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Mapa Mental por Connor O'Hare, atualizado more than 1 year ago
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Criado por Connor O'Hare
quase 7 anos atrás
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Chapter 18-
Gravitational fields
- All objects with mass create a gravitation field
- This field extends to infinity
- The force that masses would feel in a gravitational field can be
represented using 'lines of force'
- Planets or spherical masses form a radial field
- Close to the surface of a planet
it appears as a uniform field
- Planets or spherical masses form a radial field
- This field extends to infinity
- (g) Gravitational field strength- "the gravitational force
exerted per united mass at a point within a
gravitational field"
- g=F/M
- ms^-2
- Nkg^-1
- ms^-2
- g=F/M
- Newton's law of gravitation- "The force between 2 point
masses is directly proportional to the product of the masses
and inversely proportional to the square of the separation
between them
- F=-(GMm)/r^2
- G-Gravitational constant (6.67x10^-11)
- G-Gravitational constant (6.67x10^-11)
- F=-(GMm)/r^2
- Combining Newton's law of gravitation and g=F/m allows
us to calculate gravitational field strength in a radial field
- g=-(GM)/r^2
- g=-(GM)/r^2
- Kepler's laws of planetary motion
- 1st Law- The orbit of a planet is an elipse with the sun at one of the 2 foci
- The sum of the distances to the 2 foci is
constant for every point on the curve
- 'Eccentricity' is a measure of how elongated the circle is
- 'Eccentricity' is a measure of how elongated the circle is
- The sum of the distances to the 2 foci is
constant for every point on the curve
- 2nd law- A line joining the sun to a planet will
sweep out equal areas in equal time
- 3rd law- The square of the orbital period T of a planet is directly
proportional to the cube of its average distance r from the sun
- (T^2/r^3)
=k
- (T^2/r^3)
=k
- Most planets in the solar system have 'nearly' circular orbits
- We can therefore combine Gravitation force and centripetal force equations
- v^2=(GM)/r
- T^2=((4π^2)/GM)r^3
- v^2=(GM)/r
- We can therefore combine Gravitation force and centripetal force equations
- Satellites orbitng the Earth obey these laws
- The speed of a satellite remains
constant due to no air resistance
- Geostationary orbit
- Specific orbit where it remains directly
above the same point of the Earth whilst
the Earth rotates
- 1) Must be in orbit above the Earth's equator
- 2) Must rotate in the same direction as Earth's rotation
- 3) Must have an orbital period of 24 hours
- Specific orbit where it remains directly
above the same point of the Earth whilst
the Earth rotates
- Height or satellite is directly proportional to its period
- The speed of a satellite remains
constant due to no air resistance
- 1st Law- The orbit of a planet is an elipse with the sun at one of the 2 foci
- Gravitational potential (Vg)
- "the work done per unit mass to move an object to
that point from infinity"
- Jkg^-1
- When r=∞, Vg=0
- Jkg^-1
- Vg=-(GM)/r
- Moving towards a point mass results
in a decrease in gravitation potential
- Moving towards a point mass results in
a n increase in gravitation potential
- Moving towards a point mass results
in a decrease in gravitation potential
- "the work done per unit mass to move an object to
that point from infinity"
- Gravitation potential energy (E)
- "the work done to move the mass from infinity to a
point in a gravitational field"
- E=mVg
- In a radial field
- E=-(GMm)/r
- E=-(GMm)/r
- Escape velocity is the velocity needed so an object has just enough kinetic energy
to escape a gravitational field
- v^2=(2GM)/r
- v^2=(2GM)/r
- "the work done to move the mass from infinity to a
point in a gravitational field"
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