# Escape velocity

### Pages to are hidden for

"Escape velocity"

```					How many firework rockets are needed to fire Mr. Baker into orbit?

Work through the information here with students so that at the end they can tell you
how many rockets are needed. The whole thing looks at Gravitational fields,
Ft=m(v-u) and does a little practical demonstration to.

Escape velocity
The escape velocity of a planet or indeed any other gravitational system is the velocity that
it would have to be given to escape from the gravitational field of that planet. It could be a
provided in a short burst of acceleration to gain enough kinetic energy and would be
unpowered after that.
If we consider a space probe of mass m at the surface of a planet radius R then :
Gravitational potential energy = -GMm/R the energy required to escape from the field is
therefore +GMm/R.

Kinetic energy to be applied = ½ mv2 and so ½ (mv2) = GMm/R. Therefore :

Escape velocity (ve) = (2GM/R)1/2 = (2Rgo)1/2

It is interesting to think about the maximum velocity that might be reached by a
meteorite falling onto the Earth's surface. If the meteorite starts from infinity with
zero velocity and is accelerated towards the Earth by the Earth's field alone then
you should be able to see that the greatest speed that it could have when it
reached the earth is the escape velocity of the Earth.

The escape velocity is also important if we want to find whether a planet can
retain its atmosphere. The higher velocity molecules will escape the gravitational
pull if their velocity is greater than the escape velocity of the planet.

Example problems
-2
1. Calculate the escape velocity of the Earth given that go = 9.8ms and that the
6
radius of the Earth is 6.4x10 m
1/2                 6     1/2            4       -1            -1
escape velocity ve = (2Rgo)         = (2x6.4x10 x9.8)         = 1.12x10 ms = 11.2 kms
-1
2. Calculate the radius of a planet with the an escape velocity of 6.2 ms - about
the speed of take off of a top class high jumper on Earth. Assume the planet has the
-3
same average density as the Earth - 5500 kgm .
1/2                            2                3   2
Escape velocity ve = (2GM/R)               therefore R = 2GM/ve =2G(4/3)πR r/ ve
2              1/2
and so R = (ve /2G(4/3)r)
-11             1/2              3
Planet radius = (6.22/2x6.67x10 x1.33xx5500)                   = 3.53x10 m = 3.53 km!

Change in g with height – this is minimal until satellite orbit heights are reached. In fact
for a height of some 200 km above the Earth’s surface the g value has decreased from
about 9.8 ms-2 to around 7.5 ms-2.

Ft=mv-mu -
The firework rocket - upside down!
This needs to be done outside the lab and with great care. Mount a small firework rocket,
one without star shells, pointing downwards and held loosely in a tube in a clamp on the
top of a cheap top pan balance reading to an accuracy of one gram.
A safety screen is essential and you should stand well back.

Light the rocket and stand well back behind the safety
screen. The thrust of the rocket acts downwards and the
reading on the top pan balance gives the thrust of the
rocket during the firing. Use a TV camera if possible to
record this for later analysis. The "toy" chemical rockets
that are produced are sold with data sheets that give good
force against time curves and these can be used for
analysis if you do not wish to do the rocket experiment
yourselves!
Some safer alternatives would be to use a balloon, a soda
!
siphon bulb or a plastic bottle containing dilute acid and
chalk.

Age range: 16-18

Apparatus required:
Firework rocket (small - without star shells) Top pan balance
Small metal tin lid Piece of hardboard to protect balance           246
Safety screen Retort stand and two clamps Launch tube to
hold rocket

2

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 1 posted: 9/14/2012 language: simple pages: 2