I think it is fascinating that people get wound up over topics like orbital mechanics when discussing how or why a stock failed. This topic has as much to do with Globalstar's current problems as does, say, the outcome of last years Superbowl.
But, hey. I'm game for it.
You implied gravity was a variable when you said a larger satellite would fall out of LEO because of its mass. For a given orbit, a satellite has precisely the same velocity if its mass is a few grams or a several thousand kilograms. Further, its delta v requirement to maintain that orbit is precisely the same whether it is a few grams of several thousand kilograms, all other things being equal (namely area to mass ratio that can have second order effects on atmospheric drag and solar pressure perturbations - altogether different topics). However, if the orbit keeping requirements for a given orbit are 1 meter/sec/year, the satellite whose mass is several thousand kilograms is likely going to require more fuel to develop that 1 meter/sec/year, but that is not a given either - it depends on the Isp of the propellant used. The comment as I saw it was that a larger (more massive) satellite has more velocity requirements or that gravity affected it in a different way. Not true.
To answer your questions specifically:
1- the closer a body is to another body, the greater the gravitational pull. True or false? If you ask a scientist, they'd say true, but if you ask a engineer, they'd say false. Distance is a function of gravitational attraction, but for near Earth orbits, one can make the claim that the gravitational acceleration is constant and not be too far off. I did a google search on the gravitational equation and came up with the following link more or less at random:
glenbrook.k12.il.us
Here you can see that, yes, the force of gravity actually changes the further you move away from the center of the Earth. But on the surface of the Earth you are already 6400 km away from the center, and it LEO altitudes you are, say, 6700 km away. So, 100 lbs on the Earth's surface would weigh 91 lbs 300 km up. Not that much of a change, and this is not what makes up an orbit, nor does it affect a satellites stationkeeping (or delta v) requirement for a given orbit.
2- The greater the mass of a body, the greater the gravitational pull between that body and another body. True or false? False. From the above website, you can take the equation for Newton's law of gravitation and solve for g, the acceleration due to gravity:
g = 39.9e13/r^2
where r is the distance of an object from the center of the Earth in meters (so r is about 6,400,000 at the Earth's surface). Mass is not a variable, and hence, for a given distance from the center of the Earth, the acceleration due to gravity is the same on a feather or a 747.
3- One way that satellites maintain their orbit is by maintaining their velocity. True or false? It's not "a" way, it's the only way.
4- The closer a satellite is to the earth, the faster the velocity needed to maintain its orbit. True or false? I'd state it as the closer a satellite is to the Earth, the higher the velocity. Maintaining its velocity, which I understand to mean its orbit, is another question. Here's another equation for you, for a circular orbit:
V = sqrt(3.98e5/r)
where r is the distance from the center of the Earth to the satellite (this time expressed in kilometers) and V is the velocity expressed in km/sec.
5- The earth exerts a gravitational pull on its satellites. True or false? True! If it didn't, the satellites would zoom away in to interstellar space. Gravity is what keeps satellites in orbit.
6- The gravitational pull of the earth on a satellite is greater if the satellite has a greater mass. True or false? I assume by "pull" you mean acceleration. If so, the answer is no.
Again, the mass of the satellite does not affect its orbit. It will affect how much propellant it takes to put it in to its orbit, as well as how much propellant it takes to keep it in its orbit. Unless of course you are referring to atmospheric effects of the really low orbiters -- then mass can play a role, albeit a weak one. By low orbiters, I mean at 500 km and lower. At the G* orbit, 1414km there are no longer atmospheric effects.
I hope you've had as much fun with this as I have. I'm sure I've left more questions unanswered than answered - someone is going to be left wondering why a 100 lb object on the Earth's surface weigh 91 lbs 300 km up when they've seen astronauts whizzing through the space shuttle weightless. I can't answer that one right now - I've spent too much time on this. If some asks, I'll answer it, but here is jist of it: My example did not specify that the object was in orbit, just 300 km up. If the object where in orbit 300 km up, it'd be weightless too. To get to orbit, you just have to reach orbital velocity, which is about 7 km/sec at LEO altitudes. Impractical to do in the thick atmosphere, which is why its done in space.
Kind Regards
Mr A |
