The small spherical planet called \"Glob\" has a mass of 7.081018 kg and a radiu

Question

The small spherical planet called "Glob" has a mass of 7.081018 kg and a radius of 5.75104 m. An astronaut on the surface of Glob throws a rock straight up. The rock reaches a maximum height of 1.64103 m, above the surface of the planet, before it falls back down. What was the initial speed of the rock as it left the astronaut's hand? (Glob has no atmosphere, so no energy is lost to air friction. G = 6.6710-11 Nm2/kg2.) A 39.0 kg satellite is in a circular orbit with a radius of 1.45105 m around the planet Glob. Calculate the speed of the satellite.

Explanation / Answer

acceleration due to gravity on the planet glob = GM/R^2

= 6.67*10^-11 * 6.16 *10^18/(5.87*10^4)^2

= 1.192 *10^-1 = 0.1192 m/s^2

Now from third equation of motion v^2 = U^2 + 2 a S

=> 0 = u^2 + 2 (-0.1192)( 1.20*10^3)

=> u = 16.91 m/s

Centripetal acceleration = Gravitational force

mv^2/ (R+r) = GMm/(R+r)^2

v^2 = GM/(R+r) = 6.67*10^-11*6.16*10^18/(5.87*10^4+1.25*10^5)

= 2.23*10^-1 = 0.223

v = 0.4722m/s

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