The small spherical planet called \"Glob\" has a mass of 8.06×10 18 kg and a rad

Question

The small spherical planet called "Glob" has a mass of 8.06×1018 kg and a radius of 6.08×104 m. An astronaut on the surface of Glob throws a rock straight up. The rock reaches a maximum height of 2.36×103 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 = 6.67×10-11 Nm2/kg2.)

A 40.0 kg satellite is in a circular orbit with a radius of 1.50×105 m around the planet Glob. Calculate the speed of the satellite.

I need help and answers with these with each step taken and the numbers within those steps so i can see whats going on.

Explanation / Answer

initial PE of system = -GMm / d

PEi = -6.67 x 10^-11 x 8.06 x 10^18 x m / (6.08 x 10^4) = -8842.14m J

KEi = mv^2 /2

Fianl PE

PEf = -6.67 x 10^-11 x 8.06 x 10^18 x m / (6.08 x 10^4 + 2.36x10^3 )
= - 8511.75m J

KEf = 0

Using energy conservation,

-8842.14m + mv^2 /2 = - 8511.75 + 0

v = 25.71 m/s

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For satellite's circular path,

GMm / d^2 = mv^2 /d

v^2 = GM /d = 6.67 x 10^-11 x 8.06 x 10^18 / (6.08x10^4 + 1.50x10^5)

v = 50.50 m/s

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