This model represents an applied impulse (Δv) that changes an orbit.
Press ⏎ to see the model. Within the model C ⏎ is the central body that is orbited, 0 ⏎ is the initial orbit some time before the Δv is applied, 0i ⏎ is the initial orbit the moment before the Δv is applied, 1i ⏎ is the new orbit the moment after the Δv is applied, and 1 ⏎ is the new orbit some time later.
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Hohmann transfers are two-impulse coplanar circular-to-circular transfers. The first impulse changes a circular orbit into an elliptical orbit that transfers between the initial and final orbits. The second impulse circularizes the orbit at the destination altitude. The two-impulse Hohmann transfer model is built by joining two single-impulse transfer models, which the Hohmann model regards as the ΔV0T dV0T ⏎ and ΔVT1 dVT1 ⏎ variables.
Saving the International Space Station
NASA has decided to de-orbit the International Space Station (ISS). But what if your sovereign wealth fund / family foundation is interested in buying ISS and moving it to a higher orbit to preserve it as a museum for future space tourists? Is that realistic and affordable using the rockets of today? The Hohmann transfer calculator can generate some useful insights:
- The ISS is currently in circular orbit at 250 miles 0.h.mi = 250 ⏎ altitude and needs to be raised to 700 km 1.h.km = 700 ⏎ to provide a century in space before the next boost (and if humanity is unable to provide this boost a century from now, it will likely have more to worry about than a reentering space station!). The model infers that an 82 m/s burn will shift the ISS into a 250 mi x 700 km transfer orbit and that a subsequent 81 m/s burn once it reaches 700 km will circularize the orbit at that altitude. The period of the transfer orbit T.T ⏎ is 99 minutes and the ISS will only take half that time to ascend to its destination altitude.
- Is a Falcon Heavy rocket big enough to move the ISS through this orbit transfer? Let us assume that we’ll be using the Falcon’s upper stage to provide both burns and that its payload is propellant for raising the ISS’s orbit; the Falcon upper stage’s specific impulse is 348 seconds Stage.1.<Isp> = 348 ⏎ and thrust is 934 kN Stage.1.<T>.kN = 934 ⏎. The Hohmann transfer model incorporates a 2-stage rocket submodel wherein the initial mass of stage 2 is the payload mass of stage 1. To represent that the 4-ton Falcon stage provides both burns and no mass is ejected between burns, the stage 2 vehicle mass is set to 4 metric tons Stage.2.m.Mv.t = 4 ⏎ and the stage 1 vehicle mass is set to zero Stage.1.m.Mv = 0 ⏎, whereas the overall payload (which is the same as the stage 2 payload) is set to the 430 metric tons that the ISS weighs: Stage.m.M2.t = 430 ⏎. The model infers that it takes 21 metric tons of propellant to perform both burns Stage.Mx.t ⏎, which is good news because the Falcon Heavy rocket is able to carry up to 23 metric tons to LEO. At the level of thrust the second stage provides, it takes 78 seconds of burn time Stage.t ⏎ to produce the total required impulse, which is short compared to the orbit transfer duration of 50 minutes. Therefore it is feasible in principle to save the ISS using a $150M Falcon Heavy rocket.