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A spacecraft is to land on a dwarf planet or moon of mass 1.35 x1023 kg and radius 2300 km. (a) What gravitational acceleration (in m/s?) would act on the spacecraft when it is near the body's surface?

A spacecraft is to land on a dwarf planet or moon of mass 1.35 x1023 kg and radius 2300 km. (a) What gravitational acceleration (in m/s?) would act on the spacecraft when it is near the body's surface?

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A spacecraft is to land on a dwarf planet or moon of mass 1.35 x1023 kg and radius 2300 km. (a) What gravitational acceleration (in m/s2) would act on the spacecraft when it is near the body's surface? Additional question (separate entry box below, and included in accompanying work): (b) If a projectile is shot directly upward (in a radial direction) from this dwarf planet or moon's surface at 0.85 times the escape speed, what maximum height above the surface (in km) would the projectile reach? (Ignore any effects due an atmosphere, if any).
Transcribed Image Text:A spacecraft is to land on a dwarf planet or moon of mass 1.35 x1023 kg and radius 2300 km. (a) What gravitational acceleration (in m/s2) would act on the spacecraft when it is near the body's surface? Additional question (separate entry box below, and included in accompanying work): (b) If a projectile is shot directly upward (in a radial direction) from this dwarf planet or moon's surface at 0.85 times the escape speed, what maximum height above the surface (in km) would the projectile reach? (Ignore any effects due an atmosphere, if any).
Expert Solution
Step 1

Given:

M=1.35×1023kg

R=2300×103 m

v=0.85ve

Step 2

Formula used:

g=GMR2

Ve=2gR

-GMmR+12mv2=-GMmR+h

Where

M=mass of planet

R=radius of planet

G=gravity

v=velocity

 

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