Question

(a) What is the escape speed on a spherical asteroid whose radius is 590 km and whose gravitational acceleration at the surface is 2.7 m/s2? m/s

(b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s? m

(c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface? m/s

Answer #1

(a)
What is the escape speed on a spherical asteroid whose radius is
633 km and whose gravitational acceleration at the surface is 0.707
m/s2? (b) How far from the surface will a particle go if it leaves
the asteroid's surface with a radial speed of 601 m/s? (c) With
what speed will an object hit the asteroid if it is dropped from
868.7 km above the surface?

A small moon has a radius of 758 km. The acceleration due to
gravity at its surface is 1.65 m/s^2. (Assume the moon to be
spherical).
a) Calculate the escape velocity for a small spaceship trying to
leave the moon.
b) If it leaves the surface with a radial velocity of 1010 m/s,
how far from the surface will it go?
c) If the spaceship accidentally drops a crate of cargo from
183.9 km above the surface, with what
speed...

A spherical asteroid with a radius of 11 km approaches Earth
with a speed 0.3c. What is the volume of the asteroid as determined
by an Earth-based observatory.
(The volume of an ellipsoid with semi-axis a,b, and d is
4π*a*b*d/3).

Consider a spherical, homogeneous planet with a radius of
rp=3985 km and a mass of mp=8.97×1024 kg. A spherical object with a
radius of r0=9.21 m and mass m0=868 kg approaches the planet.
Part 1) When the object is 5.33×109 km away from the planet,
what is the magnitude of the force the planet exerts on the object?
F= N
Part 2) When the object is 8.10 m above the surface of the
planet, what is the magnitude of the...

For a spherical celestial object of radius R, the
acceleration due to gravity g at a distance x
from the center of the object is g =
g0R2/x2,
where g0 is the acceleration due to gravity at
the object's surface and x > R. For the moon,
take g0 = 1.63 m/s2 and R =
3200 km. If a rock is released from rest at a height of 5R
above the lunar surface, with what speed does the rock impact...

Having aced your introductory physics course, you are hired as a
summer intern at NASA. You are sent as part of a team to explore
the possibility of mining iron from a small, airless spherical
asteroid with a radius of 522 km and a surface acceleration of 2.7
m/sec2.
1)What is the mass of the asteroid?
2)What is the minimum vertical velocity you could give a 5 kg
rock from the surface of this asteroid so that it continues to...

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...

The escape speed from an object is v2 = 2GM/R, where M is the
mass of the object, R is the object's starting radius, and G is the
gravitational constant 6.67 × 10-11 m3 kg-1 s-2. What is the
approximate escape speed, in km/s, from the Solar System starting
from an orbit at 0.6 AU? In this case, the mass of the Sun, 2.2e+30
kg, can be used as the mass of the Solar system.

(A) Calculate the acceleration of gravity,
gC, on Ceres
Apply the kinematics displacement equation to the falling
rock.
(1)
Δx = 1/2at2 +
v0t
Substitute Δx = -10.0 m, v0 = 0,
a = -gC, and t = 8.06 s, and
solve for the gravitational acceleration on Ceres,
gC.
-10.0 m = -1/2gC(8.06 s)2 →
gC = 0.308 m/s2
(B) Find the mass of Ceres.
Equate the weight of the rock on Ceres to the gravitational
force acting on the...

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...

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