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Questions and Answers
What is the formula for the force of gravity?
What is the formula for the force of gravity?
Fg = G m₁m₂ / r²
What is the unit of gravitational acceleration?
What is the unit of gravitational acceleration?
m/s² or N/kg
What is the name for the acceleration of gravity in a region of space due to the presence of a mass?
What is the name for the acceleration of gravity in a region of space due to the presence of a mass?
Gravitational Field
What is the definition of the Gravitational Field?
What is the definition of the Gravitational Field?
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What are two types of mass?
What are two types of mass?
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What is the radius of the Earth?
What is the radius of the Earth?
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What is the acceleration of gravity near the Earth's surface?
What is the acceleration of gravity near the Earth's surface?
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Using information from these pages, what is the mass of the Earth?
Using information from these pages, what is the mass of the Earth?
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How much would a fully suited astronaut weighing 1400N on Earth weigh on the Moon?
How much would a fully suited astronaut weighing 1400N on Earth weigh on the Moon?
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What is the surface gravity (acceleration) on Ceres?
What is the surface gravity (acceleration) on Ceres?
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How long would it take for a hammer to fall 1.20 m on Ceres?
How long would it take for a hammer to fall 1.20 m on Ceres?
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What is Kepler's First Law of Planetary Motion?
What is Kepler's First Law of Planetary Motion?
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What is Kepler's Second Law of Planetary Motion?
What is Kepler's Second Law of Planetary Motion?
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How long does it take the Moon to orbit the Earth?
How long does it take the Moon to orbit the Earth?
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What is a geostationary satellite?
What is a geostationary satellite?
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What is the radius of the orbit of a geostationary satellite?
What is the radius of the orbit of a geostationary satellite?
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What is circular motion at a constant speed?
What is circular motion at a constant speed?
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What is the formula for the speed of an object in circular motion?
What is the formula for the speed of an object in circular motion?
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What is the relationship between gravity and centripetal acceleration for orbiting objects?
What is the relationship between gravity and centripetal acceleration for orbiting objects?
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What happens to the orbital speed of a planet as its distance from the Sun increases?
What happens to the orbital speed of a planet as its distance from the Sun increases?
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What is the formula for centripetal acceleration?
What is the formula for centripetal acceleration?
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What is the centripetal acceleration of the Moon?
What is the centripetal acceleration of the Moon?
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What is the relationship between the period of an orbit and the radius of that orbit?
What is the relationship between the period of an orbit and the radius of that orbit?
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What is the formula for the gravitational force?
What is the formula for the gravitational force?
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What is the gravitational force exerted on a 1000 kg satellite orbiting a planet with a centripetal acceleration of 5 m/s²?
What is the gravitational force exerted on a 1000 kg satellite orbiting a planet with a centripetal acceleration of 5 m/s²?
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What is the gravitational acceleration of the International Space Station (ISS) in orbit around the Earth?
What is the gravitational acceleration of the International Space Station (ISS) in orbit around the Earth?
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What is the speed of the ISS in orbit around the Earth?
What is the speed of the ISS in orbit around the Earth?
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What is the period of the ISS's orbit around the Earth?
What is the period of the ISS's orbit around the Earth?
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A spacecraft has a mass of 2250 kg and an asteroid has a mass of 4.25 x 10¹⁶kg. What is the force of gravity between them if they are 6370 m apart?
A spacecraft has a mass of 2250 kg and an asteroid has a mass of 4.25 x 10¹⁶kg. What is the force of gravity between them if they are 6370 m apart?
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What is the gravitational acceleration of a satellite orbiting the Earth at a radius of 1.45 x 10⁷m?
What is the gravitational acceleration of a satellite orbiting the Earth at a radius of 1.45 x 10⁷m?
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What is the speed of a satellite orbiting the Earth at a radius of 1.45 x 10⁷m?
What is the speed of a satellite orbiting the Earth at a radius of 1.45 x 10⁷m?
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The Moon takes 27.3 days to orbit the Earth. An artificial satellite orbits the Earth twice per day, or every 12 hours. What is the radius of the satellite's orbit?
The Moon takes 27.3 days to orbit the Earth. An artificial satellite orbits the Earth twice per day, or every 12 hours. What is the radius of the satellite's orbit?
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Study Notes
Newton's Law of Universal Gravitation
- Gravity is a force that attracts any two masses.
- Gravitational force is directly proportional to the product of the two masses.
- Gravitational force is inversely proportional to the square of the distance between the centers of the two masses.
- The formula for gravitational force is Fg = G m₁m₂/r².
- G is the gravitational constant (6.673 x 10⁻¹¹ Nm²/kg²).
- m₁ and m₂ are the two masses.
- r is the distance between the centers of the two masses.
Properties of Gravity
- Gravity is an attractive force, pulling masses toward each other.
- The force of gravity acts along a straight line connecting the two masses.
- The gravitational force on a system of multiple masses can act on the center of mass.
Gravitational Field
- Gravitational field is the amount of force per unit mass available at a particular point in space due to the presence of another mass.
- Gravitational acceleration is the acceleration experienced by a mass due to a gravitational field.
- Gravitational field strength is also often called surface gravity.
Kepler's Laws of Planetary Motion
- First Law: Planets move around the sun in elliptical orbits with the sun at one focus.
- Second Law: A line joining a planet and the sun sweeps out equal areas during equal intervals of time. Planets move faster when closer to the sun and slower when further away.
- Third Law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This is often written as R³ / T² = constant.
Combining Equations for Gravity and Circular Motion
- Circular motion at a constant speed has an acceleration that changes the direction of the mass.
- Circular motion at a constant speed has a speed (v) of v = d/t , where d = 2πr.
- The equation for the force needed to keep an object in a circular orbit is Fg = (m x v²)/r.
Further Examples/Applications (various scenarios)
- Calculations involving Moon orbit, satellite orbits, and other gravitational interactions between different objects, like spacecraft and asteroids with various masses and distances.
- Use of Kepler's Third Law to find the period of a planet’s orbit, if the average radius or vice versa is known, or use Kepler's Third Law to find the radius of an orbit knowing the period.
- Problems involving the derivation of equations from basic Newtonian principles.
- Calculations for the acceleration of gravity on different celestial bodies using radius and respective mass.
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Description
Test your understanding of Newton's Law of Universal Gravitation with this quiz. Explore key concepts such as the gravitational force, its formula, and properties of gravity. Assess your knowledge about the gravitational field and how masses interact through gravity.
