Calculating propulsion burns

If you were in a space vessel and wanted to calculate the amount of
thrust and length of a burn, what equation(s) would you need to
consider to reach a destination like an asteroid (excluding the
gravity wells of celestial bodies nearby)?

I figure you would at least need the distance to target object, your
velocity, and the velocity and heading of the target. You may also
want to consider the duration of travel and fuel consumption. Am I
missing any other parameters?

If anyone knows a web resource dedicated to this subject, please share
as well.

"Bruce C. Miller" wrote in message
oups.com...
If you were in a space vessel and wanted to calculate the amount of
thrust and length of a burn, what equation(s) would you need to
consider to reach a destination like an asteroid (excluding the
gravity wells of celestial bodies nearby)?

I figure you would at least need the distance to target object, your
velocity, and the velocity and heading of the target. You may also
want to consider the duration of travel and fuel consumption. Am I
missing any other parameters?

If anyone knows a web resource dedicated to this subject, please share
as well.


It gets complicated if spacecraft and target are in
orbits, such as around the Sun. Then there are a
whole range of tradeoffs to consider in terms of
fuel, time, windows of opportunity, and so on.

Rather than a web resource, I can recommend the book
Fundamentals of Astrodynamics by Bate, Mueller, and
White. Not expensive but quite informative.

Greg Neill wrote:

It gets complicated if spacecraft and target are in
orbits, such as around the Sun.

Basically, it isn't possible to ignore gravity unless you are
going such a short distance that you don't need to do any
calculations at all.

Rather than a web resource, I can recommend the book
Fundamentals of Astrodynamics by Bate, Mueller, and
White. Not expensive but quite informative.

I don't don't suppose that is George E. Mueller, NASA
administrator for manned flight during Apollo? I sat next
to him at lunch one time and didn't realize it until he left the
table, because I didn't know that 'Mueller' is pronounced
like 'Miller'. And also because I wasn't talkative enough to
engage him. Arrrggghh.

-- Jeff. in Minneapolis

"Jeff Root" wrote in message
oups.com...

Greg Neill wrote:

It gets complicated if spacecraft and target are in
orbits, such as around the Sun.

Basically, it isn't possible to ignore gravity unless you are
going such a short distance that you don't need to do any
calculations at all.

Rather than a web resource, I can recommend the book
Fundamentals of Astrodynamics by Bate, Mueller, and
White. Not expensive but quite informative.

I don't don't suppose that is George E. Mueller, NASA
administrator for manned flight during Apollo? I sat next
to him at lunch one time and didn't realize it until he left the
table, because I didn't know that 'Mueller' is pronounced
like 'Miller'. And also because I wasn't talkative enough to
engage him. Arrrggghh.

Cool. No, the author is Donald D. Mueller.

"Bruce C. Miller" wrote in message
oups.com...
If you were in a space vessel and wanted to calculate the amount of
thrust and length of a burn, what equation(s) would you need to
consider to reach a destination like an asteroid (excluding the
gravity wells of celestial bodies nearby)?

I figure you would at least need the distance to target object, your
velocity, and the velocity and heading of the target. You may also
want to consider the duration of travel and fuel consumption. Am I
missing any other parameters?

If anyone knows a web resource dedicated to this subject, please share
as well.


A lot of the extra complication involves arriving at the target with zero or
nearly zero relative velocity, or (if you intend this) going into an orbit
around the object.

And yes, fuel consumption is a major parameter.

Even back in the 1960s I can remember working with astro-dynamics people who
used numerical methods to calculate a minimum fuel rendezvous manoeuvre by
trial and error methods*. I am not sure if there are any simple analytical
methods other than, for example, the Hohmann ellipse.

*They used what was then a humongous computer to calculate the fuel
consumption for lots of different starting and ending points, then used
mathematical methods to locate the minimum on a contour map of the fuel used
(z-axis) vs starting date (x-axis) and finishing date (y-axis). There was
more to it than that, but you get the idea. They would use a similar method
to find the ideal direction vector for each rocket thrust manoeuvre as well.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

On Apr 28, 2:37 pm, "Greg Neill" wrote:
"Bruce C. Miller" wrote in ooglegroups.com...

If you were in a space vessel and wanted to calculate the amount of
thrust and length of a burn, what equation(s) would you need to
consider to reach a destination like an asteroid (excluding the
gravity wells of celestial bodies nearby)?

I figure you would at least need the distance to target object, your
velocity, and the velocity and heading of the target. You may also
want to consider the duration of travel and fuel consumption. Am I
missing any other parameters?

If anyone knows a web resource dedicated to this subject, please share
as well.

It gets complicated if spacecraft and target are in
orbits, such as around the Sun. Then there are a
whole range of tradeoffs to consider in terms of
fuel, time, windows of opportunity, and so on.

Rather than a web resource, I can recommend the book
Fundamentals of Astrodynamics by Bate, Mueller, and
White. Not expensive but quite informative.

Thanks for the tip. I ordered a copy of this, though I think it might
be a little overkill for my needs. This is for a simulator I'm working
on (the focus of which isn't really the space travel so much), and I
was hoping to keep things as simple as possible at first by ignoring
certain complicating permutations, then adding complexity as needed. I
suppose you can't do this completely, since as long as your target is
travelling in a elliptical solar orbit, the calculations will never
really be that simple. However, since the scope of what I'm trying to
do isn't on quite such a large scale, perhaps I can still ignore this
if both the vessel and the target object were in both orbiting the Sun
at similar relative orbits. For example, if you were in a vessel in
the asteroid belt and wanted to travel to a nearby asteroid within it,
I don't think it would kill realism too much to ignore this factor.

On Apr 29, 4:19 am, "Mike Dworetsky"
wrote:
"Bruce C. Miller" wrote in ooglegroups.com...

If you were in a space vessel and wanted to calculate the amount of
thrust and length of a burn, what equation(s) would you need to
consider to reach a destination like an asteroid (excluding the
gravity wells of celestial bodies nearby)?

I figure you would at least need the distance to target object, your
velocity, and the velocity and heading of the target. You may also
want to consider the duration of travel and fuel consumption. Am I
missing any other parameters?

If anyone knows a web resource dedicated to this subject, please share
as well.

A lot of the extra complication involves arriving at the target with zero or
nearly zero relative velocity, or (if you intend this) going into an orbit
around the object.

Yes, that's true. If we ignored gravity, and both objects started out
stationary with respect to each other, it would be a simple matter of
applying an equivalent amount of thrust in the opposite direction, I
will probably go with that for now, to keep things simple.

And yes, fuel consumption is a major parameter.

Even back in the 1960s I can remember working with astro-dynamics people who
used numerical methods to calculate a minimum fuel rendezvous manoeuvre by
trial and error methods*. I am not sure if there are any simple analytical
methods other than, for example, the Hohmann ellipse.

*They used what was then a humongous computer to calculate the fuel
consumption for lots of different starting and ending points, then used
mathematical methods to locate the minimum on a contour map of the fuel used
(z-axis) vs starting date (x-axis) and finishing date (y-axis). There was
more to it than that, but you get the idea. They would use a similar method
to find the ideal direction vector for each rocket thrust manoeuvre as well.