# Net gravitational pull from Mars

• webbwbb
I am trying to find a way to test it out. I don't even know if the calculations would work for something that long.In summary, a space elevator on Mars may be feasible due to the lower gravity. If this is for a work of fiction, you can "invent" or propose the use of materials we don't have access to, or may not exist.f

#### webbwbb

I have been working on an idea for a little while.. A large hurdle in planning for this idea is that I need to figure out what the net gravitational pull would be on a 17,200km long cable going from a geosynchronous orbit around Mars to the surface of the planet would be. Its basically something along the lines of a space elevator on Mars. It seems like it may be a bit more feasible there than on Earth due to the lower gravity on Mars in comparison to that of Earth. Any help would be greatly appreciated.

I have been working on an idea for a little while.. A large hurdle in planning for this idea is that I need to figure out what the net gravitational pull would be on a 17,200km long cable going from a geosynchronous orbit around Mars to the surface of the planet would be. Its basically something along the lines of a space elevator on Mars. It seems like it may be a bit more feasible there than on Earth due to the lower gravity on Mars in comparison to that of Earth. Any help would be greatly appreciated.

Two questions:

1.) Is this for a work of fiction?
2.) If you know what the distance is for a geo-stationary orbit around mars, do you care about the gravity?

http://en.wikipedia.org/wiki/Geostationary_orbit
Wikipedia said:
Now, by the same formula, let us find the geostationary orbit of an object in relation to Mars. The geocentric gravitational constant GM (which is μ) for Mars has the value of 42,828 km3s-2, and the known rotational period (T) of Mars is 88,642.66 seconds. Since ω = 2π/T, using the formula above, the value of ω is found to be approx 7.088218×10-5 s-1. Thus, r3 = 8.5243×1012 km3, whose cube root of is 20,427 km; subtracting the equatorial radius of Mars (3396.2 km) we have 17,031 km.

Anyway, with that you can backtrack to what you want, if the orbital distance isn't it.

I am trying to figure out how much force would be exerted upon that line to the surface. How much wieght would the line itself have; would it be more than the cable could support? I know that it would lessen as you move further away from the planet but do not know exactly how to calculate that along the entire cable. I was pretty sure this would be a calculus problem and talked to a physics professor a little about it. She confirmed this but did not have time to give me the formula. I have just started my first calculus course and really do not have the hang of things yet.

I am trying to figure out how much force would be exerted upon that line to the surface. How much wieght would the line itself have; would it be more than the cable could support? I know that it would lessen as you move further away from the planet but do not know exactly how to calculate that along the entire cable. I was pretty sure this would be a calculus problem and talked to a physics professor a little about it. She confirmed this but did not have time to give me the formula. I have just started my first calculus course and really do not have the hang of things yet.

OK, weight of the line wouldn't be the issue for a tether into GS orbit... finding a material that could span that distance RELIABLY, AND serve as a tether?.. phew... that's going to be your problem, and also why I asked if this is for a work of fiction.

If it's fiction, you can "invent" or propose the use of materials we don't have access to, or may not exist. If this is a real proposal, then I'd be worried that the planet you chose is the beginning of the asteroid belt. Besides, it's very hard to imagine that kind of tether, if it COULD be made (remember, a "space elevator" usually refers to something in LEO, maybe 100-500 KM!) safely acting as a guide for cargo or people.

If you could overcome all of that... I don't think that would be a civilization in need of a 17,000+KM tether to the martian surface... you'd have long since overcome the NEED for such a contrivance.

Well I suppose it is fiction at this time but it would be nice if at some time it was not. I am in a program called NCAS (Google it for more information). Part of my mission is that I need to return samples to Earth and I am scored on creativity. I have a material in mind that may be able to be manufactured in sufficient quantity in the next couple of years. If it were to span that wieght on Earth it would wiegh 114kg but could only support about 7kg. It would be able to withstand the temperatures required of it. I know this is a particularly absurd idea but it is the type of thing they are looking for because they may get something that could be modified to be more plausible.

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Well I suppose it is fiction at this time but it would be nice if at some time it was not. I am in a program called NCAS (Google it for more information). Part of my mission is that I need to return samples to Earth and I am scored on creativity.

OK, I'd file that under, "non-fiction", in the sense that you can't fudge details or use "neutronium" as a dodge of some kind. You really want to engineer a solution.. huh.

Well, then you already have the info you need in the previous link.

http://en.wikipedia.org/wiki/Geocentric_gravitational_constant is what you need...

And here is some info... from: http://en.wikipedia.org/wiki/Geostationary_orbit
Wikipedia said:
The geocentric gravitational constant GM (which is μ) for Mars has the value of 42,828 km3s-2

How this works with a 17K kilometer tether, I have NO idea. Personally, I think it would be easier to find someone willing to die on mars, sending a probe with samples back to earth. Somewhere between a one-way trip for some unlucky crew member, I'd think that an unmanned "moon-landing" would be useful. I just can't see that tether being workable... I mean, you'd need something MONSTROUSLY strong, and if you're unlucky enough to get a hit somewhere along its length... disaster!

OK, weight of the line wouldn't be the issue for a tether into GS orbit... finding a material that could span that distance RELIABLY, AND serve as a tether?.. phew... that's going to be your problem, and also why I asked if this is for a work of fiction.

If it's fiction, you can "invent" or propose the use of materials we don't have access to, or may not exist. If this is a real proposal, then I'd be worried that the planet you chose is the beginning of the asteroid belt. Besides, it's very hard to imagine that kind of tether, if it COULD be made (remember, a "space elevator" usually refers to something in LEO, maybe 100-500 KM!) safely acting as a guide for cargo or people.

If you could overcome all of that... I don't think that would be a civilization in need of a 17,000+KM tether to the martian surface... you'd have long since overcome the NEED for such a contrivance.

I don't believe the asteroid belt being closer to Mars makes much diference for something simply in orbit of the planet. The asteroids for the most part stay in the belt and rarely come out.

I don't believe the asteroid belt being closer to Mars makes much diference for something simply in orbit of the planet. The asteroids for the most part stay in the belt and rarely come out.

OK... am I make a poor assumption about length of the tether being an issue for other reasons? That's one hell of a venture to make without some kind of fail-safe, backup...

Actually, what effect would hard vacuum and radiation have on the materials used to make the tether? Would it be a bit like neutron bombardment of fusion shielding (brittle), or is it negligible as well?

This material has been used in aerospace environments before. I used Honeywell's Spectra 2000 fiber. The formula for the net pull on the cable is:

integral(G (lambda)MmarsD all over r2 )

Lambda is the wieght of 1m of thread (1/90).
Mmars is the mass of Mars in grams.
G is the gravity constant.
D is the distance from the center of Mars to my satellite.
r is the distance to any small piece of my tether.

This material has been used in aerospace environments before. I used Honeywell's Spectra 2000 fiber. The formula for the net pull on the cable is:

integral(G (lambda)MmarsD all over r2 )

Lambda is the wieght of 1m of thread (1/90).
Mmars is the mass of Mars in grams.
G is the gravity constant.
D is the distance from the center of Mars to my satellite.
r is the distance to any small piece of my tether.

Well, then I'm wrong!

Lambda is defined by you already
M & G you have in the formula for GS orbit...
r... seems like it would have to be quite large?

Of course, you have greatly reduced atmospheric drag, and you COULD use this as a means of power generation too.

Hm. Does this material scale well in the way you're looking at it?

It is about 5 times better than Kevlar in the strength/wieght ratio (it is light enough to float on water and is bulletproof). It also has a very low coefficient of friction (it is smoother than teflon). A 9000m length wieghs 100g on Earth and is able to hold 8.5lbs. It melts at around 150C so it could not be used for such a system on Earth and even for my application will need to be inserted at dusk in a winter and pulled out shortly after dawn to avoid risk of melting in the thermosphere.

It is about 5 times better than Kevlar in the strength/wieght ratio (it is light enough to float on water and is bulletproof). It also has a very low coefficient of friction (it is smoother than teflon). A 9000m length wieghs 100g on Earth and is able to hold 8.5lbs. It melts at around 150C so it could not be used for such a system on Earth and even for my application will need to be inserted at dusk in a winter and pulled out shortly after dawn to avoid risk of melting in the thermosphere.

Huh... well, maybe if you could engineer this material with a "self healing" sheathe... yeah, I could see it working in theory. You're definitely going to get points for creativity... GS orbit... not a bad idea at all.

If you could mix a conductive material along with the sheathe, you could use the cable to generate some power too, including capturing thermal solar energy. This could feed batteries for on-site experiments to test which samples would be best used, and even a basis for later electrolytic extraction of O, or H!

It would be a more involved project, but you wouldn't have to worry about selling this purely as an exploratory project: the tether could remain in-situ for the future, or as a means to be more selective about your samples to return to earth.

edit: Maybe a carbon-fiber sheathe or, graphene embedded in ceramic particles and a mylar coating.