A rock is released from rest, in deep space, far from the earth. At a certain point, as it falls towards us, it crosses the moon's orbit.

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1 Sir Issac Newton... We went into the garden, & drank tea under the shade of some appletrees, only he, & myself. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. "why should that apple always descend perpendicularly to the ground," thought he to him self: occasion'd by the fall of an apple, as he sat in a comtemplative mood: "why should it not go sideways, or upwards? but constantly to the earths centre? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths centre, not in any side of the earth. therefore dos this apple fall perpendicularly, or toward the centre. if matter thus draws matter; it must be in proportion of its quantity. therefore the apple draws the earth, as well as the earth draws the apple." Memoirs of Sir Isaac Newton's Life, William Stuckley,

2 moon earth rock A rock is released from rest, in deep space, far from the earth. At a certain point, as it falls towards us, it crosses the moon's orbit. When the rock is the same distance from the earth as the moon, the acceleration of the rock is A: Greater than B: Equal to C: Smaller than D: (Need more information) the acceleration of the moon As the rock falls toward the Earth, its acceleration is.. A: constant. B: not constant.

3 Mass Radius (at equator) Earth x10 24 kg km Mars x10 24 kg km Ratio Mars Mars is 1/10 the mass and ½ the size of Earth. What will gravity by like on mars? (a) 1/10 earth gravity (b)1/5 earth gravity (c) 2/5 earth gravity (d)2.5 times earth gravity (e) 5 times earth gravity (f) 10 times earth gravity 3

4 Tunguska event Northern russia Shock wave broke windows 100 miles away. Equiv to ~ 5 megaton nuclear weapon

5 As the meteorite approaches earth.. a) it s velocity increases b) it s acceleration increases c) (a) and (b)

6 Z 1 dr =? r2 i.e. we want to know: d dr?= 1 r 2 a) 1 r 3 d) 2 1 r 2 b) 3 1 r 3 e) 1 r c) 1 r 2 f) 1 r or none of the above

7 Tunguska event Assume it started with no KE K = U K = (U f U i ) Gme m Gme m K f K i = r f r i K f K i = K f K i = Gme m r e Gme m r e Gme m 1 Gme m 1 But g = Gm e r 2 e K f = Gm em r e so K f = gr e m

8 Tunguska event Rock 10 m across -> 3000 tonnes -> kg g ~ 10 m/s 2 re ~ 6000 km ~ 6e6 K f = gr e m K ~ (10)(6e6)(3e6) K ~ 18e13 J That s equivalent to a 50 MT warhead, ~ Hiroshima

9 Suppose Earth had no atmosphere and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around Earth, the ball s acceleration would 1. be much less than g (because the ball doesn t fall to the ground). 2. be approximately g. 3. depend on the ball s speed.

10 Two communications satellites are in orbit at the same height, but one weighs twice as much as the other. The speed of the heavier satellite is A: Less than B: Equal to C: Greater than D: (need more information) the speed of the lighter one.

11 An astronaut is floating around in the space shuttle's cabin. Her acceleration, as measured from the earth's surface, is A: zero - she's floating B: very small, in some random direction C: quite large, nearly g, directed towards the center of the earth D: quite large, nearly g, directed along the line of travel of the shuttle

12 The Moon does not fall to Earth because 1. It is in Earth s gravitational field. 2. The net force on it is zero. 3. It is beyond the main pull of Earth s gravity. 4. It is being pulled by the Sun and planets as well as by Earth. 5. all of the above 6. none of the above

13 When you fall, (a) PE goes increases (b) PE decreases (c) depends on where you set h=0

14 At some instant in time, two asteroids in deep space are a distance r=20 km apart. Asteroid 2 has 10 times the mass of asteroid 1. What is the ratio of their resulting acceleration (due to gravitational attraction to each other), a1 / a2 = A: B: C: D: 10:1 1:1 1:10 Not enough information

15 A rock, initially at rest with respect to Earth and located far away is released and accelerates toward Earth. An observation tower is built 3 Earth-radii high to observe the rock as it plummets to Earth. Neglecting friction, the rock s speed when it hits the ground is A: twice B: three times C: four times D: eight times E: sixteen times its speed at the top of the tower. R 3 R

16 Does escape velocity depend on launch angle? (That is, if a projectile is given an initial speed vo, is it more likely to escape an (airless) planet, if fired straight up than if fired at an angle?) A: Yes B: No

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18 planet sun When the planet is here, what is zero for the planet? Net force Net torque Acceleration Radial acceleration Tangential acceleration tangential velocity angular velocity a) None of these things b) One of these things c) Two of these things d) Three of these things e) More

19 r ds sun What is the approximate area of the shaded region? a) da = r 2 b) da = 1 /2 r 2 c) da = r ds d) da = 1 /2 r ds

20 dθ r sun What is the approximate area of the shaded region? a) da = 1 /2 dθ b) da = 1 /2 ds dθ c) da = 1 /2 r dθ d) da = 1 /2 r ds dθ e) da = 1 /2 r 2 dθ f) da = 1 /2 r 2 ds dθ

21 In the modern world: make a circle in powerpoint x 2 + y 2 = R 2 x 2 y 2 + =1 R R click and drag x 2 + y 2 = R 2 x 2 y 2 + =1 a b