I was wondering: if there really was a "jupiter" or an "earth" lurking in the far reaches beyond Neptune, would we be able to detect it with present technology? The current limiting magnitude record is magnitude 28.2 (that of Comet Halley in 2003 seen by the VLT telescope).



So here it goes: what magnitude would be a) Earth b) Jupiter at: 100 AU, 200 AU and 1000 AU respectively?



I am looking forward to the results of your calculations.

I think you'll find most of what you want in here:

http://www.ifa.hawaii.edu/~jewitt/papers/2004/J2004.pdf

The Pan-Starrs project is supposed to find asteroid threats to the Earth, but as a side-effect it ought to find remote objects too. For example, another Pluto out to 320 AU and another Jupiter out to 2140 AU. (That's between 2 and 12 light-days.) Thsoe are the distances where these bodies would be Magnitude 24 objects.

Here's the Science Goals section of the Pan Starrs site:

http://pan-starrs.ifa.hawaii.edu/public/sc...lar-system.html

Does anyone know how likely this is to actually be built?

The prototype telescope (PS-1, first of the four telescopes) has already achieved the first light meaning the project is 1/4 complete.

I've got the impression that it has got the funding it needs. The final location is still open. It's either Haleakala or Mauna Kea. The latter, although better, may not be selected because of environmental and cultural reasons (the indigenous Hawaiians are against building telescopes on their holy ground).

Should we be concerned that the project is 1/4 complete even though they haven't picked a location for it yet? :-)

Given the 'neigbourhood' clause of the IAU definition - anything they find out at those ranges will not be classified as a planet.

Doug

My calculator says (though I need to turn 200AU and 1000AU into light hours and light days, respectively):

Earth
100AU - Earth 16.1, Jupiter 10.6
200AU - Earth 19.2, Jupiter 13.7
1000AU - Earth 26.1, Jupiter 20.6

All under 28.2 - but that's a lot of sky to look around, and at 1000AU the orbital period is vast. An object at 1000AU would only move about 0.11 arcsec per day.

Andy

Neat tool AnyG.
I see you used the albedo for Earth and Jupiter in that comparision, but yes one Jupiter sized object would have a hard time escaping visual detection (not to mention the effects caused by its gravity) and even one the size of Earth seems unlikely unless perhaps at the largest distance out to 1000 AU.

I dabbled around with that tool and got a magnitude between 18 - 28 perhaps as high as 30 for a really dark Mars sized chunk which corresponds with my own guesstimate that one object of that size might be hiding there in the Kupier belt.

We should note that it's now pretty clear the classical Kuiper belt extends out to only some 52 or 54 <I think> AU. Scattered disk objects go out further, but they're not in billions-of-years-stable orbits. There are almost certainly no classical KB objects as big as Mars, though there could be scattered disk objects in the aphelion parts of their orbits far enough out to be too faint to have been spotted yet. The REAL possibility is finding large objects beyond the KB and never part of it, except at best during the very formation of the solar system.. things like Sedna, at perihelion, 70 AU in an orbit that goes out to.. was it 250 or so AU?

Many thanks. Next time I edit it I'll fix the typoes! But the maths is fine. I put it together to get an idea of the relative brightness of extrasolar planets (though the calculation is for an orb fully lit by a star, which would therefore be lost in a sun's glare) and found it works fine for our planets/dwarf planets/objects-by-other-names at opposition.

Incidentally, now that Voyager's at 100AU, I see Earth is less than magnitude 6. Or rather, I wouldn't see it. "No longer visible to the naked eye". That puts a sense of perspective on just how far away that is!

Andy

Interestingly, Venus' magnitude comes out at 4.6 which ought to be visible, if you neglect the 0.4 degree maximum angular separation from the Sun. You could just barely cover the Sun with the thumb and see a tiny speck of light right near it

Woeful understatement. Sedna's aphelion is 975 AU.

You get Jupiter and Saturn thrown in, too: at mags 4.3 and 5.9 (that last would be fairly tough - even though the nearest street lights are some way off!)

But I think oddest of all is the Sun...it's a speck. The size of a pinhead at 15 metres, yet still 45 times brighter than a full Moon. So for human eyes at Voyager, the shadows would be extremely sharp and well-defined, colour vision would be just present - but on the verge of fading to neutral greys; and you'd be leaving a system seemingly comprising two gas giants and a high albedo planet ...

Brrr!

Andy

I believe the absolute magnitude is defined wrong. It is how bright an object would appear at 1 AU from the sun and 1AU from the observer. This should depend only on the diameter and the albedo of the object. It should not change when you change the distance X from star.

Oops, you're right about absolute magnitude there alan.

Hi. I'm new here. I'm working on a school project about pluto. The teacher asks me to design a space trajectory for a spacecraft to travel to pluto and return to earth. I have no ideas what to do. Please help me...

Hi Alan!

Plugging in the figures for Jupiter, as seen from the Earth...

Ummm. Vis mag = -2.7, which is about right. Abs Mag = -5.9 - the value that Jupiter at 5.2AU has if seen from 1AU. Setting X-from-STAR and VIEWER-from-X to 1AU gives me -9.5. Ah! You're quite right: mea culpa. I shall amend that once I find the source file.

But you've now got me wondering why I've listed the mag at 1AU at all. I'm sure there was a reason for it!

Thanks for the correction!

Andy

Is it possible to use pluto's gravity to make a turn like Ulysses?

Unfortunately not - Pluto is a tiny tiny tiny tiny fraction of 9/10ths of 4/5ths of nothing in terms of mass when compared to Jupiter.

AND - Pluto & Charon is the primary goal here - to comprimise the flyby geometry for any sort of gravitational assist would be a no no I would imagine.

Doug

A trajectory to travel to Pluto and return to the Earth?

There are a number of ways you can look at this, depending on the depth you'd like to go into and the level you're looking at.

If the mission time isn't a constraint (i.e. you don't mind taking 90 years!) then the easiest trajectory to calculate is a Hohmann transfer orbit to Pluto and back. The delta_V required for this mission totals around 31km/s spread over four short chemical burns - you can work the details of these burns out with relatively easy maths and a bit of googling.

With the rocket equation you can then work out how much fuel your Pluto probe will require, as a proportion of its useful mass. (Hint - "loads". Back of an enveloping, I get well over 2300 kg of fuel per kg of payload.) Spot why New Horizons is going on a one-way-ticket!

For a more complicated approach that would save you both fuel and time, you could look into gravity assists from Jupiter and/or the other large gas giants.

And you could ditch chemical rockets and look into something with a higher exhaust velocity like an ion rocket (more efficient fuel usage) or solar sail (zero fuel usage - both very slow flight times) or something more novel & exotic like fusion rockets, fission-bomb rockets (these raise other issues, but can result in very low flight times).

Good luck with your project!

Andy

If it's just designing a trajectory, I'd guess what's wanted is to calculate the Hohmann transfer orbit from Earth to Pluto (as AndyG describes above), then compute one from Pluto back to Earth (same orbit, really), and then compute the delay between them (the amount of time you get to spend at Pluto).

If one was feeling brave.... you could seperate an impactor a few days before closest approach - and then capture the ejector using aerogel and return to earth without actually stopping

Doug

The problem with a Hohmann (Type 1) transfer to Pluto is that it would take years and years and years! We might be talking about over 100 years round trip -- can't do the math at work right now. That would be a minimal energy trajectory, but the travel time would be apalling. You'd definitely want a hyperbolic trajectory instead both toward Pluto and back. This would require a great deal more fuel, but it would be a much shorter round trip.

And if you're thinking of actually stopping at Pluto and taking your dog out for a walk, you'd have to do velocity matching, and with Pluto's poor excuse for an atmosphere, you couldn't do aerocapture to bleed off your hyperbolic excess velocity. On the other hand, heliocentric velocities are low, so it might not be much delta-V.
-John Sheff
Cambridge, MA
jsheff@comcast.net

We can do a Hohmann's Transfer over orbital plane? Great idea. I never think of it.
And, in order to do a Hohmann's Transfer, we surely need powerful thrusts. Is it possible with our current tech?

And how did NASA solve the problems of astedroids? I always imagine that sometimes a probe can be hit by one of these objects?

"asteroids".

For a school paper, though (depending on what level), I think it's enough to assume that a) Pluto's orbit is round and in the same plane as Earth's orbit Pluto and Earth are both massless points c) Velocity change is instantaneous -- there is no need to accelerate or decelerate gradually. In fact, there's probably no need to compute delta-V at all; for the one-way trip all you really need is the semi-major axis of the transfer orbit and Kepler's third law.

As Doug points out, a simple Hohmann ellipse is enough to take you there and back, except that the Earth is unlikely to be in the right place when you return. The complication in the round-trip problem (as I see it) is computing how long you need to wait at Pluto before you start your return to Earth.

Anyway, I figure 45 years each way with 280 days on Pluto.

Thanks for the answer. I guess I can use those assumption for the paper. But for mere curiosity can you suggest a practical way to travel forth and back to Pluto? The one that can be carried out in a next few years....

Uhm, djellison, can you explain more about your idea? I still don't understand it. Thanks a lot.

Hi Hermes,


Do you know about the Deep Impact mission? That was launched to a comet, but about 24 hours before it arrived it split into two - an 'impactor' and a flyby spacecraft.

The impactor had a camera and the software on board to navigate its way to hit the comet - and the flyby spacecraft manouvered away from the comet and flew past it - to obseve the impact and recieved, record, and relay the data sent back from the impactor.

This is not TOO disssimilar to a planned missiont he moon ( whos name esacpes me ) where they plan to have two spacecraft - one to impact the moon and one to fly through the ejecta to 'sniff', hopefully, the water involved.

Also - it reminds me a little of the Mars 'SCIM' Scout mission - which would fly through the upper martian atomsphere to take a sample of it and perhaps capture some high altitude dust and return it to Earth for analysis.

When thinking about an Earth-Pluto-Earth mission, I didn't think there would be much point in coming back without something to show for it. However - Landing on Pluto, sampling, and coming back would require such a huge ammount of fuel that it might be impossible given even the largest launch vehicles we have now - or even the Ares V in the next decade or so.

So - I wondered if it might be fun to try and take the deep-impact idea, but take it all the way to Pluto - and not try and observe the ejecta - but use the Stardust mission style of sampling..... use an aerogel capture array and fly through the ejecta hopefully capturing some of it on the way - and then return that to Earth....essentially the KBO bastardisation of Stardust, SCIM and Deep Impact

If you wanted a NASA style acronym for it...

Pluto In Situ Sample Earth Delivery

I'm not sure how easy or hard it would be to calculate trajectorys for spacecraft with Ion engines - but I think you would almost certainly want to look at those - using very large solar arrays - as perhaps an electric propulsion stage for the inner-solarsystem section of the trajectory just to help cut down on flight time.

Doug

You'd definitely want to go for Radioisotope Electric Propulsion (REP), this was already mentioned before. Basically, dump the solar arrays and use the RTG surplus energy during cruise to cut down trip times.

P.S. Catchy name, I like it

I think solar arrays are a bit optimistic. Look at the size of Rosetta's solar arrays and that's only going to stay relatively close. I'm afraid it's nuclear all the way, especially if you want to come back as well.

Dear djellison,
I'm just curious about how all the probes can avoid collision. Can they recognise near by asteroids?
Thank you very much.

"Near by" is a misleading term. New Horizons happened to pass some 100 000 km from an asteroid, and even that was pure luck. Statistically it was supposed to pass by maybe a few asteroids at a million kilometers distance. That's hardly near by.
The asteroid belt (the whole solar system in fact) is basically huge, empty space. You have to try really hard to hit something -- or have incredibly bad luck.
Forget the way asteroid belts are portrayed in Hollywood movies -- all packed up with rocks colliding and stuff. Saying that's far from reality is a BIG understatement.

Oh, I didn't know that. I thought space is filled with asteroids. And by the way, when a probe wants to turn around, its acceleration must be larger or equal to its current velocity, isn't it?

They don't call it *space* for nothing. Space is big, very very big, and almost completely empty. Despite what you've seen in the movies the asteroid belt is mostly full of nothing, in fact if you were standing on an asteroid in the asteroid belt you would be very lucky to see another asteroid with the naked eye. The positions of tens of thousands of asteroids and other minor bodies in the solar system are known, however, the chances of your planned trajectory intersecting a known asteroid are infestimaly small.

in the words of 'The Guide':

"Space," it says, "is big. Really big. You just won't believe how vastly hugely mindboggingly big it is. I mean you may think it's a long way down the road to the chemist, but that's just peanuts to space

I was just talking innner solar system - i.e. a '4th' stage of the LV that operates for say, 6 months.

Doug

Either way, the delta-V imparted by a solar-powered ion engine would be small, especially since you'd likely be escaping out of the inner solar system fast. You'd still need a (probably large) "deep space" maneuver once past Pluto to retarget back to Earth. I don't know how useful it would be to use up launch mass for expendable solar arrays when you'd need RTGs anyway and they would provide power all the way. The extra mass would be better used for useful payload, IMO.

Dear ugordan,
Can you tell me more about the deep space maneuver? Is there any object massive enough for us to use to retarget back to eath?

Nope. If you took that Hohmann transfer trajectory, which requires the least fuel, you'd practically be already set up for the return trip so the maneuver wouldn't be large. However, that trajectory would take decades to get there and decades to get back so it's not very useful. If you used a fast trajectory, after Pluto flyby you'd have to brake and change the velocity to a similar trajectory inwards to Earth. This would need a very big maneuver and Pluto is worthless for the purpose. You'd need you own engines to do it. Again, ion engines seem just about right for the job, they are the only ones that can give you a large velocity change for a fairly low amount of fuel.

Dear ugordan,
You mean the ion thruster? Are they ready for application? I heard that they are still in reseach.

SMART-1, DEEP SPACE 1 and Hayabusa all used ion engines.

JFGI

The Dawn mission launching in less than a year will use ion propulsion.

PM sent on Newtonian mechanics.

Thanks a lot everybody.
Still, is there anyway that a probe from Pluto can apply the gravity assist from Jupiter or Neptune to return to Eath?

Gravity assists in principle can work both ways. Just as you can launch slow then pick up speed at Jupiter, you could return from Pluto fast and use Jupiter to slow down a bit so you don't have to brake as much when you get back to Earth. I don't know if that would be very useful because you would prolong the return trip and you can always lose the extra velocity when entering Earth's atmosphere anyway.
But, yes, a return gravity assist can be done.

Dear Ugordan, can you explain to me again? I'm unclear that how we can return fast from Pluto? Is is by our own propulsion?

To put it short, yes, by your own propulsion. Whether you simply fly by Pluto and return to Earth or enter orbit around Pluto and then return, you will need your own propulsion. There's virtually nothing to gain from Pluto via a gravity assist. The faster you can launch back from Pluto, the faster you get back and the more fuel you need. It's a matter of finding a trade-off between short trip times and low propellant usage. Do a google search on orbital mechanics and transfer trajectories, there's bound to be an introductory site somewhere.

Thanks Ugordan.

If it were, when you looked at the night sky, it wouldn't be mostly black.

A typical (>99.9999%) vector from your eye into deep space does not encounter an asteroid, even in the plane where asteroids are densest. If it did, that area of the sky would feature a visible, bright ring. It doesn't. With the exception of Vesta and possible Ceres, which can appear as two single very dim points, the asteroid belt, collectively, is so sparse that if they were all there were in space, the night sky would be almost totally black. There is dust that can reflect some light, though. See:

http://en.wikipedia.org/wiki/Zodiacal_light