Editing Newton's laws of motion (section)

====Uniform circular motion====
{{Main|Circular motion}}
[[File:Binary system orbit q=3 e=0.gif|thumb|Two objects in uniform circular motion, orbiting around the [[barycenter]] (center of mass of both objects)]]
When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius <math>r</math> at a constant speed <math>v</math>, its acceleration has a magnitude<math display="block">a = \frac{v^2}{r}</math>and is directed toward the center of the circle.{{refn|group=note|Among the many textbook explanations of this are Frautschi et al.<ref name=":0" />{{Rp|page=104}} and Boas.<ref name="Boas">{{Cite book |last=Boas |first=Mary L. |title=Mathematical Methods in the Physical Sciences |title-link=Mathematical Methods in the Physical Sciences |date=2006 |publisher=Wiley |isbn=978-0-471-19826-0 |edition=3rd |location=Hoboken, NJ |oclc=61332593 |author-link=Mary L. Boas}}</ref>{{Rp|page=287}}}} The force required to sustain this acceleration, called the [[centripetal force]], is therefore also directed toward the center of the circle and has magnitude <math>mv^2/r</math>. Many [[orbit]]s, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude <math>GMm/r^2</math>, where <math>M</math> is the mass of the larger body being orbited. Therefore, the mass of a body can be calculated from observations of another body orbiting around it.<ref>{{Cite book |last=Brown |first=Mike |title-link=How I Killed Pluto and Why It Had It Coming |title=How I Killed Pluto and Why It Had It Coming |date=2010 |publisher=Spiegel & Grau |isbn=978-0-385-53108-5 |edition=1st |location=New York |oclc=495271396 |author-link=Mike Brown (astronomer)}}</ref>{{Rp|page=130}}

[[Newton's cannonball]] is a [[thought experiment]] that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward direction, and its effect is not diminished by horizontal movement. If the cannonball is launched with a greater initial horizontal velocity, then it will travel farther before it hits the ground, but it will still hit the ground in the same amount of time. However, if the cannonball is launched with an even larger initial velocity, then the curvature of the Earth becomes significant: the ground itself will curve away from the falling cannonball. A very fast cannonball will fall away from the inertial straight-line trajectory at the same rate that the Earth curves away beneath it; in other words, it will be in orbit (imagining that it is not slowed by air resistance or obstacles).<ref>{{Cite journal |last1=Topper |first1=D. |last2=Vincent |first2=D. E. |date=1999-01-01 |title=An analysis of Newton's projectile diagram |url=https://iopscience.iop.org/article/10.1088/0143-0807/20/1/018 |journal=[[European Journal of Physics]] |volume=20 |issue=1 |pages=59–66 |doi=10.1088/0143-0807/20/1/018 |bibcode=1999EJPh...20...59T |s2cid=250883796 |issn=0143-0807}}</ref>