Need technical help

[utopian]

Hi, I'm Malcolm from India.
Here's my problem : A satellite is steadily orbitting a planet. Now what would be the force required to send this satellite into an inwardly spiralling orbit so that it finally collides with the planet?

 

[Green Knight]

Depends on the altitude of the satellite, its mass, its current velocity (which will be proportional to its altitude; there is a set formula for altitudes/speeds for stable orbits which I can't recall offhand).

But with this knowledge, the answer is simple. ANY force that slows your satellite down, however small, will eventually send the satellite crashing to earth. (Actually I tell a lie... it has to slow it down enough to enter the atmosphere at a fairly steep angle, otherwise it will bounce off the outer atmosphere like a rubber ball).

Orbiting spacecraft generally fire retro rockets to bring themselves back down to Earth... usually for less than a minute of burn time.

Hope this helps! I'm sure there are websites that can tell you the precise details better than I can right now...

 

[utopian]

Thanks Knight,
Would be glad if anyone could direct me to a link for a mathematical expression for this.

 

[chrispenycate]

Since the equation is going to involve the original height of the satelite (is its original orbit a geostationary (um, planetostationary? Oh, what the, I'll use the terms for Earth), LEO, or, following your "steadily" comment, in a stable LaGrange type or trojan orbit? Circular or elliptical, and if elliptical, how much divergence from the circular. What is the effective depth of the atmosphere (the real depth is of course infinite, there being no surface to an atmosphere; it just dwindles away.)

Effectively, any satelite is losing energy all the time due to electromagnetic and tidal forces- but if it holds in place for a couple of hundred tousand years, we consider it stable.

If you tried to write an equation taking all these factors into consideration, inluding the vector of the force and the point in the orbit at which it was applied, your equation would run to several pages- essentially, if the orbit's high enough, you need an enormous force, and even then the probability is that it'll go into a more extreme ellipse with only the very closest bits giving atmospheric braking, while a low orbit a tiny wobble will build up rapidly to disaster. It's not a straightforward "frictional braking is proportional to the density of the medium through which you are passing, the square of the velocity and the solid angle subtended by the relevand body" type calculation.

 

[Brian G Turner]

Hi, I'm Malcolm from India.
Here's my problem : A satellite is steadily orbitting a planet. Now what would be the force required to send this satellite into an inwardly spiralling orbit so that it finally collides with the planet?

Rather than the force required, but about the required concept, ie, mis-firing thruster?

 

[utopian]

Chris, your reply suggests there isn't an exact mathematical expression for the problem. What could be a plausible approximation for the force required to spiral the satellite?

 

[Green Knight]

Utopian, it might help a little to know why you need to know so precisely! You seem to be angling for something very specific.

As I, Brian suggests, surely a more interesting question is the mechanism, rather than the force per se, that causes the satellite to crash? This could come from any number of sources, from a meteor impact, to gravitational perturbation from a passing vast object (asteroid or star ship!), eddy currents in the metal from passing through the planet's magnetic field (thus slowing its motion), atmospheric drag (ditto) and a myriad others.

You're the writer - you can set all the parameters, within reason. Or is there a particular real satellite you have in mind, such as the International Space Station?

 

[utopian]

Okie let me be specific. I want the moon to crash into the earth?

 

[Green Knight]

I see!

Well, Anthony Burgess does this in one of his SF books (not that you can't too, of course). What Burgess contrives is another planet, a rogue interstellar object, hurtling into the solar system. It captures the moon in its stronger gravity and takes it away. It circles the sun and comes back round again towards Earth, dragging the moon with it.

The moon hits the Earth like the ball on the end of a chain... with predictable consquences.

I'd be interested to see if you can devise a method different from Burgess's... I'm sure there is one.

 

[chrispenycate]

Well, if the moon masses 7,35 times ten to the power 19 tonnes, and orbits at 363 thousand kilometers from the Earth at perigee, and for any apreciable amount of atmospheric braking this perigee must be below 30 kilometers, you're going to need quite large quanties of energy to acheive your aim- certainly the explosion of the worlds entire nuclear arsenal at the optimum point in its orbit wouldn't make a hundredth of the nescessary delta v. Add to this, slowing the moon (as by the energy involved in the tides) is moving the moon slowly away from the Earth, rather than the contrary. A series of calculated comet strikes maybe? Take lots of comets, and very accurately aimed, over a long period of time- ah, yes, how many centuries am I allowed? After all, it's only travelling at a kilometer per second, seven thousand three hundred million tons- and it's going to take a lot of atmospheric passages to slow that down much, probably easier to go for a direct impact rather than spiralling in- wouldn't that make a dinosaur killer? Still, if you ever did manage to shift its orbit, you wouldn't be try ing to put it back, or wondering about survivors it's "all organisms hoping to survive the next decade are to move off planet as soon as possible"

 

[Green Knight]

What about the return of Theia/Orpheus (the hypothetical planet-sized mass that is meant to have created the moon originally by striking the Earth)?

Or what if all the Clangers jumped together?

 

[Mark Robson]

Or what if all the Clangers jumped together?

Nice to see someone thinking at my technical level!

 

[Glyptus]

Okie let me be specific. I want the moon to crash into the earth?

The truth is finally dragged out of him. Heh heh! So- you want the moon to crash into the earth, do you? Well, who doesn't? I've been working on the problem for many years. Also, how to destroy the sun... ("Since the beginning of time, man has yearned to destroy the sun!" C. Montgomery Burns "The Simpsons"). Also, how to disturb the San Andreas fault line, enough to set off California's "Big One"... All works in progress.