Earth-Jupiter fast transit

I'm trying to figure out time-of flight for hyperbolic fast transits
from Earth to Jupiter, and it's not going well. Can anybody point me
towards either a table of such (with, say, varius departure V's at
earth, and the time of flight to Jupiter orbit), or perhaps a
spreadsheet or some such that does the same?

Alternatively... if you wanted to get to Jupiter in 3 months, or six
months, and you had an arbitrarily short thrust time (i.e. high thrust
system), how fast would you have to go? And how fast would you be going
at Jupiter?

Elliptical Hohmann orbits are *so* much easier...

--
Scott Lowther, Engineer
Remove the obvious (capitalized) anti-spam
gibberish from the reply-to e-mail address

Scott Lowther wrote:
I'm trying to figure out time-of flight for hyperbolic fast transits
from Earth to Jupiter, and it's not going well. Can anybody point me
towards either a table of such (with, say, varius departure V's at
earth, and the time of flight to Jupiter orbit), or perhaps a
spreadsheet or some such that does the same?

Alternatively... if you wanted to get to Jupiter in 3 months, or six
months, and you had an arbitrarily short thrust time (i.e. high thrust
system), how fast would you have to go? And how fast would you be going
at Jupiter?

Elliptical Hohmann orbits are *so* much easier...


That's a good homework problem


Given the departure state you calculate the eccentricity and semi-major
axis. Knowing the Jupiter radius, you get the true anomaly
(phase angle of the transfer) at that radius from inverting the
radius equation:

r = p / (1 + e * cos(true_anomaly))

where p = h^2 / mu, h = angular momentum, mu = G * Msun

With the true anomaly you can get the time-of-flight from Kepler's
equation:

t = sqrt(a^3 / mu) (E - e Sin(E))
where E is the eccentric anomaly.
(Here I have assumed starting from periapsis to simplify,
but this is not required)

Cos(E) = (e + cos(true_anomaly) / (1 + e * cos(true_anomaly))

These are for elliptical orbits. There are similar
time-of-flight equations for parabolic and hyperbolic orbits
if required.


Given the semi-major axis (hence energy) and the Jupiter radius
you calculate the velocity at Jupiter, or do the vectors if
you need velocity relative to Jupiter.


Looks like you can get down to 0.5 months before needing to
go hyperbolic

- Matt

JRS: In article , seen in
news:sci.space.tech, Scott Lowther .
com.retro.com posted at Mon, 29 Dec 2003 04:17:09 :-

Alternatively... if you wanted to get to Jupiter in 3 months, or six
months, and you had an arbitrarily short thrust time (i.e. high thrust
system), how fast would you have to go? And how fast would you be going
at Jupiter?

Earth's orbit radius ~ 150 Gm
Jupiter's orbit radius ~ 750 Gm
Distance ~ 600 - 900 Gm
Take worst case ; 900 Gm in 90 days is 10Gm / day.
One day is 0.1 Ms (-15%)
Hence speed required is 0.1 Mm/s

That's reasonable, since IIRC Ulysses took something like 15 months,
implying 20km/s, which seems feasible.

As you described it, you would be going 0.1 Mm/s if you did not want to
stop, or were using Jovo-braking - and, I suggest, nearer 0.0 Mm/s if
you did want to stop gently.

Earth's speed is about 30 km/s - so a significant navigational
correction hardly affecting the principle.

--
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Web URL:http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms & links;
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