The Best of Creative Computing Volume 1 (published 1976)
Escape
Perhaps both these arguments sound reasonable to you.
But they can't both be right! And one can't decide between
them except by doing calculations to find out. (Or by doing
an experiment - can one fire something off into space so
that it never comes back?)
This is where the computer can help. It has been
programmed to answer different questions to do with
launch velocity and distance travelled. Of course, it has to
assume a theoretical basis on which to make these
calculations. lt has been programmed to assume that the
gravitational force falls off according to the inverse-square
law, and that there is no air resistance. Other simplifying
assumptions have been made, such as:
> the earth is the only body in the Universe
> the probe is always launched vertically upwards
The computer can tell you:
A What launch velocity is needed to fire a probe to a
particular chosen distance.
B What velocity the probe has left at certain distances,
for a particular launch velocity.
C At what distance does the probe stop and turn
around and begin returning to earth, for a chosen
launch velocity.
Your job is to use the computer to help answer the problem
posed earlier: "ls it possible to fire something so fast that it
will never return?"
Decide which of the three questions (A, B or C above)
would be the most helpful.
For each question you will have to give some information.
For example, if you ask for question C to be answered
you will have to choose values for the launch velocity of
the probe, and its mass.
To help you find the answer to the problem use the
computer to anwver these specific questions:
Q3 Does die mass of the probe affect how far it will travel
for a given launch velocity, or what launch velocity it
must be given if it is to reach a certain distance; lf so,
how?
Q4 Suppose the last question were asked about energy
instead of velocity - would the answer be the same?
(Does the mass of the probe affect how far it will travel
for a given initial kinetic energy, or what energy it
must be given if it is to reach a certain distance?)
Q5 The earth's radius, R is about 6,000km (6 x 10^6m).
What launch velocity is needed to carry a probe from
the earth's surface to a distance R from it?
The next question refers to the distance from earth to
the moon, the sun, etc., but in answering it you should
assume, as before, that the earth is the only body in the
Universe.
Q6 What launch velocity is needed to get a probe as far as
the moon (earth - moon distance is about 380 x 10^6m)?
- as far away from the earth as the sun is (150x 10^6m)?
- as far as Pluto, the furthest known planet
(about 60 x 10^12m)?
- as far as the nearest star (about 40 x 10^15m)?
- as far as you like.
Sample output is shown only for Question A. Run the
program yourself to see how it works for Questions B and
C.
I INPUT DO YOU WANT?
TYPE LAUNCH VELOCITY TO REACH A CHOSEN HEIGHT
OR 2 FOR VELOCITY AT DIFFERENT HEIGHTS, FOR A CHOSEN LAUNCH VELOCITY
OR 3 FOR HEIGHT REACHED FOR A CHOSEN LAUNCH VELOCITY
T0 INTERRUPT THE PROGRAM T0 GET DIFFERENT OUTPUT
TYPE 0 WHEN YOU ARE ASKED T0 INPUT MASS, OP HEIGHT
MASS OF PROBE (KG) HEIGHT (M) LAUNCH VELOCITY (M/S)
7l000
7150000
1700.22
70
TO GET ANOTHER OUTPUT AS LISTED ABOVE TYPE I,2 OR 3
TYPE 4 IF YOU WOULD LIKE A TABLE OP GRAPH SHOWING
THE LAUNCH VELOCITY NEEDED T0 PEACH CHOSEN HEIGHTS
TYPE 0 TO END THE PROGRAM
74
TYPE (1) FOR TABLE
OR (2) FOP GRAPH
72
TOTAL HEIGHT <METRES>:7400000
HT. LAUNCH VELOCITY (M/S)
(M) 0 2724.71
----------|----------|----------|----------|----------|
+
+
+
+
40000. - *
+
+
+
+
80000. - *
+
+
+
+
120000. - *
+
+
+
+
160000. - *
+
+
+
+
200000. - *
+
+
+
+
240000. - *
+
+
+
+
280000. - *
+
+
+
+
320000. - *
+
+
+
+
360000. - *
+
+
+
+
400000. - *
TYPE 1 IF YOU WANT TO RE-RUN THIS PART OF THE PROGRAM
70
