sling shot problem

[siarad]

The BBC program Space Odyssey said it's spaceship did a slingshot around the Sun accelerating it to-wards a planet. I can't work out how that's possible as there's no relative motion between it & a planet. Sling-shotting around a planet moving relative to another can impart acceleration but I'm stumped as to how the Sun can do it. Surely the BBC was wrong or maybe I misheard.

 

[siarad]

It's OK the BBC removed the forum or something but another forum replied to me saying it was rubbish. Typical wait a week then post here & beeb replies.

 

[nacnud]

The only reason I can think for than manure might be because it was quicker to go via the sun given the alignment of the planets at the time, and that it gives a chance to take a close look at the sun.<br /><br />Then the script writers got involved and confused things <br />

 

[siarad]

Yes script writers with their arts degrees <img src="/images/icons/laugh.gif" />

 

[siarad]

Just had another reply although this didn't happen in the program.<br />Speed can be gained by 'a perihelion burn' - a trick spacecraft nav. people use to maximise the fuel efficiency - burning the engine at the closest approach to a body and therefore the fastest part of the orbit gives more speed from the engine burn than at a slower point in the orbital trajectory.<br />This goes against Relativity which says it's more difficult to accelerate the faster you go.<br />Is it something to do with being closer to the exhaust gas speed?<br />Any explanation?

 

[spacechump]

<i>This goes against Relativity which says it's more difficult to accelerate the faster you go. </i><br /><br />This is only a problem at relativistic speeds. That is where the effect is much more noticeable.

 

[remcook]

unfortunately, spacecraft don't travel at relativistic speeds. so we can just view it in the classical way

 

[siarad]

That was just an aside. Classically I don't understand how the same fuel burn produces more effect during a perihelion burn.

 

[remcook]

OK. it's basically just conservation of energy. Whenever the engine is not burning, energy is conserved. Now, the total energy (per unit mass) is:<br /><br />Ek + Ep = 1/2 M V^2 - GM/r = const.<br /><br />it's basically because the kinetic energy increases with the square of the velocity that enables this.<br /><br />Say if your speed at perigee is 10. Your kinetic energy = 50. (1/2 V^2)<br /> and you increase it with 1, your kinetic energy becomes: 121/2 = 60.5<br />so, your increase is: 60.5 -50 = 10.5<br /><br />Now, say that your speed at apogee is 5 (a lower number in any case). your kinetic enrgy is 12.5.<br />increase with the same 1 gives a new kinetic energy of:<br />36/2= 18<br />Increase in energy is: 18-12.5 = 5.5 < 10.5<br /><br />By burning, you can only change your kinetic energy, not your potential energy (you can't suddenly move yourself discontinuously), so you can better do it where speed is highest.<br />

 

[siarad]

Thanks it's nice to be reminded things are not as simple as I think.

 

[spacester]

I was delighted to see a post from remcook elsewhere, I didn't know if he was still with us. So I did a search on his posts to see how long he's been back, and discovered this thread, which I missed before . . .<br /><br />So I'm not trying to one-up anybody, but . . . in the interest of accuracy . . . you know how it is around here . . <img src="/images/icons/smile.gif" /><br /><br />It's not that un-simple . . . <br /><br />The burn to raise the orbit actually slows you down. A higher orbit has less velocity, so <i>less</i> kinetic energy. Weird, huh?<br /><br />It took me a long time to figure this out, but look up the "vis-viva equation". It shows, not so transparently, that when you raise an orbit, you increase the potential energy by twice the amount that you decrease the kinetic energy. <br /><br />Of course it is true that you cannot discontinuously change the potential energy, but that's not required to increase the total orbital energy. The potential energy of the bound orbit is increased, but you do not see the greater distance from the orbited body until after periapse. (It is not the same thing as a block of matter statically held in a gravity field.)<br /><br />But to the question at hand, the reason the burn at periapse is more effective is it minimizes gravity losses. <br /><br />Anytime you burn your spaceship's engines in a gravity field, some of the energy is "wasted". The losses increase as a function of the time of the burn, the angle from the local horizontal, and decrease as the radius of the orbit during the burn. A periapse burn is going to have essentially zero angle, and we are asking what's the difference between periapse and apoapse for the same burn time. So what matters is the orbital radius. It's a minimum at periapse, so that's when you want to do the burn.<br /> <div class="Discussion_UserSignature"> </div>

 

[nacnud]

I find the best way to get a handle on these kinds of problems is to do everything in terms of total energy (potential + kinetic), where an infinite distance from the earth or solar system etc is at zero energy...<br /><br />...well it works for me <img src="/images/icons/smile.gif" /><br />