Question about Hohmann transfer

[njezza]

I have a question about hohmann transfer, actually its about the influence of gravity.<br /><br />assume we going from earth to mercury, and i have calculate the delta-v required for the transfer, i want to know at which point in the hohmann transfer the influence force of gravity changes from Earth to Sun, that is the point at which the spacecraft is under the influence of the sun only.<br /><br />many thanks!!

 

[jimfromnsf]

If you are using hand calculations, you need to use patched conics. <br />On an Earth to Mercury transfer, a hyperbolic trajectory is required to escape the gravity well of the Earth, an elliptical trajectory is required to transfer from Earth's sphere of influence to Mercury's using the Sun as the only influence and then hyperbolic "flyby" of Mercury so it can be captured .

 

[njezza]

thanks for the answer Jim.<br /><br />anyone have a good website for how to determine the position along hyperbolic trajectory, I just read through the notes about determine the position along the elliptical orbit, but notes doest say how to calculate it for hyperbolic trajectory.

 

[tony873004]

Your spacecraft will never be under the influence of the Sun only. But you might consider the Hill Sphere as the place where you've left Earth's influence. Even deep in Earth's Hill Sphere, you're still on a hyperbolic trajectory the moment you complete your burn.<br /><br />Calculate how much delta v you need to get from the orbit of Earth to the orbit of Mercury. Then use the formula sqrt(2GM/r + v), where v is the delta v you just computed, M is the mass of the Earth (5.97e24) and r is your distance from Earth in a circular orbit. This calculates how much delta v you need to escape Earth, and give you the required extra velocity to reach Mercury's orbit. Make sure you perform your burn such that your trajectory away from Earth is in line with Earth's orbital motion in a retrograde direction. And do it at the right time of year so that when you reach the orbit of Mercury, Mercury is there waiting for you.

 

[njezza]

Thanks for the reply Tony.<br /><br />The v in the the formula sqrt(2GM/r + v) is the first delta v which make the s/c leave the earth, isnt it? not the toltal delta v cuz the total delta v includes another delta v at the other end of the hohmann transfer.

 

[tony873004]

The v is the amount of excess hyperbolic velocity you need to get from the orbit of Earth to the orbit of Mars. This formula computes for you the total delta v for a single burn from low earth orbit to the orbit of Mars.<br /><br />Most real spacecraft that we send to Mars use just a single burn to escape low earth orbit and propel them towards Mars, and then some minor correction burns along the way that are rather insignificant to the first burn.<br /><br />In real life, the fact that Earth and Mars do not share orbital planes complicates things a bit, but Mars can still be reached directly from low Earth orbit plus some fine tuning correction burns along the way.