Please see the attached file. This solution consists of all the detailed explanation given at the end, after the table.

http://hyperphysics.phy-astr.qsu.du/hbase/vesc.html#ves
Use the following applet to calculate the escape velocity. Do not use commas when putting numbers into this applet.

1 2 3 4 5 6 7 8

m2 r g a=gx10m/sec2 m1 f=m1x a 0.22f Applet
escape
planet mass planet gravitational acceleration your your your velocity
pull of g mass weight weight km/sec
(earth=1) radius (earth= 1 g) newton pd
(x) (y) g(x/y2)

1 1 1g 10 m/sec2 60kg 600 N 132 11.2

1 2 1(g/4) 2.5 m/sec2 60kg 150 N 33 7.84

2 2 1(g/2) 5.0 m/sec2 60kg 300 N 66 11.2

318 11.2 2.535 g 25.35 m/sec2 60kg 1521N 334.62 59.68
(jupiter)

0.002 0.17 0.069g 0.69 m/sec2 60kg 41.4 N 9.108 1.215
(pluto)

95 9.4 1.075g 10.75 m/sec2 60kg 645 N 141.9 35.6
(saturn)

100,000 0.01 109 g 1010 m/sec2 60kg 6 x 1011 1.32x1011 35420
(neutron
star)

Formulae used in above table:
• Column 3 (g): Gravitational pull:
Gravitatoinal acceleration due to the planet in multiples of g:
Gravitatoinal acceleration due to the planet
For earth, Gravitational acceleration
For a planet with mass m2 =mp = xme and Rp = yRe,

The 1st column of mass m2 denotes the ratio of mass of the planet to that of the earth i.e. (mp/me) while the second column of radius r denotes the ratio of radius of the planet to the radius of the earth.

• Column 4 (a) Gravitational acceleration of the planet:
Gravitational acceleration of the planet: (Column3)x (g due to earth, 10m/s2)

• Column 5 Given

• Column 6 f = ma i.e. f = (column 5) x (column 4)

• Column 7 = 0.22 x (Column 6)

• Column 8 Escape velocity from the surface of a planet
----- (1)
Radius of the planet = y (Radius of the Earth)
i.e. Rp = y Re ----- (a) (Get y from column 2)

From column 3, get gp = (x/y2)g ----- (b)
Substituting (a) and (b) in equation (1), we get

i.e. ---- (2)
Escape velocity from the surface of the earth ---- (3)
[This value is a standard value. If required, it can be calculated by substituting
g = 10 m/s2 and radius of the earth R = 6400 km = 6.4 x 106 m in equation (3) ]
Dividing equation (2) by (3), we get the escape velocity from the surface of the
planet in terms of escape velocity from the surface of the Earth as

i.e. ----- (4)
i.e. in km/s ----- (5)
Use equation (5) for the calculation of the escape velocities for all the planets in last column.
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