Nasa lands a 10kg space probe on planet Zero (mass of5.0x10 23 kg, radius of 3.0

Question

Nasa lands a 10kg space probe on planet Zero (mass of5.0x1023kg, radius of 3.0x106m, noatmosphere). (A) If the probe is to acheive a maximum distance of2.0x106m from the SURFACE of Zero, with what initialspeed must it be launched directly upward from the surface ofZero? (B) In a separate situation, supposed the probe moves in acircular orbit about Zero with radius 5.0x106m. Nasawishes to move the probe to a new circular orbit of radius4.0x106m by executing a series of thruster burns. Forhow many total seconds must the thrusters burn if they produce100kW of power? [hint: remember that power*time - energy and for acircular orbit Emech = -KE = 1/2Ugrav] Thanks for your help! Nasa lands a 10kg space probe on planet Zero (mass of5.0x1023kg, radius of 3.0x106m, noatmosphere). (A) If the probe is to acheive a maximum distance of2.0x106m from the SURFACE of Zero, with what initialspeed must it be launched directly upward from the surface ofZero? (B) In a separate situation, supposed the probe moves in acircular orbit about Zero with radius 5.0x106m. Nasawishes to move the probe to a new circular orbit of radius4.0x106m by executing a series of thruster burns. Forhow many total seconds must the thrusters burn if they produce100kW of power? [hint: remember that power*time - energy and for acircular orbit Emech = -KE = 1/2Ugrav] Thanks for your help!

Explanation / Answer

(a) conservation of energy... .    initial K   + U  =    final K +   U .         (1/2) mv2     - G M m / R  =    0     -   G M m /r .         v2   =   2GM/R   -   2GM/r   =     2GM (r -R) / rR = .                = 2 * 6.673 x 10-11 * 5.0 x 1023(2.0 x 106 ) / (5.0 x 106 ) (3.0 x106) = .                  =    8.8973 x106       but...   v is the sq root of this or .   v =    2983 m/s .

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