HopDavid
Hop David
Whan a transfer orbit is tangent to both departure and destination orbits, velocity vectors point in the same direction and no delta V is needed for direction change, only speed change.
The most well known tangent transfer orbit is the Hohmann transfer orbit which links two coplanar, circular orbits:
But what if the destination orbit is an ellipse?
Then there are many possible transfer orbits:
Note the purple transfer orbit moves less than 180 degrees about the sun to reach it's destination. So it's possible to reach the destination in substantially less time than a standard Hohmann orbit.
I whomped up a spreadsheet to find tangent transfer orbits:
http://clowder.net/hop/TMI/TanEll.xls
You type in the destination orbit's semi major axis (in A.U.) and the destination orbit's eccentricity in the colored cells in the upper left corner. You get a range of transfer orbits from rendezvous at destination orbit's aphelion to destination orbit's perihelion.
Trip time cells have conditional formatting that make shortest trip time easy to find.
V infinity at earth departure and destination arrival are given.
In the uploaded verion, a1 = 1.52, e1 = .093, which describes Mars' orbit. I found a trip time of 210 days, earth Vinf 2.68 km/sec, Mars Vinf 2.85 km/sec.
A pdf that tries to explain reasoning behind cell formulas:
http://clowder.net/hop/TMI/TanEll.pdf
Some caveats:
Assumes coplanar orbits.
Assumes circular earth orbit, r=1 A.U.
Assumes destination orbit has perihelion > 1 A.U.
Sadly, I make lots of misteaks and the spreadsheet is large and complicated. There may still be errors hiding in the woodwork.
I hope this spreadsheet will be useful to some folks.
Haven't figured out how often windows to tangent transfer orbits occur. I will venture a guess once each synodic period. I would also guess windows to best trip time tangent transfer orbits are a rare event.
The most well known tangent transfer orbit is the Hohmann transfer orbit which links two coplanar, circular orbits:
But what if the destination orbit is an ellipse?
Then there are many possible transfer orbits:
Note the purple transfer orbit moves less than 180 degrees about the sun to reach it's destination. So it's possible to reach the destination in substantially less time than a standard Hohmann orbit.
I whomped up a spreadsheet to find tangent transfer orbits:
http://clowder.net/hop/TMI/TanEll.xls
You type in the destination orbit's semi major axis (in A.U.) and the destination orbit's eccentricity in the colored cells in the upper left corner. You get a range of transfer orbits from rendezvous at destination orbit's aphelion to destination orbit's perihelion.
Trip time cells have conditional formatting that make shortest trip time easy to find.
V infinity at earth departure and destination arrival are given.
In the uploaded verion, a1 = 1.52, e1 = .093, which describes Mars' orbit. I found a trip time of 210 days, earth Vinf 2.68 km/sec, Mars Vinf 2.85 km/sec.
A pdf that tries to explain reasoning behind cell formulas:
http://clowder.net/hop/TMI/TanEll.pdf
Some caveats:
Assumes coplanar orbits.
Assumes circular earth orbit, r=1 A.U.
Assumes destination orbit has perihelion > 1 A.U.
Sadly, I make lots of misteaks and the spreadsheet is large and complicated. There may still be errors hiding in the woodwork.
I hope this spreadsheet will be useful to some folks.
Haven't figured out how often windows to tangent transfer orbits occur. I will venture a guess once each synodic period. I would also guess windows to best trip time tangent transfer orbits are a rare event.
