Questions and Answers
Which of the following statements are true? (Select all that apply)
If the distance between the centers of two gravitationally attracting objects decreases by a factor of 2, how does the gravitational force between them change?
If the mass of each object doubles, how does the gravitational force between them change?
A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?
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If planet A and planet B have the same surface gravity, but planet B has twice the radius of planet A, how does the mass of planet B compare to the mass of planet A?
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What happens to Earth's orbital speed when it is closer to the Sun?
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Why does a satellite in a circular orbit travel at a constant speed?
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Study Notes
Gravity and Force Relationships
- Gravitational force is not proportional to the distance between two objects; it is inversely proportional to the square of the distance.
- Gravitational force is proportional to the product of the masses of the two objects.
- When masses increase, gravitational force increases quadratically (a factor of 4) if each mass doubles.
Gravitational Force and Distance
- If the distance between two gravitationally attracting objects decreases by a factor of 2, the gravitational force increases by a factor of 4.
- Understanding the inverse-square relationship is crucial for calculating gravitational force changes with distance.
Acceleration Due to Gravity
- A hypothetical planet with one-third the mass and three times the radius of Earth results in an acceleration due to gravity of g/27.
- The relationship between a planet's mass, radius, and gravity is fundamental in comparative planetary science.
Mass Comparison of Planets
- For two planets with the same surface gravity, if one planet (planet B) has double the radius, its mass is four times that of the other planet (planet A).
- This reveals the significance of the volume and density relationship in determining mass from radius and gravitational effects.
Earth's Orbital Dynamics
- Earth's orbital speed is higher when it is closer to the Sun, highlighting the effects of gravitational attraction in elliptical orbits.
- The variation in orbital speed depends on the distance from the Sun, illustrating Kepler's laws of planetary motion.
Satellite Motion in Circular Orbits
- A satellite in a circular orbit travels at a constant speed because there is no net force acting along its direction of motion.
- The gravitational force balances the centrifugal force, allowing for stable circular motion without acceleration variation.
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Description
Test your understanding of gravitational forces and Newton's Synthesis with these flashcards from Chapter 6. Identify true statements about the relationship between mass and distance in gravitational interactions and reinforce your knowledge of key concepts in physics.
