Motion and Its CausesForce and Newton’s Laws of Motion |
What’s the strength of the gravitational field of Earth? |
Earth’s mass is 5.9736 x 10^{24} kg and the gravitational constant is 6.673 x 10^{-11} N m^{2} kg^{-2}. At the surface of Earth, 6.4 x 10^{6} m from the center, then g = 9.8 N/kg. Thus a kilogram of meat, for example, experiences a gravitational force of 9.8 N toward Earth’s center.
The International Space Station orbits at about 320 km above Earth’s surface. How large is the gravitational field at that altitude? Its distance from Earth’s center is about 6.7 x 10^{6} m, so g = 8.9 N/kg. That’s not much different than at Earth’s surface.
The moon is 384 x 10^{6} m from the center of Earth. At that distance g = 0.0027 N/kg. So the force of Earth’s gravity on the same kilogram of meat would be only three thousandths of a Newton! How does this very small gravitational field keep the moon in its orbit? The answer, of course, is that the moon has a large mass, 7.2 x 10^{22} kg, and so the force on it is 2.0 x 10^{20} N. When we explore orbits later we’ll use this result.