Apollo 11 mission – Data Analysis! A large-scale experiment in space




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Apollo 11 mission – Data Analysis!

A large-scale experiment in space
Detailed data are kept of every space flight. These data, giving speeds and distances of Apollo 11 as it went to and returned from the Moon, are extracted from data supplied by NASA. They can be thought of as the results of an experiment to probe Earth’s gravitational field.
You will need

  • computer running a spreadsheet (excel or LoggerPro)

  • data table (see next page)


Finding the gravitational field at different distances

The spreadsheet just provides raw data. To get information from it you will have to select and process data from it.

The flight data have a number of values of velocity and distance, arranged in pairs measured 10 minutes (600 seconds) apart. You can see how far Apollo 11 travelled in 10 minutes. You can see that Apollo 11 is decelerating on the way out and accelerating on the way home. You can find the acceleration and so the gravitational field at different distances:
1. Calculate the changes in velocity between each pair of distances.

2. Calculate the average distance for each pair.

3. Calculate the average acceleration at each distance, from the change in velocity and the time interval (600 s).

4. Plot one or more graphs to test whether the acceleration varies as the inverse square of the distance. Take trouble to find the graphs which best tell the message in these data. Give the graphs a caption saying what they have to tell.


Warning: the velocities given point approximately away from the centre of the Earth, but the space flight does change direction. So a simple calculation of the acceleration is only roughly an indication of the Earth’s gravitational field at that point.
Data from the Apollo 11 mission













Events

Ground elapsed time / hours:minutes:seconds




Distance r from centre of Earth / 106 m

Velocity v / m s–1




launch from surface of Earth

00:00:00













ignition to inject into coasting orbit to Moon (5 m 20 s burn)

02:44













coasting begins with no rocket burn

03:08:00

1

11.054

8406






















10 minute =

03:58:00

2

26.306

5374




600 s interval

04:08:00

2A

29.030

5102






















10 minute =

05:58:00

3

54.356

3633




600 s interval

06:08:00

3A

56.368

3560






















10 minute =

09:58:00

4

95.743

2619




600 s interval

10:08:00

4A

97.242

2594






















10 minute =

19:58:00

5

169.900

1796




600 s interval

20:08:00

5A

170.945

1788






















no rocket burn until this time

26:44:57.92

6

209.228

1531.56




3.55 second burn

26:45:01.47

7

209.232

1527.16






















10 minute =

32:58.00

8

240.624

1356




600 s interval

33:08:00

8A

241.417

1352




Landing on Moon. Moon walk.
















Rocket burn to return

150:28













Coasting back to Earth
















10 minute =

166:38:00

9

241.637

1521




600 s interval

166:48:00

9A

240.740

1524






















10 minute =

172:18:00

10

209.722

1676




600 s interval

172:28:00

10A

208.737

1681






















10 minute =

178:28:00

11

170.891

1915




600 s interval

178:38:00

11A

169.766

1923






















10 minute =

187:58:00

12

96.801

2690




600 s interval

188:08:00

12A

95.241

2715






















10 minute =

191:48:00

13

56.368

3626




600 s interval

191:58:00

13A

54.310

3699






















10 minute =

193:48:00

14

28.427

5201




600 s interval

193:58:00

14A

25.640

5486






















10 minute =

194:38:00

15

13.311

7673




600 s interval

194:48:00

15A

10.036

8854




Rocket burn on re-entry

195:03











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