Unformatted text preview: 2/17/10 Newton’s Laws of Mo9on and Gravity 1. Iner9a Astro 109 Lecture 9: Newton’s Laws of Mo9on and Gravity 2. F = m a 3. Ac9on and reac9on Feb. 17 4. Gravity: F = G M m / r2 • Also: circular mo9on, 9dal forces Feb. 17 Discussion Ques9on Discussion Ques9on If I hit all three bricks with the same force, which one will have the greatest accelera9on? When we turn on the fan with the sail in place, the cart will A.
B.
C.
D. the spongy brick the wooden brick the lead brick none of the above; they will all have the same accelera9on Feb. 17 A.
B.
C.
D.
E. Feb. 17 Discussion Ques9on When we turn on the fan with the sail removed, the cart will A.
B.
C.
D.
E. Feb. 17 move toward the leT of the lecture hall. move toward the right of the lecture hall. move toward the front of the lecture hall. move toward the back of the lecture hall. not move. move toward the leT of the lecture hall. move toward the right of the lecture hall. move toward the front of the lecture hall. move toward the back of the lecture hall. not move. Discussion Ques9on When I swing the ball in a circle at a constant rate, A.
B.
C.
D.
E. the ball is not accelera9ng. the ball is accelera9ng toward me. the ball is accelera9ng away from me. the ball is accelera9ng in the “forward” direc9on. the ball is accelera9ng in the “backward” direc9on. Feb. 17 1 2/17/10 What is the required force? (What puts the “fall” in “free fall”?) Discussion Ques9on So what can we say about the force on the ball? A.
B.
C.
D.
E. There is no net force on it. There is a net force toward me. There is a net force away from me. There is a net force in the “forward” direc9on. There is a net force in the “backward” direc9on. Feb. 17 Feb. 17 Newton’s Law of Universal Gravita9on • “Two objects a_ract each other with a force that is directly propor9onal to the mass of each object and inversely propor9onal to the square of the distance between them.” Feb. 17 Feb. 17 Discussion Ques9on Accelera9on by gravity Suppose you traveled to a planet with 3 9mes the mass and 3 9mes the diameter of Earth. Compared to your weight on Earth, your weight on the other planet would be A.
B.
C.
D.
E. Feb. 17 Each mass feels the same force (Newton’s 3rd law). F
GM m
r2 9 9mes larger. 3 9mes larger. the same. 3 9mes smaller. 9 9mes smaller. = ma
= ma a= GM
r2 All objects fall at the same rate! At surface of Earth, a = 9.8 m/s2. Feb. 17 2 2/17/10 Discussion Ques9on Orbit shapes During the Apollo 15 mission to the Moon, astronaut David Sco_ dropped a hammer and a feather together. What happened? A.
B.
C.
D. hammer The hammer landed ﬁrst. The feather landed ﬁrst. The hammer and feather landed at the same 9me. The feather blew away. feather Feb. 17 Feb. 17 Modify Kepler’s 3rd law Modify Kepler’s 1st law • Old: • Newton’s 3rd law: if Sun pulls on Earth, then Earth also pulls on Sun. [P (yr)]2 = [P (yr)]2 = F = ma • Both move! ⇔ a= F
m Feb. 17 [a (AU)]3
m1 + m2 (M⊙ ) • New: • Eﬀect is small in Solar System. • One of the ways we detect extrasolar planets. [a (AU)]3
M (M⊙ ) • With Sun+planet, m2 is small enough that we can neglect it. Feb. 17 Tidal force Feb. 17 Feb. 17 3 2/17/10 Eﬀects of 9dal forces • Earth’s rota9on is slowing down – the day is lengthening by 0.0016 seconds per century. • The Earth raises 9des on the Moon – in rocks! The Moon is “9dally locked” so it keeps the same face toward Earth. • If 9dal forces get strong enough, a moon can be ripped apart
> Saturn’s rings. Feb. 17 Feb. 17 Example: Tidal force from Moon R⊕
Fnear = 6378 km
= (6.67 × 10−11 N m2 /kg2 )(7.35 × 1022 kg)(1 kg)
(1 km)2
×
(384400 km − 6378 km)2
(103 m)2 = 3.43 × 10−5 N
Ffar = (1 km)2
(6.67 × 10−11 N m2 /kg2 )(7.35 × 1022 kg)(1 kg)
×
(384400 km + 6378 km)2
(103 m)2 = 3.21 × 10−5 N
diﬀerence Feb. 17 = 0.22 × 10−5 N Feb. 17 4 ...
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