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### Universal Gravitation

Physics

Warm-Ups

- What is Newtonian Synthesis?
- Same laws of physics that apply to Earth, also apply to the heavens

Warm-ups

- A physics student has a mass of 70 kg and is separated from Earth by a distance of 6.60 x 106 m. What is the force of gravity between the physics student and Earth, if the mass of the Earth is 5.98 x 1024 kg?
- 686 N

Warm-Ups

- Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?
- It would not change

Warm-ups

- If the mass of the moon is 7.34 x 1022 kg, the radius is 1.74 x 106 m, and G = 6.67 x 10-11 Nm2/kg2, what is g on the moon?
- 1.62 m/s2

Speed of an Object in Circular Orbit

- V = √ Gm/r
- V : speed of object in orbit
- G : 6.67 x 10-11 Nm2/kg2
- m : mass that the object is orbiting
- r : distance between two objects (orbiting object and mass that it is orbiting)

Example Problem

- If the mass of the sun is 2 x 1030 kg and the distance between mars and the sun is 2.28 x 1011 m, what is the orbiting speed of mars around the sun?
- 2.42 x 104 m/s

Period of Orbiting Object

- T = 2*pi*r √r/Gm
- r : distance between 2 objects
- G : 6.67 x 10-11 Nm2/kg2
- m : mass that object is orbiting

Example Problem

- For the previous example problem, find the orbiting period of mars around the sun.
- 5.9 x 107 s

Satellite Warm-UP

- The mass of the Earth is 6 x 1024 kg and the radius of the Earth is 6.4 x 106 m. What is the value of g 1000 km above Earth?
- 7.31 m/s2

Weightlessness

Why do astronauts orbiting in space feel weightless?

Weightlessness

- Astronaut and spaceship are free falling at the same rate of acceleration (g) and the normal force on the astronaut is 0

Weightlessness

- How does a spaceship stay in orbit if it is free falling?
- Given a fast enough initial velocity and misses the Earth because it is curved

Einstein’s Theory of Gravity

- Gravity is not a force, but an effect of space itself
- A mass causes space to be curved, an other masses are accelerated because of the way they follow this curved space

Einstein’s Theory of Gravity

- Called General Theory of Relativity
- During an eclipse, light was deflected by the sun, which provided evidence for this theory

Moon of Saturn Problem

- Mimas, a moon of Saturn, has an orbital radius of 1.87 x 108 m and an orbital period of 23 hours (convert). Find the mass of Saturn.
- 5.65 x 1026

Gravitational Field Strength

- Gravitational force per unit mass on an object
- g = Fg/m
- Units: Newton/kg

Gravitational Field Strength

The gravitational field strength is 7.83 N/kg at the altitude of the space shuttle. (a) How much does an 80 kg astronaut weigh on the shuttle? (b) How much did the astronaut weigh on earth? (1 N = .22 lbs.)

a) 137.8 lb b) 172.5 lb

Review for Quiz

- Work in groups to finish back of review handout , pg. 188 (#6,7), and pg. 196 (#52)
- Have me check off your paper when your group is done

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