Escape Speed

1
Escape Speed
Escape speed The minimum speed required for a
projectile to escape the gravitational effects of
an object. For the purist The escape speed is
defined to be the speed at which all kinetic
energy at the surface of the object (planet,
star.) is sufficient to allow the object to
escape the influence of gravity. The calculation
is based on conservation of energy arguments.
2
Escape Speed
In general
(
)
1/2
2 G M
vescape
R
Note This looks like the relationship we have
used in the past relating masses to orbital
speeds, but watch out for the 2.
3
Escape Speed
Show that the escape velocity for rockets leaving
the surface of the earth is 11 x 103 m/sec.
M 5.97 x 1024 Kg
R 6.378 x 106 m
vescape, earth 2 (6.6 x 10-11 N m2 /kg2 )
(5.97 x 1024 Kg) / (6.378 x 106 m) 1/2
11 x 103 m/sec
4
Escape Speed
What is the escape velocity for a typical white
dwarf? For a white dwarf, use
M 2.18 x 1030 Kg
R 5.1 x 106 m
vescape, dwarf 2 (6.6 x 10-11 N m2 /kg2 )
(2.18 x 1030 Kg) / (5.1 x 106 m) 1/2
7.5 x 106 m/sec
5
Escape Speed
What is the escape velocity for a typical neutron
star? For a neutron star, use
M 3.3 x 1030 Kg
R 2.0 x 104 m
vescape, neutron 2 (6.6 x 10-11 N m2 /kg2 )
(3.3 x 1030 Kg) / (2.0 x 104 m) 1/2
1.4 x 108 m/sec
6
Escape Speed
Interesting piece of information IF the earth
(magic?) could be collapsed to a radius of
0.008756 m (just about a centimeter)
Some numbers From the surface of the earth,
M 5.97 x 1024 Kg
R 8.756 x 10-3 m
vescape, dwarf 2 (6.6 x 10-11 N m2 /kg2 )
(5.97 x 1024 Kg) / (8.756 x 10-3 m) 1/2
vescape, earth 3.0 x 108 m/sec