Flashcards in 10.3 Motion In A Gravitational Field Deck (8)

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1

## What is the derivation for the gravitational force when a point mass m orbits a spherical mass M the orbital radius is r and the orbital speed is v?

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The gravitational force provides the centripetal force on m and so

GMm/r^2 = m(v^2/r) -------> v^2 = GM/r

The formula says that the loser m is to M the faster it moves.

2

## What is the speed for circular motion in general?

### v = 2pir/T where T is the period (the time for one full revolution).

3

## What is Kepler's third law?

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It relates the period to the orbital redius. Taking M to be the mass of the sun and m the mass of a planet we deduce by coming the last two formulas that

(2pir/T)^2 = GM/r -------> T^2 = (4pi^2/GM)r^3

4

## How is the total energy of a moving satellite defined?

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A satellite orbits a spherical mass M. The kinetic energy of the orbiting satellites is

Ek - 1/2mv^2 and since v^2 = GM/r we have that Ek = 1/2(GMm/r) The total energy is therefore

Et = Ep + Ek = 1/2(GMm/r) - GMm/r = -1/2(GMm/r)

the total energy is negative.

5

## What is significant about the satellite being a potential well?

### Energy must be supplied if it is to move away.

6

## What is escape speed?

### The minimum launch sped of a projectile at the surface of a planet so that the projectile can move far away (to infinity).

7

## What is the total energy at launch at the surface of the planet?

### Et = Ek + Ep = 1/2mv^2 - GMm/R where R is the radius of the earth.

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