Ok, scientific types,  here's a challenge:


Review your orbital mechanics classes in high school?

No?

Well, how about some basic info you got on orbital mechanics during your physics class,
or any other?



OK, here's a very brief review, instead:


For any given celestial body,    earth, for example,   there is a minimum theoretical velocity at which
an object can be in orbit around it.      This is the minimum orbital velocity.   At this velocity,
the object in orbit is falling toward the planet at the same rate that the planet is falling away from it.

On earth, orbit isn't practical unless the orbit is high enough that the atmosphere is not a significant
drag factor for the item in orbit.   And of course the orbit must clear all obstacles such as mountain ranges, etc.


The minimum orbital height is also the point at which the time of orbit is least.    The fastest
circuits around the planet are at the minimum orbital distance.

However, in terms of raw speed,  the fastest orbital time is achieved at the SLOWEST possible
orbital velocity.

If you have surplus orbital velocity,  you end up in a higher orbit,  and since the distance to travel
around the planet increases greatly,  being a much larger circumference,  you will end up in an
orbit that takes longer to complete even though you're actually moving faster.

This is why satellites that are in high geosynchronous orbits (they hover over one given spot on earth)
have to be boosted to much higher orbital velocities.      A geosynchronous orbit of earth
occurs at 22,400 miles altitude,  assuming you have the velocity to maintain it.

So the higher you orbit, the faster your satellite must be moving, and the longer the orbit takes.


Now let's complicate things by changing a condition,   and that condition is gravity.


As you get farther away from earth,   the strength of gravity diminishes.

As the strength of gravity is much less at a high orbit,   the orbital velocity has to be REDUCED
to maintain an orbit.

The farther away from earth,   the slower the orbital velocity must be,  BEYOND A CERTAIN DISTANCE.

To launch a satellite into a VERY high orbit,  it has to be sent out fast to get high enough,
and then, at a certain point,  a stable orbit beyond it requires the satellite to be slowed DOWN
for insertion into the desired high orbit.

Otherwise, it'll just fly off into space as gravity won't hold it.


My challenge to you is,   post formulas or charts that show this.   Orbital velocities required
to achieve different orbits, from low earth orbit to the very large orbits (like the moon's orbit)
where the orbital velocity is LOWER than that of satellites in lower orbits.


I've never yet seen any charts or formulas that explain this.


Can you come up with it?


CJ

Quoted: I see where you are coming from. I am using the gravitational constant whereas you are assuming the reduction in gravity as the radius increases.

Yes.   The two interact strongly beyond a certain point.

I have yet to see this rolled together neatly into one formula, graph, or chart.

But somebody must know.


We couldn't have made it to the moon without it.

CJ

Quoted: So the higher you orbit, the faster your satellite must be moving, and the longer the orbit takes. You have one thing wrong, and I admit it does seem a bit confusing.  Objects at higher orbits actually orbit at slower speeds in addition to having a longer path to orbit.  They do not travel faster.  The farther away you get, gravity has less of an effect so you don't have to travel as fast.

No, I wasn't wrong there,  THAT is the whole idea, summed up.

For a given body....earth....the required velocity to achieve a circular orbit (always assume circular rather than any other orbit to keep this from being too hairy)  increases with distance (altitude) but
only to a certain point.  Beyond that point,  gravitational attraction has reduced the orbital velocity requirement.


What I want to know is,  what IS the point of maximum orbital velocity and what's that orbital height?

And,  what's a graph, chart, or forumula that allows you to calculate the CORRECT orbital velocity
for any given distance,  assuming the body being orbited is always the same (earth) and is massive,
and the satellite has negligble mass?    (Fewest variables.)


Nice to see some brains being put to work here!

CJ