QUESTION:
QA: Guiding a Shuttle

I am an 8th grader at Shore school Australia. For science I need to answer 
the question on how a spaceship would be guided to Mars without the help of 
intruments (autopilot, etc.)! 


ANSWER from Bruce Thompson on August 31, 2000:

Short answer:

It can't be done.

Slightly longer answer:

It *still* can't be done. At the velocities and distances involved, every 
calculation must be correct to the last decimal place and every velocity 
change must be made at the exact split second.

Let's go through some of the factors you need to take into consideration. 
Assuming that your space ship is already in Earth orbit, it is moving around 
the Sun at an average velocity of 29.79 kilometres per second. I say 
'average' because Earth's orbit is not circular and varies between 152.6 
million and 147.4 million kilometres from the Sun. At perihelion (closest to 
the Sun) it is moving faster than when it is at aphelion (furthest). Added to 
that, is your orbital velocity of 7.5 km/sec.

Mars orbits the Sun at an average velocity of 24.13 km/sec, but its orbit is 
even more eccentric than Earth's, varying between 249.2 million km and 207.3 
million km. So, if you intend arriving at Mars during perihelion, your travel 
time will be shorter, but your velocity will be higher than if you took the 
longer road to arrive at a slower velocity at aphelion. If all this is not 
enough, you have to take into account Mars' orbital inclination, which, 
relative to Earth, is 1.308 degrees.

Then, you need to consider what sort of orbit are you going into when you 
arrive at Mars. Will it be an equatorial orbit, or a polar orbit, or 
something in between? Don't forget that Mars' rotational axis is inclined at 
25.19 degrees to its orbit. You also need to consider the angle of your own 
orbit around the Earth, in relation to the plane of the ecliptic.

All these factors, and probably others that I have missed, must be taken into 
account when planning your trajectory. The most favourable launch windows 
from Earth to Mars open around every two years, when the two planets are in 
the best alignment for a Hohman transfer orbit, which is the most 
fuel-efficient course between two bodies in space, but it is also the 
slowest. 

To leave Earth orbit, you must accelerate above 11.2 km/sec, which is the 
Earth escape velocity. You will be aiming at a point far around Mars' orbit 
in the certainty that when you arrive, perhaps ten or eleven months later, 
Mars will have reached that point at the same time. You must therefore know 
how fast the two planets are moving in their respective orbits at the time of 
your departure, and how fast Mars will be moving when you arrive. You must 
accelerate out of Earth orbit, beginning at precisely the right second, at 
precisely the right rate, then cutting your engine at precisely the right 
instant when the exact interplanetary velocity has been acquired.

After that, you coast in a curving trajectory that takes you out from Earth's 
orbit to intersect that of Mars. Over such a long journey, no amount of 
calculating can put you on the correct course from the moment you leave Earth 
orbit, so you need to make further calculations during the trip, and course 
corrections, which also have to be conducted to the same level of precision.

Then, when you arrive at Mars, and you find it is right where you want it to 
be, you must decelerate to achieve your desired orbit around the planet. If 
you are going to use rocket braking, you fire up the engine again, but you 
have to know precisely when, for precisely how long, at what level of thrust, 
and in which direction you point the ship during braking. If you are going to 
use aerobraking, like the Mars Climate Orbiter was supposed to, you need to 
be able to control the exact angle you have to dip your space ship into the 
atmosphere. Go in too steeply and watch your hull burn away around you, while 
the surface comes up at you like a war god's fist. Go in at too shallow an 
angle and you will skip out of the atmosphere and back into orbit around the 
Sun.

Yet another factor to consider when planning aerobraking is the depth of the 
Martian atmosphere at the time of your arrival. At perihelion, when Mars is 
closest to the Sun, the planet is warmer, the melting polar caps have 
released huge quantities of carbon dioxide and water vapour into the 
atmosphere, and the denser atmosphere extends further into space than at 
aphelion. It could be embarrassing to begin your aerobraking descent into the 
atmosphere, only to find that the atmosphere is not where you thought it 
would be.

As much as we would like them to be, flying real space ships is not like 
flying the Millennium Falcon. Without the computers to carry out the 
navigation, real space ships cannot go anywhere.