Newton’s Law of Gravity
(Dr. Andrei Galiautdinov, UGA)
PHYS1211/1111 - Spring 2015
1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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This slide shows Newton’s reasoning for arriving at his Law of Gravity.
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Cavendish’ experiment to determine G.
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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g on Earth:
REarth = 6,371 [km]
MEarth = 5.97 x 1024 [kg]
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g on Mars:
RMars = 3,396 [km]
MMars = 6.42 x 1023 [kg]
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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International Space Station
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International Space Station
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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Calculating orbital parameters for Earth & Pluto.
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Calculating orbital parameters for Pluto using the mass of the
Sun.
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1. Some history: Galileo, Brahe, Kepler, Newton
2. Newton’s Law of Universal Gravitation
3. Gravitational constant G (and Cavendish’ experiment to determine it)
4. Finding gravitational acceleration g from G, M, and r:
g = GM/r2
5. An aside: Centripetal acceleration
ac = v2/r
6. Putting a satellite in a circular orbit: how to choose v
v = (GM/r)1/2
7. Orbital period
T = 2πr/v
8. Circular planetary orbits
9. Gravitational potential energy (“corrected”) and the LCE
U = - GmM/r
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Total energy E stays the same, so if U
increases, K decreases, and vice versa.
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The End
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