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I've got an assignment for my University orbital mechanics course. I couldn't find the place in the 'Homework' section, so i thought here would be ok.

I've got a few pretty simple questions, however I can't find any info in my lecture notes, or off the internet that answers them enough.

1)

When leaving a low earth orbit (LEO) to another planet, or moon, or anywhere on a hohmann transfer, do you have to leave from an equitorial orbit, where the inclination is 0? If so, why?

Why can't you just be on an orbit of 28 degrees latitude, and then fire the rockets to get into a Hohmann transfer?

Spoiler 2)

If doing an inclination change for a Low earth orbit (LEO), the formula is delta V = 2vsin∆i/2. For example, if the initial circular orbit velocity was 10km/s and the deltav was 0.5km/s , would the final velocity be 10.5km/s? Would both orbits still be the same radius? Or would the spacecraft have to reduce 0.5km/s after it does the plane change to get back to 10km/s to stay in the same radius LEO?

3)

A Hohmann transfer is the most fuel efficient (lowest deltav) method only if the r2/r1 < 11.8 (from my lecture notes). If I have radioactive material in a LEO around Earth, and I want to send it into the sun, the ratio of r2/r1 is WAY bigger than 11.8. Does this mean, that thebest deltav (lowest deltav)is not a Hohman transfer? If not, what is the best deltav?

Spoiler 4)

How do you calculate the deltav for going from LEO to a polar orbit around Mars.

I have so far gathered the following, but am a bit unsure about some parts:

Leave LEO and go into a Hohmann transfer to Mars orbit

When in mars orbit, change inclination to 90 degrees

Firstly calculate the velocity required to get into an elliptical orbit with Mars at the apohelion, and Earth at the perihelion. Then minus this velocity from the velocity the Earth is travelling relative to the Sun.

My lecture notes go on to find another deltav, for the hyperbolic escape from LEO. So you find the perigee velocity (or apogee, i forget which is which), using the velocity found just before, and minus that from the initial speed you have in the LEO, and that is the deltav. Why do you have to find two deltav ? Which one is the actual deltav required to send the spacecraft to Mars?

5)

Finally, and hopefully my last question:

How do you escape from the solar system. I know you need a hyperbolic escape (because parabolic has zero energy at radius infinity). But do you only need hyperbolic escape from Earth, or do you take into account the Sun also. I mean, do you have to do two Hyperbolic escapes? One for Earth, then another for the Sun also?

I really really really appreciate any feedback, comments, help, detailed help :)

Thanks in advance for anything and sorry if this is a repeat of a topic made earlier today, or yesturday. I did a quick search, but i admit i didnt spend long enough searching. I actually don't know what to search for, and I'm sick of searching after spending the last two days on the computer searching.

John.

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# Help with basic orbital mechanics

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