Newton’s Law of Gravity

1. Newton’s Law of Gravity I wonderwhat’s forlunch?

2. Where did it come from? • Newton was watching the full moon one day, wondering why inertia didn’t cause the moon to fly off into space. • He realized that some force must be holding the moon near to the earth.

3. Where did it come from? • When an apple fell near Newton, he realized that the force pulling the apple down towards the earth was the same force holding the moon in its orbit.

4. Newton realized 3 things: • There was a force of attraction between the earth & the moon, and the force was somehow related to the earth’s mass. Hey, baby,I’m attractedto you!

5. Newton realized 3 things: • From his 3rd law of motion, Newton knew that if the earth was pulling on the moon, the moon was also pulling on the earth equally hard. • Therefore, the force of gravity also depended on the mass of the object orbiting the earth (the moon.)

6. Newton realized 3 things: • Just like a magnetic force, as the distance between the two masses increased, the force of gravity would grow weaker, not slowly & evenly, but very quickly. Think about how magnets attract each other.

7. The Inverse Square Law • As the distance between the 2 objects increases, the force of gravity decreases with the square of the distance. • F is proportional to 1/d2, not just 1/d.

8. Inverse Square Law F = 1 • If you double the distance between 2 objects, the force of gravity between them shrinks to ¼. F = ¼

9. Inverse Square Law • If you triple the distance between 2 objects, the force of gravity between them shrinks to (1/3)2 or 1/9th . • It works the opposite way when 2 objects move closer together…

10. Inverse Square Law • If the distance between the earth & the moon somehow were decreased to ½ what it is now, the force of gravity between the earth & the moon would increase to 4 times stronger than it is right now.

11. Let’s put it all together • F is the force of gravity. • F = G x Massearthx Massmoon(distance between them)2 • The ‘G’ in the formula is just a factor that makes all the units work out correctly.

12. Law of Gravity Equation • The equation can be applied to any 2 objects in space. • F = G x Mass1x Mass2(distance)2 • G is a constant (a scaling factor) equal to 6.67 x 10-11 Nm2/kg2

13. Consequences for Astronomy • This means that every object in the universe, every planet, star, even hydrogen atom, attracts every other object in the universe. • When the 2 objects are very far apart, the attractive force is very small, but it’s still present.

14. I can still feelyou, even wayover there! Gravity never sleeps!

15. Consequences for Astronomy • The gravity law explains why planets orbit stars… • why stars orbit the center of the galaxy… • why all the galaxies in the universe should be attracted to one another.

16. Some examples • The acceleration due to gravity is 9.8 m/s2 at the earth’s surface. • If you climbed to the top of the highest mountain, you would be a little further from the earth’s center. An object dropped here would weigh a little less and drop slightly slower than it would at the earth’s surface.

17. What would happen if…? • If the earth suddenly shrank to ½ its current size…the acceleration due to gravity would be 4 times what it is now. • You would feel 4 times heavier.

18. I simply MUSTlose someweight!

19. What would happen if…? • If you visited a planet that was the same size as the earth, but had twice the mass…you’d feel twice as heavy, and you’d accelerate twice as fast in a fall.

20. What would happen if…? • If you visited Mars, where the gravity is less than it is on earth…you’d be able to lift 2.5 times what you can lift on earth…you’d be able to throw a baseball 2.5 times farther.

21. What would happen if…? • …if you were in a spaceship orbiting a star, and the star suddenly shrank to become a black hole only 1/1000th of its former size? • Would you be instantly ‘sucked in?’

22. What would happen if…? • Neither your mass, nor the mass of the star has changed. • Your distance from the center of mass of the star hasn’t changed. • The force of gravity between you and the new black hole would be exactly the same as it was before the star became a black hole. You would NOT be sucked in.

23. But, I thought… • But don’t black holes have enormous gravity? • Yes, they do…at their surfaces! • If you were standing on the surface of the star when it shrank and became a black hole, you would be instantly crushed by the increase of gravity.

24. I’m confused… • Look at the law of gravity.F = G x Mass1x Mass2(distance)2 • The only thing that changes between when the star is large and when it shrinks to become a black hole is the distance between you (at its surface) and the center of the star’s mass.

25. Uh…OK…maybe • In the equation, the distance factor between you and the black hole’s center, d, gets very small, making the force of gravity very large.

26. Let’s add just a little more • Newton realized that his new law of gravity could be combined with Kepler’s 3rd law – the one that relates the size of an object’s orbit to its orbital period. (period)2 = (orbit radius)3 or p2 = a3

27. The combined equation looks like… p2 = 4 2 a3 . G (Mass1 + Mass2) • It may look complicated, but it’s soooo useful.

28. What can this equation do? • There are 4 terms in the equation that are ‘unknowns’. These are p, a, Mass1 and Mass2. • If you are able to measure any 3 of the terms, you can calculate the 4th term.

29. What can this equation do? • The equation can be used to… • …calculate the mass of the sun • …calculate the mass of any planet that has a moon • …look for planets orbiting other stars • …discover new planets!

30. What can this equation do? • This equation was used by a British astronomer, John Couch Adams, and a French astronomer, Urbain Leverrier, to predict the position of the planet Neptune in 1845…a whole year before it was ever observed with a telescope!

31. Wow! They ‘found’ a planet? • The 2 astronomers noticed that the planet Uranus would sometimes speed up, then slow down in its orbit. They believed that this change in speed was due to the gravitational tug of another, more distant planet. The other planet was Neptune.

32. Let’s use the equation!! • The equation has been used to calculate the mass of the sun, starting with the orbit of the earth. • We know that the earth takes 365.24 days to make 1 orbit. Converting this to seconds equals 31,600,000 seconds.

33. Keep going… • We also know that the earth orbits the sun at a distance of 1 A.U. or 150,000,000 kilometers • Convert this distance to meters, equals 150,000,000,000 meters. • Now, let’s re-arrange the equation.

34. A re-arrangement p2 = 4 2 a3 . G (Masssun + Massearth)becomes (Masssun + Massearth) = 4 2 a3 G p2

35. Keep going… • Now, if you realize that the mass of the earth is tiny, compared to the enormous mass of the sun, you can just ignore Mearth in the calculation, without being very far off in your answer.

36. So the equation becomes • …it becomes Masssun = 4 2 a3 G p2

37. If you’ve been paying attention… • If you’ve been paying attention, and writing everything down to this point, you now have enough information to solve Newton’s equation for the mass of the sun. • Go ahead, give it a try. It’s question #17 on your homework!

38. Thanks for watching… …now it’s homework time!