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Newton’s Universal Law of Gravitation 2
 The motion of a satellite around the Earth is a circular motion where Earth’s
gravitational force acts as a centripetal force, therefore:
𝑚𝑀𝐸 𝑚𝑣 2
𝐹𝑐 = 𝐺 2 =
𝑟
𝑟
where m is the satellite’s mass, ME is Earth’s mass, v is the velocity of the satellite
and r is the distance of the satellite from the center of the Earth.
1.
The mass of the Hubble Space Telescope is 11,600 kg. Determine
the weight of the telescope:
a) when it was resting on the Earth
b) as it is in orbit 598 km above the Earth’s surface
2.
Determine the speed of the Hubble Space Telescope orbiting at a
height of 598 km above the Earth’s surface.
3.
The Hubble telescope has detected the light being emitted from
different regions of galaxy M87, which is shown above. The black
hole identifies the center of the galaxy. From the
characteristics of this light, astronomers have determined an
orbiting speed of 7.5x105 m/s for matter located at a distance of
5.7x1017 m from the center. Find the mass M of the object located
at the galactic center.
4.
The Moon orbits the Earth at a distance of 3.85x108 m. Assume
that this distance is between the centers of the Earth and the
Moon. Find the period for the Moon’s motion around Earth. Express
the answer in days and compare it to the length of a month.
5.
A satellite is placed in orbit 6.00x105 m above the surface of
Jupiter. Jupiter has a mass of 1.90x1027 kg and a radius of
7.14x107 m. Find the orbital speed of the satellite.
6.
The Earth orbits the Sun once a year (365 days). Venus orbits the
Sun at a
distance of 1.08x1011m. This distance is between the
centers of Venus and the Sun. The mass of the Sun is
𝑀 = 2.0 × 1030 𝑘𝑔. How long (in Earth days) does it take for Venus
to make one orbit around the Sun?
7.
A satellite has a mass of 5,850 kg and is in a circular orbit
4.1x105 m above the surface of the planet. The period of the
orbit is two hours. The radius of the planet is 4.15x106 m. What
is the true weight of the satellite when it is at rest on the
planet’s surface?
8.
The mass of a robot is 5,450 kg. This robot weighs 3,620 N more
on planet A than it does on planet B. Both planets have the same
radius 1.44x107 m. What is the difference MA – MB in the masses
of the planets?
9.
The drawing above (not to scale) shows one alignment of the Sun,
Earth and Moon. The gravitational force FSM that the Sun exerts on
the Moon is perpendicular to the force FEM that the earth exerts
on the Moon. The mass of the sun is 2.0x1030 kg. The distances
shown in the diagram are rSM =1.50x1011 m and rEM = 3.85x108 m.
Determine the magnitude and direction of the net gravitational
force on the Moon.