How low can you orbit?

In article ,
Jan Philips wrote:
Some of the early US manned orbital flights orbited only a little more
than 100 miles up. How low can you orbit? What is the relationship
between height and the maximum number of orbits?

There isn't a simple relationship, because it depends on things like the
density of the satellite and the state of the (highly variable) upper
atmosphere. Generally speaking...

Orbits at 200km and below are now considered suitable only as short-term
(a few hours) parking orbits; the decay in altitude is quite noticeable
and the orbital lifetime is a few days at most. About the lowest orbit
that has seen practical use is the 160km parking orbit used by the later
Apollos, which were leaving orbit (one way or another) within hours.

LDEF was retrieved by the shuttle when its orbit had decayed to about
240km, and that was considered a last-minute save -- the mission would not
have been feasible had it gotten much lower. There have been only one or
two other shuttle flights that low.
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |

Jan Philips writes:

Some of the early US manned orbital flights orbited only a little more
than 100 miles up. How low can you orbit? What is the relationship
between height and the maximum number of orbits? For instance, if you
go into a circular orbit at 100 miles, how many orbits can it stay in
orbit? Can you orbit at 95 miles? Etc.

Bear with me, I'll answer most of your questions.

First, there is no simple answer to how low can you orbit, although 100
miles (and note, every time I say miles I mean statute miles, which is
what you meant too. The only reason I feel I have to mention this is
that NASA, in its quest to use units no one in their right mind would
use, often expresses heights in nautical miles (AND statute miles AND
feet AND (but rarely) kilometers). When you are in an elliptical orbit,
force applied at the perigee (low point) tends to modify your apogee
(high point) and vice versa. The effect of this, for elliptical orbits,
is that they tend to become circular, as the larger friction force at
perigee lowers the apogee much quicker than the smaller friction force
applied at apogee (this is, of course, a simplification, as friction
operates all through the orbit, not just at apogee and perigee). Then,
once the orbit becomes circular, it tends to stay pretty circular,
although it is really spiralling in faster and faster. It turns out
that a 100 mile high circular orbit will last about a day, give or take
hours (this number varies because the density of the atmosphere varies,
mostly due to solar activity, and I might be off about a day, but it's
the right order of magnitude).

So, some examples. John Glenn's Friendship 7 entered a 99x165 mile
orbit, and he was told he was "go for 7 orbits". That doesn't mean that
he would have reentered after 7 orbits, just that the ground was certain
he wouldn't enter any earlier than that, so there was no need to worry
about completing his 3 orbit mission. Valery Bykovsky's Vostok 5
entered a 108x138 mile orbit, which was too low for its planned 8 day
mission, and by 5 days into the flight had decayed into an orbit below
100 miles circular and had to be brought down.

Some earlier US spy satellites would lower themselves from an orbit
about 400 miles circular to one of about 75x400 miles for an orbit or
two to get that much close to the target they were filming. They would
have to get out of that orbit quickly to avoid reentering and/or burning
up.

The shuttle's so-called direct insertion trajectory puts it into an
"orbit" with a perigee around 30 miles and an apogee above 200 miles.
This is not an orbit that will last even twice around the earth, which
is the reason for the OMS burn performed at first apogee to raise the
perigee safely out of the dense atmosphere. Even the reentry burn
doesn't really take a spacecraft out of orbit; it lowers the perigee so
low (around 20 - 30 miles) that the frictional losses quickly do the
rest and take the spacecraft out of orbit.

On Tue, 23 Sep 2003 14:29:42 -0400, Chris Jones wrote:

First, there is no simple answer to how low can you orbit, although 100
miles (and note, every time I say miles I mean statute miles, which is
what you meant too.

Right. Some of the early missions had perigees as low as 154 km (e.g.
Sigma 7), which is ~95.7 statute miles.

It turns out
that a 100 mile high circular orbit will last about a day, give or take
hours (this number varies because the density of the atmosphere varies,
mostly due to solar activity, and I might be off about a day, but it's
the right order of magnitude).

So a 95 statute mile circular orbit may last a few hours? At 80-90
miles would you be able to make one orbit? (Assume average
atmospheric conditions and a Mercury or Gemini spacecraft.)

Some earlier US spy satellites would lower themselves from an orbit
about 400 miles circular to one of about 75x400 miles for an orbit or
two

That must be just about the limit, since I've read that at 400,000
feet (75 miles) you start to get noticeable drag.

On or about Tue, 23 Sep 2003 17:29:08 GMT, Henry Spencer
made the sensational claim that:
There isn't a simple relationship, because it depends on things like the
density of the satellite and the state of the (highly variable) upper
atmosphere. Generally speaking...

Because you're Henry...What about a lunar orbit?
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In article ,
says...
On or about Tue, 23 Sep 2003 17:29:08 GMT, Henry Spencer
made the sensational claim that:
There isn't a simple relationship, because it depends on things like the
density of the satellite and the state of the (highly variable) upper
atmosphere. Generally speaking...

Because you're Henry...What about a lunar orbit?

LOL -- I'm not Henry, but sometimes I play him on TV... well, OK, on my
video camera...

Obviously, lunar orbits are not affected in the same way by atmospheric
drag. The Apollo landings temporarily doubled (or more) the Moon's
atmosphere with the gas from the LM engine exhausts. So drag is not an
issue. You can remain in orbit with no drag effects at an altitude of as
low as 10 miles.

However, lunar orbits deteriorate quickly because of the Moon's uneven
gravitational field. The maria deposited into impact basins are made of
basaltic rock that is denser than the surrounding terrain, so there are
positive gravitic anomalies over most of the maria. That means that
spacecraft "fall" faster as they pass over these mass concentrations
(mascons) and "slow down" as they pass away from them. This disturbs
lunar orbits, causing them to become more and more misshapen over
relatively short timeframes.

The subsatellite carried by Apollo 16 was released into an orbit that was
roughly 70 statute miles high, circular. (It was actually a slightly
lopsided orbit, but close enough to 70 miles circular to make no
difference in the current discussion.) That satellite was drawn into an
orbit that intersected the surface after only six weeks.

My impression is that lunar orbital spacecraft aren't "dragged down" by
having energy removed from their trajectories, as upper atmospheric drag
does to earth orbital vehicles. It's more that the *shape* of their
orbits are changed by the mascons until the trajectory intersects the
surface.

--

Do not meddle in the affairs of dragons, for | Doug Van Dorn
thou art crunchy and taste good with ketchup |

In article ,
says...
On Tue, 23 Sep 2003 14:29:42 -0400, Chris Jones wrote:

snip

So a 95 statute mile circular orbit may last a few hours? At 80-90
miles would you be able to make one orbit? (Assume average
atmospheric conditions and a Mercury or Gemini spacecraft.)

Yes, a 95 statute mile orbit would last a few hours. The J mission
Apollo spacecraft entered circular parking orbits that were about 95
miles high and stayed there for one and a half orbits prior to TLI.
These missions launched into parking orbits about 10 miles lower than the
earlier missions to accomodate the greater weight of the spacecraft --
they spent a little less energy getting to the parking orbit to leave
enough for a TLI maneuver to get the whole package out to the Moon.

--

Do not meddle in the affairs of dragons, for | Doug Van Dorn
thou art crunchy and taste good with ketchup |

In article ,
Doug... wrote:
...spacecraft "fall" faster as they pass over these mass concentrations
(mascons) and "slow down" as they pass away from them. This disturbs
lunar orbits, causing them to become more and more misshapen over
relatively short timeframes.

The effect of a single mascon is relatively simple to analyze to a first
approximation: it changes the *direction* of the orbital motion slightly
without changing the speed. This translates into (skipping some details)
a semi-random change in the eccentricity of the orbit: the overall size
of the orbit doesn't change, but how elliptical it is does. The change
can be for better or for worse, i.e. less or more elliptical.

My impression is that lunar orbital spacecraft aren't "dragged down" by
having energy removed from their trajectories, as upper atmospheric drag
does to earth orbital vehicles. It's more that the *shape* of their
orbits are changed by the mascons until the trajectory intersects the
surface.

Correct. As the value of the eccentricity wanders around randomly, the
orbit gets less or more elliptical. If it ever gets elliptical enough
that its lowest point is at or below the surface, it's game over. For a
low lunar orbit, mascon effects are strong enough that this tends to
happen fairly quickly.

(It is possible that there are stable low orbits around the Moon, where
the mascon effects cancel out, at least for a while. We don't know enough
to predict where they might be, because we don't have good gravity maps of
the lunar farside. All gravity mapping to date has been based on tracking
from Earth, which is impossible over most of the farside. You can get a
little bit of information by looking at how the orbit has changed when the
spacecraft comes back into view, but not very much. There have been many
proposals to do farside gravity mapping, using a pair of satellites and an
intersatellite radio-tracking link, but so far it hasn't been done.)
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |

In article , says...
In article ,
Doug... wrote:

snip

My impression is that lunar orbital spacecraft aren't "dragged down" by
having energy removed from their trajectories, as upper atmospheric drag
does to earth orbital vehicles. It's more that the *shape* of their
orbits are changed by the mascons until the trajectory intersects the
surface.

Correct. As the value of the eccentricity wanders around randomly, the
orbit gets less or more elliptical. If it ever gets elliptical enough
that its lowest point is at or below the surface, it's game over. For a
low lunar orbit, mascon effects are strong enough that this tends to
happen fairly quickly.

Consider that the Apollo 15 CSM/LM stack was placed into the descent
orbit on LOI day, at the end of the second rev. The crew went to bed as
per the flight plan, the next day being PDI day. They were awoken a bit
early because, in roughly 12 hours after the DOI burn, the pericynthion
that had started at 50,000 feet had degraded to about 35,000 feet -- the
height at which airliners fly over the earth. And that was after only 12
hours. (They had to do a quick RCS bail-out burn to get back into the
proper orbit for CSM circ and LM PDI later that day.)

Of course, Apollo 15 was the first Apollo mission to directly overfly the
large mascons of Serenitatis and Imbrium, so there wasn't a lot of
experience in how those mascons would affect a descent orbit. However, I
will point out that Apollo 17, which overflew the same mascons, was put
into a descent orbit with an 80,000-foot pericynthion. This was because
the landing site was farther east, and if there had been an overburn on
the DOI-1 burn, there might not have been time to track and establish the
correct bail-out burn parameters before impact. But I think a small part
of the reason for the 80,000-foot PC was that the mission planners
remembered the degradation of 15's descent orbit and wanted to give the
stack a little more leeway, just in case it happened again.

--

Do not meddle in the affairs of dragons, for | Doug Van Dorn
thou art crunchy and taste good with ketchup |

On Tue, 23 Sep 2003 17:14:02 -0400, Chris Jones wrote:

I'm taking a somewhat educated guess here, and my guess is "maybe". At
the high end (90 miles), I'd guess probably, and at the low end (80
miles), I'd guess "probably not",

Thanks, that gives me a good enough idea.

(Henry Spencer) writes:

[...]

Correct. As the value of the eccentricity wanders around randomly, the
orbit gets less or more elliptical. If it ever gets elliptical enough
that its lowest point is at or below the surface, it's game over. For a
low lunar orbit, mascon effects are strong enough that this tends to
happen fairly quickly.

(It is possible that there are stable low orbits around the Moon, where
the mascon effects cancel out, at least for a while. We don't know enough
to predict where they might be, because we don't have good gravity maps of
the lunar farside. All gravity mapping to date has been based on tracking
from Earth, which is impossible over most of the farside. You can get a
little bit of information by looking at how the orbit has changed when the
spacecraft comes back into view, but not very much. There have been many
proposals to do farside gravity mapping, using a pair of satellites and an
intersatellite radio-tracking link, but so far it hasn't been done.)

What this means is that the orbital environment around the moon is chock
full of opportunities and hazards for spacecraft spending a bit of time
there, and that accurate charts of its gravitation field will be a
precious thing for navigators to have. So the low grade rumble you're
hearing throughout this discussion is a wish for some attention to be
paid to acquiring this information.