Satellite magnetometry is plagued by the Backus effect which renders m
aps of the magnetic field derived from measurements of the total field
intensity unreliable, especially near the geomagnetic equator. The on
ly remedy is to use oriented, vector component data in addition to sca
lar intensity data, but this requires either accurate determination of
the satellite attitude or the use of data from permanent magnetic obs
ervatories. The former adds considerably to the cost and complexity of
satellite magnetometry; the latter suffers in practice from the poor
geographical distribution of magnetic observatories. Here we re-examin
e the problem of attitude determination, and ask how well the attitude
needs to be determined to alleviate the Backus effect. We show that t
he use of a more complete model of the errors in satellite vector comp
onent data allows the requirements on attitude determination to be rel
axed significantly, so that lower-cost means of obtaining attitude det
ermination, such as GPS, can be employed.