Gravity Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
GRAVITY Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you! Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Use this formula to find the magnitude of the gravity force. Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity. There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you! Newton’s law of gravitation gives us a formula to calculate the attractive force between 2 objects: m1 and m2 are the masses, and r is the center-to-center distance between them G is the gravitational constant – it’s tiny: G≈6.674*10-11 Nm2/kg2 Use this formula to find the magnitude of the gravity force. Use a diagram or common sense to find the direction. The force will always be toward the other mass. m1 r F2 on 1 m2 F1 on 2 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg We should start by defining our coordinate system. Let’s put the origin at planet H and say positive is to the right. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg We can also draw the forces on planet H in our diagram. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Our formula will find the forces (we supply the direction from looking at the diagram): Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Our formula will find the forces (we supply the direction from looking at the diagram): Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Our formula will find the forces (we supply the direction from looking at the diagram): This is negative because the force points to the left Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Our formula will find the forces (we supply the direction from looking at the diagram): This is negative because the force points to the left This is positive because the force points to the right Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Find the net gravitational force on planet H (the middle one). Example: Three planets are aligned as shown. The masses and distances are given in the diagram. Find the net gravitational force on planet H (the middle one). 1012 m 3 x 1012 m FApes on H FDP on H Planet of the Apes: mass=6 x 1024 kg Planet Hollywood: mass=6 x 1020 kg Daily Planet: mass=3 x 1025 kg Our formula will find the forces (we supply the direction from looking at the diagram): This is negative because the force points to the left This is positive because the force points to the right Net force is to the left Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Add the forces to get the net force on H:
GRAVITY m Rplanet One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet. m Rplanet Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
GRAVITY One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet. We already know that Fgrav is the weight of the object, and that should just be mg (if the planet is the Earth) m Rplanet Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
GRAVITY One more useful detail about gravity: The acceleration due to gravity on the surface of a planet is right there in the formula. Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet. We already know that Fgrav is the weight of the object, and that should just be mg (if the planet is the Earth) m Rplanet This part is g Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Kepler’s Laws 1st Law: The orbits of the planets are elliptical, with the sun at one focus of the ellipse. a=Semi-major axis Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Kepler’s Laws 2nd Law: A line from the sun to a given planet sweeps out equal areas in equal times. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Kepler’s Laws 3rd Law: The periods of the planets are proportional to the 3/2 power of the major axis length. Here is a formula: Radius of orbit (assuming circular instead of elliptical) Mass of central object – orbiting mass does not matter Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB