The small spherical planet called \"Globus\" has a mass of 6.8 × 1018 kg and a r

Question

The small spherical planet called "Globus" has a mass of 6.8 × 1018 kg and a radius of 57000 m. An astronaut on the surface of Globus throws a stone up. The rock reaches a maximum height of 1800 m above the surface of the planet before falling back. Neglecting the height of the astronaut.

A) What was the initial speed of the stone when it left the hands of the astronaut?
(Globus has no atmosphere, therefore there is no energy to be lost due to friction.)

B) A 48 kg satellite is in a circular orbit (radius 140000 m) around the planet Globus. Calculate the magnitude of the satellite speed. (G = 6.67 × 10-11 Nm2 / kg 2).

Explanation / Answer

Mass of the planet   MP = 6.8e+18 kg

Radius R   = 57000 m

garvitational acceleration on the planet   g = G MP /R2 ( we ingnore the impact of height h)

                                                                   =6.67e-11*6.8e+18/ 570002

                                                                   = 0.139 m/s2

max. height reached by the stone h = 1800 m

v = sqrt(2gh) = sqrt(2*0.139*1800) = 22.42 m/s

B) radius of the satellite     r= 140000 m

              mass                   m = 48 kg

when the satellite is in orbit

centrifugal force   mv2/r = GmM /r2 , Gravitational force

          v = sqrt(GM/r)   = sqrt( 6.67e-11 *6.8e+18/1.4e+5)

                 = 56.92 m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.