Practice: Two spheres of mass 300 kg and 500 kg are placed in a line 20 cm apart. If another sphere of mass 200 kg is placed between them, 8 cm from the 300 kg sphere, what is the net gravitational force on the 200 kg sphere?

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Practice: Two spheres of mass 300 kg and 500 kg are placed in a line 20 cm apart. If another sphere of mass 200 kg is placed between them, 8 cm from the 300 kg sphere, what is the net gravitational force on the 200 kg sphere?

Practice: A 2,000-kg spacecraft is blasting away from the surface of an unknown planet the same size as the Earth. At 1500km above the surface, an instrument onboard reads the gravitational force to be 18000 N. What is the planet’s mass?

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Concept #1: Universal Law of Gravitation

Example #1: Where is Net Force on middle object zero?

Practice #1: Find Net Force on middle object

Concept #2: Center of Mass Distance

Example #2: Find force between spheres with radii

Practice #2: Find Mass of Planet given Force at height

The gravitational force of a star on an orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2.What is the ratio F2/F1? You can ignore the gravitational force between the two planets. Express your answer using two significant figures.

In recent years, astronomers have found planets orbiting nearby stars that are quite different from planets in our solar system. Kepler-12b, has a diameter that is 1.7 times that of Jupiter (RJupiter = 6.99 × 107 m), but a mass that is only 0.43 that of Jupiter (MJupiter = 1.90 × 1027 kg ).What is the value of g on this large, but low-density, world?

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