Lowest orbital altitude

[orionrider]

What is the lowest orbital altitude around an (almost) airless body (apart from the obvious highest mountain)?
Could a spacecraft zip at several km/sec just meters above the peaks of Mercury?

And what about the Earth or Mars? Is it just a question of coping with the effects of the high atmosphere (drag, ionization, heating,...) ?

Thanks in advance

 

[a_lost_packet_]

Well, theoretically, anytime your physically separated from the surface of the Earth you're "in orbit" so to speak. Jump up into the air and, there ya go, you're in "orbit"... but, not for long. *

As far as traveling through an atmosphere, it's the atmosphere that provides the effects which would limit or otherwise dictate a craft's speed. One is, after all, traveling within and "through" something when flying in an atmosphere. A very light atmosphere would have consequently lighter friction related effects. But, that wouldn't do much for making "wings" useful, would it? In fact, "flying" would, by definition, be a bit difficult to do. With less of an atmosphere one would need larger wings to provide lift along with the ability to maintain enough speed for them to work... a careful balancing act. That's not much of a problem for a spacecraft as they don't rely on wings. But, in a dense atmosphere, some sort of wings would certainly be handy to help maintain the craft's stability much like a ship's rudder keeps a ship on course.

Mass plays a part in your scenario as well as the capabilities of the craft. Gravity is the result of mass and a craft will experience a stronger effect the closer it is to a mass as a result of the inverse square nature of gravity. For instance, one could travel at a relatively more speedy pace over the surface of the Moon than they could over the Earth expending the same amount of energy. But, maintaining the same distance from the Event Horizon of a Black Hole would require much more velocity.

IMO, your scenario requires three variables be known which will then dictate the answer to your question: The composition of the atmosphere, the capabilities of the craft and the mass of the planet.

*On "orbit" - You're not really in orbit as a planet's atmosphere is really part of "the planet" itself and to achieve orbit one thing you must not do is intersect the planet in any way, including its atmosphere. See aremisling's post on "Orbits"

 

[orionrider]

Well then, lets say my spacecraft is in a stable, power-off, circular orbit 200Km above the planet Mercury (no atmosphere to speak of). What if I wanted to go lower, like very low? After the necessary burn, could my craft keep a stable, un-powered circular orbit just a few meters above the highest mountain?

 

[3488]

Quick chime in, lunch time.

Well above Earth, a circular orbit of 209 KM / 130 miles is considered to be the lowest attainable (some satelitte Perigees are lower than that), but even then it would not last long due to orbital decay from atmospheric drag.

Regarding Mercury, that's interesting. Mercury's atmosphere has a TOTAL mass of only 8 tons (yes that is correct, about the mass of a small truck). Atmospheric drag will be a non issue.

Regarding skimming over mountain tops of Mercury. The orbit would NOT be stable long term. Reason being, mountains, basins, varying densities inside the planet, would cause the orbit to decay fairly quickly.

MESSENGER spacecraft on the first Mercury pass in January 2008, detected a MASCON, a MASsCONcentration, capitalized the letters the highlight the acronym, from 200 KM / 124 miles (the moon has been known to have these for quite some time, more recently as have the Jupiter moons Ganymede & Io, earlier this year ESA Mars Express detected one inside the Mars moon Phobos).

A possible extended mission of MESSENGER (assuming the one year primary mission is successful & MESSENGER is still operational, at least the main instruments), is that the Periherm (lowest point in an orbit around Mercury, apoherm the highest) of MESSENGER may be reduced to 30 KM / 18 miles, to image portions of the surface at better than one metre resolution, but also to measure smaller MASCONS.

Andrew Brown.

 

[yevaud]

Since you're on the topic, here's a useful equation: Satellite altitude/orbital characteristics

T[sub]o[/sub] = 2pi * (R[sub]p[/sub] + H') Sqrt (R[sub]p[/sub] + H' / G[sub]s[/sub] * R[sub]p[/sub][super]2[/super])

T[sub]o[/sub] = Orbital period, in seconds
R[sub]p[/sub] = Planetary radius, in Km (6800 Km for Earth)
H' = Orbital altitude, in Km, above the planet's surface
G[sub]s[/sub] = Gravitational acceleration at planet's surface (.00981 Km/S[super]2[/super] at Earth's surface)

..

 

[orionrider]

Thanks a lot!

yevaud: Cool. One could play hours with that one ;-)

Even if a gravity-alone orbit would not be stable close to the ground, a high-speed lowpass of for instance Io could still be real low. If you plan the trajectory very carefully and using very little propellant you could even skim the surface between volcanoes at incredible velocities :shock:
If they ever do that I hope they beam back some mpeg movies :mrgreen:

 

[yevaud]

Not that long ago, people were mulling around the possibility of deep tunnels, evacuated of all air, and used for mag-lev trains operating at incredible speeds. Technically, one of those in operation is in fact orbiting the Earth.

 

[orionrider]

You wouldn't even need the maglev. Once the train is accelerated to about 87 minutes per lap it is essentially weightless and goes on forever. But beware of MASCONS! And Coriolis, I guess... :shock:
And, how does one gets off at Waterloo Station? :?

On a more practical scale, I guess a SR-71 pilot flying at 1,000m/s while following the curvature of the Earth is about 1/7th lighter than lying in his bed.

 

[LKD]

3488,

Considering the proximity of the Sun to Mercury, wouldn't that be a huge factor in denying the orbiting craft from maintaining a constant hight around Mercury even before inclusion of MASCON's?

 

[normalthinker]

Assuming no atmosphere, and a perfectly smooth planet, you could in theory orbit at any height provided you are moving at the correct velocity for that height.

So yes, you could orbit a super-smooth airless planet at 1 meter altitude.

In reality, as other posters have mentioned, most planets have an atmosphere which gets in the way of ultra low orbits. The lowest stable orbit around Earth is around 85 miles. At this height your spaceship will not be heated too much by atmospheric friction, but even so an orbit at this height will decay quite quickly, less if you had a streamlined ship (i.e. shaped like a supersonic jet).

On a real airless planet, the lowest safest height would need to be above the tallest mountains, so for the Moon, 10 miles would be fine.

 

[MaDeR]

Atmosphere, atmosphere - but some seemed to forgot about grav field. It is not perfect! For example, around Moon almost no orbit (unpowered) is stable for significant amount of time due to mascons.

 

[spacefire]

I don't think "mountains and changes in density" would cause an orbit to decay. They do not substract or add energy to the spacecraft. I think once you achieve a stabel orbit over an airless planet, at any altitude, your spacecraft would continue indefinitekly.

 

[orionrider]

ah, but if you go too low the mountains can unexpectedly happen to be right on your path.
Ouch.

MASCONs would cause small changes in altitude that could be fatal if you were really skimming and not expecting the effect.

 

[Nutcracker]

The non-sphericity of the body is a major factor of the stability of the orbit. Imagine orbiting about a tear-drop shaped object. As you orbit the larger part, gravity is more significant while the top portion is much smaller and less significant. This means that as you orbit this portion the force of gravity on the ship is less, allowing you to drift slightly higher because gravity isn't holding you as tight. Now each time that you orbit you drift that much more. A few orbits later and your not even close to your original orbit.

At low orbits, atmospheric drag and gravitational distribution are key. As you get further from the body, it becomes more like a singular point mass and the uneven distribution doesn't matter as much. In higher orbits, other issues come up; such as gravitational pull from other bodies (like the sun and moon) and radiation pressure from the sun.

Simply put, the gravitational distribution does matter.

 

[orionrider]

Thanks Nutcracker, it makes sense, I hadn't thought of that. Let's fire the Vasimr to get back to a safer orbit

I see it's your first post, and a good one too. Welcome to SDC!

 

[aremisasling]

From http://en.wikipedia.org/wiki/Mass_conce ... (astronomy)

"The lunar mascons alter the local gravity in certain regions sufficiently that low and uncorrected satellite orbits around the Moon are unstable on a timescale of months or years. This acts to distort successive orbits, causing the satellite to ultimately impact the surface. "

Given the documented trajectory and velocity changes made to the Apollo missions, it's pretty clear that MASCON's are a problem for low orbits. If after only a few orbits, the MASCON's are able to put the lunar lander off course by as much as 100 miles (at a shallow trajectory, 100 miles is less than it sounds), the possibility of making the orbital characteristics so erratic as to knock a craft entirely out of orbit is very real. But gravity's effects are lessened with distance and the MASCONs' effect is diluted by surrounding terrain at the higher orbits as well, so higher orbits should remain relatively stable.

 

[sailonbye]

?? Has there been some breakthrough in physics or change of definition of 'orbit' I missed??
When did 'jumping into the air" constitute 'being in orbit "sort of" ?

 

[orionrider]

It is not clear to me if you really have to jump to be "in orbit". :?
But it is a fact that we all literally trace an 'orbit' around the center of the Earth. It may not be a 'gravitational orbit', but an orbit it is.
Maybe that is what a_lost_packet meant :?:

 

[aremisasling]

An orbit is any path that has enough velocity tangential to the surface of the body it is gravitationally bound to in order for it's path to not intersect the atmosphere or surface of that body during one revolution. As such, jumping doesn't put you in orbit, even if you were able to hover 5 ft above the ground for a full revolution. SpaceShipTwo never orbits either, as it's trajectory intersects with the atmosphere and subsequently the surface before completing one revolution. Those bodies unable to sustain tangential motion long enough for a full orbit are subdivided into non-orbital and sub-orbital based on whether or not they have reached 'space', which by international standards is 62 mi or roughly 100km for the Earth.

For a body with essentially no atmosphere, like Mercury (an exosphere, which Mercury does have, is not considered fully and atmosphere), jumping would technically put you into sub-orbit provided your jump was sufficiently tangential to the surface. However, it would be a very, very short one. On an asteroid, you may be able to jump to orbit or even into an open orbit and escape its gravity entirely. But you couldn't jump straight up into a elliptical orbit as you wouldn't have the tangential velocity component and would just fall back down. You'd have to jump at an angle to the surface. Otherwise you'd be on a ballistic 'sounding' trajectory.

 

[Jeroen94704]

But it is a fact that we all literally trace an 'orbit' around the center of the Earth. It may not be a 'gravitational orbit', but an orbit it is.

Unless you are standing exactly at the equator, you are not tracing an orbit around the center of the earth, but around some point along the length-axis (or axis of rotation) of the earth. Imagine you are standing a foot away from the north-pole. That means you are tracing a circular path with a one foot radius, and you can pretty much see the point you are orbiting around, which is definitely not the center of the earth.

Contrast this to what you call "gravitational" orbits, which are ALWAYS around the center of gravity of the Earth, and you will see these are two fundamentally different kinds of movement.

In fact, some bodies have a 2- (or more) axis rotation, induced for example by collisions. When standing on the surface of one of those, you will trace a wildly fluctuating and chaotic path. Nothing at all like a circle. Gravitational orbits around such a body, on the other hand, will still be nicely elliptical.

 

[Jeroen94704]

I don't think "mountains and changes in density" would cause an orbit to decay. They do not substract or add energy to the spacecraft. I think once you achieve a stabel orbit over an airless planet, at any altitude, your spacecraft would continue indefinitekly.

Unfortunately, this is not the case. Mountains and other geological features that affect the mass distribution of a body definitely have an effect on objects in orbit around that body.

Keep in mind that when thinking of the problem as "1 craft in orbit around 1 planet", you simplify the problem by assuming 2 point-masses (that is, objects with mass, but with a size of 0).

This approach is accurate enough when dealing with real-life orbits where the size of the geological features is small compared to the radius of the orbit (an 8 km mountain is small compared to a 300 km orbit). But it is, of course, not how it is in reality. When you start thinking about orbits that are close to the surface, these imperfections start to play a bigger role.

Jeroen

 

[Jeroen94704]

To reply to the original question: Practicalities like atmospheres and mountains aside, there is no lower altitude limit to be in orbit.

If we would ever find a planet that was perfectly spherical, with completely homogeneous mass distribution, then it would be possible to be in orbit a fraction of an inch above the surface.

In case of more real-world examples like the Moon and Mercury, you can still get pretty low, but I don't know how stable such low orbits would be given the uneven mass-distribution of these bodies.

Jeroen

 

[orionrider]

Thanks Jeroen, you are obviously right about the Equator and the North Pole... More of a 'circular path' than an 'orbit'

 

[p0odd]

Thanks a lot!

yevaud: Cool. One could play hours with that one ;-)

Even if a gravity-alone orbit would not be stable close to the ground, a high-speed lowpass of for instance Io could still be real low. If you plan the trajectory very carefully and using very little propellant you could even skim the surface between volcanoes at incredible velocities :shock:
If they ever do that I hope they beam back some mpeg movies :mrgreen:

hahaha

 

[drwayne]

I don't think "mountains and changes in density" would cause an orbit to decay. They do not substract or add energy to the spacecraft. I think once you achieve a stabel orbit over an airless planet, at any altitude, your spacecraft would continue indefinitekly.

One might think this (I know I did), but it is not true. Many orbits of our own moon are unstable due to mass concentrations.

http://science.nasa.gov/science-news/sc ... _loworbit/