Question

A deorbit burn has been performed. During this deorbit burn a pre-calculated Delta V (change in velocity) of 290 ft/s (or 88.4 m/s) will be used to decrease the Shuttle’s altitude from 205 miles to 60 miles at perigee. The Shuttle’s Orbital Maneuvering System (OMS) engines provide a combined thrust of 12,000 force-pounds or 53,000 Newtons. The Shuttle weighs 2.50 x 105 lbs when fully loaded. The Shuttle has a mass of 1.13 x 105 kg when fully loaded.
Calculate how long a de-orbit burn must last in minutes and seconds to achieve the Shuttle’s change in altitude from 205 miles to 60 miles at perigee.

Answer 1

Method 1

Step 1: Solve for acceleration
From F=ma, rearrange to a=F/m
a=F/m= (53000 N)/(1.13 x 〖10〗^5 kg)= .469026549 〖m/s〗^2

Step 2: Solve for time
t=∆v/a=(88.4 m/s)/(.469026549 〖m/s〗^2 )=188.4754716 seconds

Step 3: Convert seconds to minutes
(188.4754716 seconds)/60=3.141257859 minutes

Step 4: Convert minutes to seconds
.141257859 × 60=8.47547154 seconds

Final answer:
It would require 3 minutes and 8 seconds of burn time to change the Shuttle’s altitude from 205 miles to 60 miles at perigee.