We saw a tweet earlier today from @DrHughLewis:
@esaoperations if “reboost” = increase in altitude, does the orbital speed really increase?
— Hugh Lewis (@DrHughLewis) August 15, 2014
As with many tough, technical questions, we passed this to the ATV-CC flight dynamics experts! The reply below was provided by Arnaud Boutonnet (Thanks, Arnaud!).
Let us assume that the orbit of the ISS is initially circular.
When a reboost is performed, the speed increases and the orbit becomes slightly elliptical. The point where the boost is performed is the perigee, the point with the lowest altitude, which turns out to be the initial altitude.
The opposite point on the orbit is the apogee, the point with the highest altitude; therefore at this point the altitude is larger than the initial altitude. However orbital mechanics dictate that at this point the speed will have been reduced; it will actually be smaller than the speed on the initial orbit before the reboost!
But the orbit of the ISS can be circularised at the higher altitude by performing a second reboost at the apogee of the (new) elliptical orbit; therefore the ISS will be at a higher altitude. And here comes the trick! As said above, the speed at apogee is smaller than the speed on the initial orbit. And even after the second reboost, it is still smaller.
Conclusion: after two reboost manoeuvres, which both increased the speed, the ISS ends up at a higher altitude with a lower speed compared to the initial orbit. Interesting, no?