1. Arrange the following motions in order of increasing velocity: orbitof Earth around the Sun; an orbit around Earth near Earth's surface;an object just barely escaping Earth; orbit of the Moon around Earth;orbit of a geosynchronous satellite2. Arrange the following motions in order of increasing acceleration: adragster car; an object dropped off a cliff near the top of Mt. Everest;an object dropped by an astronaut standing on the Moon; an objectdropped from the top of a New York City skyscraper

1. Arrange the following motions in order of increasing velocity: orbit of Earth around the Sun; an orbit around Earth near Earth's surface; an object just barely escaping Earth; orbit of the Moon around Earth; orbit of a geosynchronous satellite

1. Arrange the following motions in order of increasing velocity: orbit of Earth around the Sun; an orbit around Earth near Earth's surface; an object just barely escaping Earth; orbit of the Moon around Earth; orbit of a geosynchronous satellite

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Question

1. Arrange the following motions in order of increasing velocity: orbit
of Earth around the Sun; an orbit around Earth near Earth's surface;
an object just barely escaping Earth; orbit of the Moon around Earth;
orbit of a geosynchronous satellite
2. Arrange the following motions in order of increasing acceleration: a
dragster car; an object dropped off a cliff near the top of Mt. Everest;
an object dropped by an astronaut standing on the Moon; an object
dropped from the top of a New York City skyscraper

Expert Solution

Step 1

Any object moving in a circular orbit experiences a centripetal force due to the circular motion of the object, given as

$F_{c} = \frac{m v^{2}}{r} m i s t h e m a s s o f t h e o b j e c t v i s i t s o r b i t a l v e l o c i t y r i s t h e r a d i u s o f t h e o r b i t$

For an object revolving in a circular orbit around another planetary object, this centripetal force is provided by the gravitational force of the planetary object given as

$F_{g} = G \frac{m M}{r^{2}} G i s u n i v e r s a l g r a v i t a t i o n a l c o n s \tan t M i s m a s s o f t h e p l a n e t a r y o b j e c t$

At equilibrium,

$F_{c} = F_{g} \frac{m v^{2}}{r} = G \frac{M m}{r^{2}} v^{2} = G \frac{M}{r} v = \sqrt{G \frac{M}{r}}$

Thus it can be seen that for any planetary body, the orbital velocity is inversely proportional to the radius of the orbit, while it is directly proportional to the mass of the object it revolves around

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