2103 Univ Grav Notes

8/13/2019 2103 Univ Grav Notes

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UNIVERSAL GRAVITATION & PLANETARY MOTION

Warm-up: A mass of 0.38 kg is tied to a string and allowed to revolve in a

circle of radius 1.16 m on a horizontal, frictionless table. The other end of

the string passes through a hole in the center of the table and a mass of

0.94 kg is tied to it. The suspended mass remains in equilibrium while the

puck revolves. The acceleration of gravity is 9.8 m/s2.

a.)What is the tension in the string?

b.)What is the speed needed by the 0.38 kg mass to maintainequilibrium?

On your own: Who are Tycho Brahe & Johannes Kepler?http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Keplers Laws of Planetary Motion

1st The Law of Orbits: Planets move in elliptical orbits with the Sun at one

of the foci.

2ndThe Law of Areas: A line from the Sun to a planet sweeps out equal

areas in equal lengths of time.

3rd

The Law of Periods: The square of the orbital period of a planet isdirectly proportional to the cube of the average distance of the planet

from the Sun.
http://csep10.phys.utk.edu/astr161/lect/history/kepler.htmlhttp://csep10.phys.utk.edu/astr161/lect/history/kepler.htmlhttp://csep10.phys.utk.edu/astr161/lect/history/kepler.html


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Example: An asteroid revolves around the sun with an average orbital

radius twice that of Earths. Predict the period of the asteroid in Earth

years.


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Period of Planetary Motion:

* In this derivation of the equation, orbits are assumed to be circles

** Newton found the same result for elliptical orbits

On your own: Research Henry Cavendish &

the universal gravitation constant


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Example:

What is the gravitational force between you and the earth, if your mass is

65 kg, the Earths mass is 5.98x1024kg, and the radius of the Earth is

6.38x106m?

Questions:

1. Earth is attracted to the sun by the force of gravity. Why doesnt the

Earth fall into the sun?

2. If Earth began to shrink but had its mass remain the same, what would

happen to g on Earths surface?

3. Picking up a rock requires less effort on the moon than on Earth. How

will the weaker gravitational force on the moons surface affect the path

of the rock if thrown horizontally?


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Using the Law of Universal Gravitation

Example: Two bowling balls (each with a mass of 6.8 kg) are next to each

other. Their centers are 21.8 cm apart. What gravitational force do they

exert on one another?

Givens: Equations:

Unknown: Substitute & Solve:

Motion of Planets & Satellites

What if an object fell at the same rate and distance that the Earths surface

curved away?

Centripetal Acceleration equation:

Centripetal Force equation:

Law of Universal Gravitation:

Combine, then solve for v.

The speed of an object in

circular orbit:

Period for Satellite Circling Earth:

(can apply to another body

being orbited)


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Practice Problems:

1) What keeps a satellite up?

2) A satellite is going around the Earth. On which of the following does the

speed depend?

a) mass of satelliteb) distance from the Earth

c) mass of the Earth

3) The asteroid Ceres has a mass of 7x1020kg and a radius of 500 km.

a) What is g on its surface?

Givens: Substitute & Solve:

Unknowns:

Equations:

b) How much would an 85-kg astronaut weigh on Ceres?


Unknowns:

Equations:

4) Apollo 11 is orbiting the moon with an average orbit of 111 km. The

radius of the moon is 1785 km, and the mass of the moon is 7.3x1022kg.

a) What is the period of Apollo 11 around the moon?


Unknowns:

Equations:

b) At what speed did Apollo 11 orbit the moon?


Unknowns:

Equations:

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2103 Univ Grav Notes