# RE: STS-107 Abort to ISS Possible?

From: Ted Molczan (molczan@rogers.com)
Date: Tue Feb 04 2003 - 23:16:51 EST

• Next message: Tony Planinac: "Re: Oh you will love this"

```Curt Porter wrote:

>   If, flight day one, it was decided that Columbia was
> mortally damaged,
> then standard flight safety margins are no longer useful. Making the
> most economical use of propellant, using time windows when the orbits
> were advantageous, using even preturbations from Sun and
> Moon, all would take time, but they would have two weeks or more to do it.

The formula for the change in velocity (delta V) required to change
inclination is:

deltaV = 2 sin(deltaI / 2) V

where deltaI = change in inclination

V = orbital velocity

For STS 107 to ISS, deltaI = 51.6 - 39.0 = 12.6 deg

To save propellant, the inclination change would be performed after STS 107
manoeuvred to ISS' altitude, which had a mean orbital velocity of 7.68 km/s.

deltaV = 2 sin((51.6 - 39.0) / 2) * 7.68

= 1.69 km/s

This is roughly four times the total deltaV available from the OMS, including
the portion that otherwise would have been used for de-orbit.

If inclination had not been an issue, the difference in ascending nodes still
would have been. At launch, Columbia's plane was about 168 deg east of ISS's.
Columbia's plane precessed westward 1.68 deg/d faster than ISS's, so it would
have caught up to ISS in 168/1.68 = 100 d, long after life-support would have
been exhausted. In fact, Columbia might well have decayed in that time.

Ted Molczan

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