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Kushal C
Kushal C
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I would like to use calculus to try and model the optimal path to mars in space, assuming the rocket starts with an initial velocity in the vacuum of space, and only accelerates due to the Sun's gravity. By ideal, I mean the path where the sun has the greatest positive effect on the rocket (bringing it closer to mars). So far, I have set the starting point of the path at the perihelion of earth, in order to maximize the assistive gravitational forces when the rocket initially leaves Earth. I know of Hohmann transfer, and that it is the best path for the rocket, but I need to know how to show this using calculus for my mathematics project. I have not found any calculus based, or even any proof for the Hohmann transfer. It is hard question to visualize due to its vagueness perhaps, so I am sorry about that.

I would like to use calculus to try and model the optimal path to mars in space, assuming the rocket starts with an initial velocity in the vacuum of space, and only accelerates due to the Sun's gravity. By ideal, I mean the path where the sun has the greatest positive effect on the rocket (bringing it closer to mars). So far, I have set the starting point of the path at the perihelion of earth, in order to maximize the assistive gravitational forces when the rocket initially leaves Earth. I know of Hohmann transfer, and that it is the best path for the rocket, but I need to know how to show this using calculus for my mathematics project. I have not found any calculus based, or even any proof for the Hohmann transfer. It is hard question to visualize due to its vagueness perhaps, so I am sorry about that.

I would like to use calculus to try and model the optimal path to mars in space, assuming the rocket starts with an initial velocity in the vacuum of space, and only accelerates due to the Sun's gravity. By ideal, I mean the path where the sun has the greatest positive effect on the rocket (bringing it closer to mars). So far, I have set the starting point of the path at the perihelion of earth, in order to maximize the assistive gravitational forces when the rocket initially leaves Earth. I know of Hohmann transfer, and that it is the best path for the rocket, but I need to know how to show this. I have not found any calculus based, or even any proof for the Hohmann transfer. It is hard question to visualize due to its vagueness perhaps, so I am sorry about that.

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Kushal C
Kushal C
  • 31
  • 3

How can I show the ideal path from Earth to Mars in a vacuum using calculus?

I would like to use calculus to try and model the optimal path to mars in space, assuming the rocket starts with an initial velocity in the vacuum of space, and only accelerates due to the Sun's gravity. By ideal, I mean the path where the sun has the greatest positive effect on the rocket (bringing it closer to mars). So far, I have set the starting point of the path at the perihelion of earth, in order to maximize the assistive gravitational forces when the rocket initially leaves Earth. I know of Hohmann transfer, and that it is the best path for the rocket, but I need to know how to show this using calculus for my mathematics project. I have not found any calculus based, or even any proof for the Hohmann transfer. It is hard question to visualize due to its vagueness perhaps, so I am sorry about that.