Question

The Little Prince lives on an asteroid with a radius of 10 km made up of volcanic rock (density 2,500 kg/m3). His mass is 30 kg. a) What is his weight on the asteroid? On Earth he can jump to a height of 1 m. With that knowledge, he jumps up on the asteroid as hard as he can. b) Will he be able to escape the asteroid? The mass of the Earth is 6 x 1024 kg. The radius of the Earth is 6370 km. The universal gravitational constant is 6.67 x 10-11 Nm2kg-2.

Answer #1

The Little Prince lives on an asteroid with a radius of 10 km
made up of volcanic rock (density 2,500 kg/m3). His mass
is 30 kg. a) What is his weight on the asteroid?
On Earth he can jump to a height of 1 m. With that knowledge, he
jumps up on the asteroid as hard as he can. b) Will he be able to
escape the asteroid?
The mass of the Earth is 6 x 1024 kg. The radius...

A satellite is set to orbit at an altitude of 20200 km above the
Earth's surface. What is the period of the satellite in hours?
(Earth radius 6.378×1066.378×106 m, Earth mass 5.97×10245.97×1024
kg, Universal Gravitational constant
G=6.67×10−11m3kg−1s−2G=6.67×10−11m3kg−1s−2 ).

An astronaut stands on the surface of Vesta, which, with an
average radius of 270 km, makes it the third largest object in the
asteroid belt. The astronaut picks up a rock and drops it from a
height of 1.4 m. He times the fall and finds that the rock strikes
the ground after 3.4 s.
(a) Determine the acceleration due to gravity at the surface of
Vesta.
m/s2
(b) Find the mass of Vesta.
kg
(c) If the astronaut...

The asteroid 243 Ida has a mass of about 4.0×1016kg
and an average radius of about 16 km (it's not spherical, but you
can assume it is). Calculate the acceleration of gravity on 243
Ida. What would an astronaut whose earth weight is 700 N weigh on
243 Ida? If you dropped a rock from a height of 2.0 m on 243 Ida,
how long would it take to reach the ground? If you can jump 53 cm
straight up...

he mass of a meteor with a radius of 1 km is about 9 x 1012 kg.
The mass of a meteor also is proportional to the cube of its
radius. Suppose a meteor with a radius of 8.2 km is moving at 1.9 x
104 m/s when it collides inelastically with the Earth. The Earth
has a mass of 5.97 x 1024 kg and assume the Earth is stationary.
The kinetic energy lost by the asteroid in this collision...

The mass of a meteor with a radius of 1 km is about 9 x 1012 kg.
The mass of a meteor also is proportional to the cube of its
radius. Suppose a meteor with a radius of 8.1 km is moving at 2 x
104m/s when it collides inelastically with the Earth. The Earth has
a mass of 5.97 x 1024 kg and assume the Earth is stationary. The
kinetic energy lost by the asteroid in this collision will...

The mass of a meteor with a radius of 1 km is about 9 x 1012 kg.
The mass of a meteor also is proportional to the cube of its
radius. Suppose a meteor with a radius of 8.5 km is moving at 2.0 x
104 m/s when it collides inelastically with the Earth. The Earth
has a mass of 5.97 x 1024 kg and assume the Earth is stationary.
The kinetic energy lost by the asteroid in this collision...

The mass of a meteor with a radius of 1 km is about 9 x 1012 kg.
The mass of a meteor also is proportional to the cube of its
radius. Suppose a meteor with a radius of 11.4 km is moving at 1.8
x 104 m/s when it collides inelastically with the Earth. The Earth
has a mass of 5.97 x 1024 kg and assume the Earth is stationary.
The kinetic energy lost by the asteroid in this collision...

2.) The mass of a meteor with a radius of 1 km is about 9 x 1012
kg. The mass of a meteor also is proportional to the cube of its
radius. Suppose a meteor with a radius of 10.7 km is moving at 1.7
x 104 m/s when it collides inelastically with the Earth. The Earth
has a mass of 5.97 x 1024 kg and assume the Earth is stationary.
The kinetic energy lost by the asteroid in this...

Assume the earth is a uniform sphere of mass M and
radius R. As strange as it may sound, if one can dig a
long tunnel from one side of the Earth straight through the center
and exit the other end, any object falling into the tunnel will
appear at the other end (i.e. the opposite side of the Earth) in
just 2530 s (42.2 min). Call that time t. Let t
be a function of G, M, and R,...

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