FH payload - Discussion of Orbits

[RDoc]

Does anyone know what kind of orbit Elon's talking about? Is it some kind of Earth/Mars orbit?

 

[dhanson865]

Roadster cannot take pictures of Mars so I don't see any reason to get close to Mars. They can measure its orbit and verify it is correct transfer orbit to Mars. Hohmann orbit with target close to Mars limits launch window. If you want to launch outside launch window you have to forget Hohmann or meeting with Mars. FH probably has fuel for non Hohmann transfer orbit, but why would they do that?

OK so a full Hohmann transfer requires two major burns, one leaving earth orbit (the green circle) and one entering the final circularized orbit (the red circle).

You already said they can't do an insertion burn, but you also can leave out the circularizing burn. That leaves out the second burn and leaves the ship on the yellow orbit.

There is nothing magical about that yellow orbit, you can aim it to meet up with mars at any time. You just have to have enough fuel to create the yellow orbit in the shape you want at the time you leave earth. No further burns required.

Windows are about fuel limits not some hard and fast law of the universe.

SpaceX will know how much fuel they have left when they get to low earth orbit. They'll pick a flight path that gets them as close to mars as they can on an elliptical orbit with Apoapsis near Mars' orbit of the sun and Periapsis near Earth's orbit of the sun. It'll sit on that yellow orbit never hitting earth or mars for pretty much forever.

Elon Musk on Twitter

Payload will be my midnight cherry Tesla Roadster playing Space Oddity. Destination is Mars orbit. Will be in deep space for a billion years or so if it doesn’t blow up on ascent.

There is the possibility you could interpret that tweet to mean that they will send it on an even further out ellipse that it will cross Mars orbit and work outwards from there but I'm assuming they'll keep it between Earth orbit and Mars orbit just doing ellipses in between the two orbits.

 

[jkn]

OK so a full Hohmann transfer requires two major burns, one leaving earth orbit (the green circle) and one entering the final circularized orbit (the red circle).

You already said they can't do an insertion burn, but you also can leave out the circularizing burn. That leaves out the second burn and leaves the ship on the yellow orbit.

There is nothing magical about that yellow orbit, you can aim it to meet up with mars at any time. You just have to have enough fuel to create the yellow orbit in the shape you want at the time you leave earth. No further burns required.

Windows are about fuel limits not some hard and fast law of the universe.

SpaceX will know how much fuel they have left when they get to low earth orbit. They'll pick a flight path that gets them as close to mars as they can on an elliptical orbit with Apoapsis near Mars' orbit of the sun and Periapsis near Earth's orbit of the sun. It'll sit on that yellow orbit never hitting earth or mars for pretty much forever.

Elon Musk on Twitter



There is the possibility you could interpret that tweet to mean that they will send it on an even further out ellipse that it will cross Mars orbit and work outwards from there but I'm assuming they'll keep it between Earth orbit and Mars orbit just doing ellipses in between the two orbits.

Hohmann orbit (=minimum delta-v) is elliptic orbit around the Sun with min distance from Sun same as Earth's and max same as Mars has. I already wrote that non-Hohmann transfer orbits are possible. But I don't see why they would do it. Point is to prove that FH can get to Mars transfer orbit. They might do faster than Hohmann for crew. Non-Hohmann would only increase risk of colliding with Mars in future. Your picture is a Hohmann orbit. Without ion drive transfer orbit is an ellipse. What transfer orbit do you suggest? If you change first delta-v, shape and size of transfer orbit will change.

I cannot now imagine slower than Hohmann transfer orbit that would stay between Mars and Earth. Going inside of Earths orbit would increase risk of collision with Earth, but not with Mars (not before close pass of Earth would change orbit). I don't see why they would do it.

 

[dhanson865]

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Hohmann orbit (=minimum delta-v) is elliptic orbit around the Sun with min distance from Sun same as Earth's and max same as Mars has. I already wrote that non-Hohmann transfer orbits are possible. But I don't see why they would do it. Point is to prove that FH can get to Mars transfer orbit. They might do faster than Hohmann for crew. Non-Hohmann would only increase risk of colliding with Mars in future. Your picture is a Hohmann orbit. Without ion drive transfer orbit is an ellipse. What transfer orbit do you suggest? If you change first delta-v, shape and size of transfer orbit will change.

I cannot now imagine slower than Hohmann transfer orbit that would stay between Mars and Earth. Going inside of Earths orbit would increase risk of collision with Earth, but not with Mars (not before close pass of Earth would change orbit). I don't see why they would do it.

Hohmann orbit is elliptic orbit around the Sun with min distance from Sun same as Earth's and max same as your target has. But it isn't limited to just targeting Mars directly or using minimum delta v. Any orbit with that min and max sent at any time of the year is still a Hohmann orbit.

You keep talking about non-Hohmann orbits as though if you start from a suboptimal placement it isn't still Hohmann. Take a look at the definition again

In orbital mechanics, the Hohmann transfer orbit (/ˈhoʊmən/) is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it.

It says nothing about windows or optimal placement or minimum dV used. The key concept is that you use 2 burns, one at LEO and one when you meet your target at the Apoapsis of the transfer orbit.

Your elliptical orbit for a hohmann transfer can be nearly circular or super stretched out past the oort cloud or anywhere in-between. The size of the transfer is only one factor in the hohmann method.

You elipse can be started from anywhere in the 360 degrees of the LEO, just wait until you are at the right part of the orbit to start your burn and you have moved the elipse to point further ahead or behind. That change in starting point doesn't make it non-hohmann.

You absolutely can use a hohmann transfer outside the optimal earth to mars window without calling it non-hohmann.

Since SpaceX isn't trying to insert into mars orbit the goal is up to them but I'm assuming it is a hohmann transfer that gets them as close to mars as possible without entering the gravity well (avoiding any change of the transfer orbit) and just staying in the transfer orbit.

It is possible that they are going to do the circularizing 2nd burn in the hohmann method. But personally I don't see the need if you are just going to let it orbit the sun why bother with circularizing.

Either way the end game is an eliptical or circular orbit near the orbit of mars but still actually orbiting the sun. So long as it doesn't hit anything bigger than a baseball in the next hundred years it doesn't matter too much what the specific shape of that orbit is. But I do think they'll try to get close to mars on the first pass.

 

[jkn]

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Hohmann orbit is elliptic orbit around the Sun with min distance from Sun same as Earth's and max same as your target has. But it isn't limited to just targeting Mars directly or using minimum delta v. Any orbit with that min and max sent at any time of the year is still a Hohmann orbit.

You keep talking about non-Hohmann orbits as though if you start from a suboptimal placement it isn't still Hohmann. Take a look at the definition again



It says nothing about windows or optimal placement or minimum dV used. The key concept is that you use 2 burns, one at LEO and one when you meet your target at the Apoapsis of the transfer orbit.

Your elliptical orbit for a hohmann transfer can be nearly circular or super stretched out past the oort cloud or anywhere in-between. The size of the transfer is only one factor in the hohmann method.

You elipse can be started from anywhere in the 360 degrees of the LEO, just wait until you are at the right part of the orbit to start your burn and you have moved the elipse to point further ahead or behind. That change in starting point doesn't make it non-hohmann.

You absolutely can use a hohmann transfer outside the optimal earth to mars window without calling it non-hohmann.

Since SpaceX isn't trying to insert into mars orbit the goal is up to them but I'm assuming it is a hohmann transfer that gets them as close to mars as possible without entering the gravity well (avoiding any change of the transfer orbit) and just staying in the transfer orbit.

It is possible that they are going to do the circularizing 2nd burn in the hohmann method. But personally I don't see the need if you are just going to let it orbit the sun why bother with circularizing.

Either way the end game is an eliptical or circular orbit near the orbit of mars but still actually orbiting the sun. So long as it doesn't hit anything bigger than a baseball in the next hundred years it doesn't matter too much what the specific shape of that orbit is. But I do think they'll try to get close to mars on the first pass.

I avoided apoapsis (= point in elliptical orbit farthest from central mass) and periapsis (= closest) because I assume not all readers know those terms, but for clarity I'll use them.

Hohmann transfer orbit - Wikipedia
"In orbital mechanics, the Hohmann transfer orbit (/ˈhoʊmən/) is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane."

Picture shows an elliptical transfer orbit with periapsis same as radius of inner circular orbit and apoapsis radius of outer one. This is minimum delta-v transfer orbit. According to my memory this is also in definition of Hohmann transfer orbit. Jerry Abbott in talk page of above link verifies this and gives more info.

With these conditions everything becomes fixed. Launch time is set by launch window, first burn has fixed delta-v vector and second delta-v is also fixed (can be done with aerobrake, but is not done for Roadster). Travel time is also fixed. Wikipedia page derives equation for travel time. It depends only on radiuses of from and to orbits (and mass of the Sun). So only one travel time is possible. In real situation they don't follow Hohmann orbit exactly, this increases delta-v and changes travel time.

They want Roadster not to collide with Earth or Mars for millions of years, so apoapsis and periapsis should be between orbits of Earth and Mars. Rocket burn done at periapsis changes apoapsis of the orbit and vice versa. This creates a problem because upper stage of Falcon is not designed to operate long in space (battery power, temperature control). I don't know how long it remains operational, so I don't know if they can significantly rise periapsis. Rising periapsis will increase period of orbit. Lower apoapsis will shorten period of orbit. So if Roadster is launched before launch window, it will not get close to Mars on first orbit.