate this to "mps" (the speed unit of choice for GURPS Spaceships). The Halfway to Anywhere “Mission to Mars" profile on page 33 of Pyramid #3/79: Space Atlas breaks the 3.4 mps ΔV of the Hohmann transfer orbit into two burns (1.8 mps at Earth orbit and 1.6 mps at Mars) and adds a 0.6 mps burn “to account for a 1.85° difference in orbital planes”. Ve = 6.96 mps (SS1 p.37) making Vo = Ve /sqrt(2) = 4.92 mps. So ΔV = sqrt(6.96^2 + 1.8^2) - 4.92 = 2.27 mps. (I could have directly converted the numbers, but I like using official sources.) Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

Dalton “just when I think I'm getting it, what I get is confused” Spence

[Ulzgoroth]

Originally Posted by DaltonS

Okay, let's translate this to "mps" (the speed unit of choice for GURPS Spaceships). The Halfway to Anywhere “Mission to Mars" profile on page 33 of Pyramid #3/79: Space Atlas breaks the 3.4 mps ΔV of the Hohmann transfer orbit into two burns (1.8 mps at Earth orbit and 1.6 mps at Mars) and adds a 0.6 mps burn “to account for a 1.85° difference in orbital planes”. Ve = 6.96 mps (SS1 p.37) making Vo = Ve /sqrt(2) = 4.92 mps. So ΔV = sqrt(6.96^2 + 1.8^2) - 4.92 = 2.27 mps. (I could have directly converted the numbers, but I like using official sources.) Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

Dalton “just when I think I'm getting it, what I get is confused” Spence

There's no 'reverse Oberth effect'. The Oberth effect helps you make your transfer burn and helps you make your orbital insertion burn.

[Anthony]

Originally Posted by DaltonS

Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

The Oberth effect applies at both ends (it's not reverse).

[DaltonS]

Originally Posted by Anthony

The Oberth effect applies at both ends (it's not reverse).

Mars Ve is 3.1 mps making Vo = 2.19, so ΔV = sqrt(3.1^2 + 1.6^2) - 2.19 = 1.3 mps. That makes the total ΔV for the trip = 2.27 + 0.6 + 1.3 = 4.17 mps, which according to my ΔV calculator spreadsheet would take 10 tanks of fuel with a TL8 NTR.

Dalton “did I get this right?” Spence

[Anthony]

Originally Posted by DaltonS

Mars Ve is 3.1 mps making Vo = 2.19, so ΔV = sqrt(3.1^2 + 1.6^2) - 2.19 = 1.3 mps. That makes the total ΔV for the trip = 2.27 + 0.6 + 1.3 = 4.17 mps, which according to my ΔV calculator spreadsheet would take 10 tanks of fuel with a TL8 NTR.

Note that the thrust of a TL 8 NTR is low enough that the limit case approximation isn't correct. I'm not aware of a simple solution for the moderate thrust case.