Question

In this problem, you are going to explore three different ways
to determine the gravitational constant *G*.

**Part (a)** By observing that the centripetal
acceleration of the Moon around the Earth is *a*_{c}
= 2.65 × 10^{-3} m/s^{2}, what is the gravitatonal
constant *G*, in cubic meters per kilogram per square
second? Assume the Earth has a mass of *M*_{E} =
6.02 × 10^{24} kg, and the mean distance between the
centers of the Earth and Moon is *r*_{m} = 3.83 ×
10^{8} m.

**Part (b)** Measuring the centripetal acceleration
of an orbiting object is rather difficult, so an alternative
approach is to use the period of the orbiting object. Find an
expression for the gravitational constant in terms of the distance
between the gravitating objects *r*_{m}, the mass of
the larger body (the earth) *M*_{E}, and the period
of the orbiting body *T*.

**Part (c)** The gravitational constant may also be
calculated by analyzing the motion of an object, launched from the
surface of the earth at an initial velocity of
*v*_{i}. Find an expression of the gravitational
constant from the initial velocity, mass of the earth
*M*_{E}, and the initial and final heights. Use the
parameter *φ* = 1/*r _{initial}* -
1/

Answer #1

2. In 1993 the Galileo spacecraft sent home an image of asteroid
“243 Ida” and a tiny moon “Dactyl” orbiting the asteroid. Assume
that the small moon orbits in a circle with a radius of r = 100 km
from the center of the asteroid with an orbital period of T = 27
hours.
a) Show and explain how we derived Kepler’s 3rd
law in class using Newton’s 2nd Law, the definition
for centripetal acceleration, and the equation for the...

9. In 1993 the Galileo spacecraft sent home an image of asteroid
“243 Ida” and a tiny moon “Dactyl” orbiting the asteroid. Assume
that the small moon orbits in a circle with a radius of r = 100 km
from the center of the asteroid with an orbital period of T = 27
hours.
a) Show and explain how we derived Kepler’s 3rd law in class
using Newton’s 2nd Law, the definition for centripetal
acceleration, and the equation for the...

Consider a satellite of mass m in a circular orbit of radius r
around the Earth of mass ME and radius RE.
1.
What is the gravitational force (magnitude and direction) on
the satellite from Earth?
2.
If we define g(r) to be the force of gravity on a mass m at a
radial distance r from the center of the Earth, divided by the mass
m, then evaluate the ratio g(r)/g(RE)to see how g varies with
radial distance. If...

i) Explain the difference between a man-made and a
natural satellite.
ii) State two important advantages of weather
satellites.
iii) Starlink is a satellite constellation being
constructed by SpaceX to provide global satellite Internet access.
The constellation will consist of thousands of small satellites in
low earth orbit. A Starlink launch to an altitude of 550km is
required. The Falcon 9 launcher delivers 9.0 metric tonnes payload
into a LEO orbit. The lift-off mass is 318 tonnes. The U of...

Two asteroids in space that are near each other experience a
force of 5,107 N due to the gravitational force between
them. If their positioning was changed so that they were
spaced 2 times their original distance apart, what would the new
force of attraction between them be?
A Ferris wheel at a carnival has a radius of 12 m and turns so
that the speed of the riders is 4.9 m/s. What is the magnitude of
the centripetal acceleration that...

In a class question you solved the problem of the "Ballistic
Pendulum". This problem might be called a "Ballistic Spring".
A spring of equilibrium (un-stretched) length L 0 is hung
vertically from one end. A mass M is attached to the other end of
the spring and lowered so that the mass hangs stationary with the
spring stretched a distance Δ L.
The position of the bottom end of the un-stretched spring is
defined as y = 0 and shown...

ch 6
1:
It is generally a good idea to gain an understanding of the
"size" of units. Consider the objects and calculate the kinetic
energy of each one.
A ladybug weighing 37.3 mg
flies by your head at 3.83 km/h
.
×10
J
A 7.15 kg
bowling ball slides (not rolls) down an alley at 17.5 km/h
.
J
A car weighing 1260 kg
moves at a speed of 49.5 km/h.
5:
The graph shows the ?-directed force
??...

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