Keeping in mind that a free-body diagram shows all the forces acting on an object, and that those forces come from interactions between that object and other objects, what does the free-body diagram look like for the Earth in its roughly circular orbit around the Sun?
The only interaction we've got to worry about is the force of gravity. The Sun exerts a gravitational force on the Earth that points toward the Sun.
Knowing the distance to the Sun and how long it takes the Earth to orbit the Sun, we can calculate the acceleration the Earth is experiencing.
r = 150 million km = 1.5 x 1011 m
T = 1 year = π x 107 s
| v | = |
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= |
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= | 30000 m/s | = | 30 km/s |
| ac | = |
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= |
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= |
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= | 6 x 10-3 m/s2 |
Pretty small, but just right to keep us in orbit.
