At what angular speed (in rpm) should it spin?

Question

There is strong evidence that Europa, a satellite of Jupiter, has a liquid ocean beneath its icy surface. Many scientists think we should land a vehicle there to search for life. Before launching it, we would want to test such a lander under the gravity conditions at the surface of Europa. One way to do this is to put the lander at the end of a rotating arm in an orbiting earth satellite.

1) If the arm is 4.25 m long and pivots about one end, at what angular speed (in rpm) should it spin so that the acceleration of the lander is the same as the acceleration due to gravity at the surface of Europa? The mass of Europa is 4.8 x 10^22 kg and its diameter is 3138 km.

thank you

Answer 1

Let:

G be the gravitational constant,

M be the mass of Europa,

m be the mass of an object on Europa,

g be the acceleration due to gravity on Europa,

R be the radius of Europa,

w be the angular velocity of the lander arm.

GMm / R^2 = mg

GM / R^2 = g

rw^2 = g

Eliminating g:

w^2 = GM / (R^2 r)

w = sqrt[ 6.674 * 10^(-11) * 4.8 * 10^22 / (3.138 * 10^6)^2 * 4.25 ] * 60 / (2pi)

= 2.64 rev / min.