## Shop Windows to the Universe

Science, Evolution, and Creationism, by the National Academies, focuses on teaching evolution in today's classrooms. Check out the other publications in our online store.

On a small moon with low gravity, a fastball pitcher could throw a ball into orbit. Gravity always pulls the ball towards the center of the moon. However, if the ball was moving fast enough, the moon's surface would curve away beneath the ball as quickly as gravity curved the ball downward. The ball would be in orbit!
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Windows to the Universe original artwork.

# The Heart of Satellite Orbits

Starting at the same altitude above the surface of a small moon, balls are thrown at different speeds. Regardless of the horizontal speed of the balls, they all fall at the same rate and hit the surface at the same time. The faster balls go further, in the same elapsed time as the slower balls, before hitting the ground. Finally, a ball travels so fast and thus so far before falling, that the ground doesn't appear flat but curves away beneath the ball. At just the correct speed, the ground curves away at the same rate that the ball drops. The ball has achieved orbit.

If the baseball player were to climb a high mountain and repeat the same exercise, the moon would appear smaller with the ground curving away more sharply. The speed that the ball needs to achieve orbit gets slower and slower as altitude increases and the curvature gets more pronounced. The combination of forward speed and falling determine the curvature of the ball's path. Matching this curvature to the curvature of the moon's surface at each altitude is at the heart of satellite orbits. The satellite drops forever towards the moon's surface but since the moon's surface curves away at the same rate, the satellite remains suspended forever at the same height above the surface. It is in orbit.

Why do satellites sometimes fall out of the sky? Frictional forces like the drag of the atmosphere on the satellite can cause the forward speed of the satellite to decrease. As a result, the curvature of the orbit changes, decreasing so that it no longer matches the curvature of the moon's surface at this altitude. It is now like one of the "too slow" balls in the cartoon. The satellite begins to drop. As it drops it increases in speed in the vertical direction due to gravity, but never again moves fast enough in the horizontal direction to maintain its orbit. The satellite will slowly descend to the surface unless it is reboosted to speeds sufficient to achieve orbit at its new altitude.

#### Shop Windows to the Universe Science Store!

Our online store includes issues of NESTA's quarterly journal, The Earth Scientist, full of classroom activities on different topics in Earth and space science, ranging from seismology, rocks and minerals, oceanography, and Earth system science to astronomy!

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Windows to the Universe, a project of the National Earth Science Teachers Association, is sponsored in part is sponsored in part through grants from federal agencies (NASA and NOAA), and partnerships with affiliated organizations, including the American Geophysical Union, the Howard Hughes Medical Institute, the Earth System Information Partnership, the American Meteorological Society, the National Center for Science Education, and TERC. The American Geophysical Union and the American Geosciences Institute are Windows to the Universe Founding Partners. NESTA welcomes new Institutional Affiliates in support of our ongoing programs, as well as collaborations on new projects. Contact NESTA for more information.