# summary_ch4.pdf

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University of Toronto Mississauga

Astronomy

AST101H5

Fournier

Fall

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AST 101H5F
Solar System Astronomy
University of Toronto Mississauga
Summary of Chapter 4
Understanding Motion, Energy and Gravity
th
Essential Cosmic Evolution, 6 Edition
The key points from Chapter 4
1. Deﬁnitions of terms relating to motion:
(a) speed = change of location in some time interval, m/s or km/h
(b) velocity = change of location and direction in some time interval, m/s
2
(c) acceleration = change of velocity in some time interval, (m/s)/s = m/s
(d) momentum = mass × velocity
2. Momentum changes because of a net force
Example: as it orbits around Earth, the Moon is constantly changing the direction of its
motion = changing velocity, which is caused by the force of Earth’s gravity
3. Net force is the result of summing all the separate forces aﬀecting an object
Example: the Moon’s orbit is aﬀected by Earth’s gravity + Sun’s gravity + Jupiter’s
gravity + ...
4. Mass = total amount of matter in an object, expressed in kilograms (kg)
5. Weight = force of gravity on a mass, expressed in Newtons
Example: a mass of 50 kg on Earth, where the acceleration of gravity is about
10 m/s , has a weight of 50 kg × 10 m/s = 500 Newtons
6. Newton’s three laws of motion
• If there is no net force, the momentum does not change
• If there is a net force, the momentum does change
Because changing momentum is usually a changing velocity = acceleration, this is
usually written F = ma.
• Forces come in equal but opposite pairs, force = reaction force AST 101H5F Chapter 4 2
M1M 2
7. Newton’s universal law of gravity: G = G d2
• F depends directly on each mass
G
• F depends inversely on the square of the separation
G
• G is a universal constant
• F extends forever, until the separation in inﬁnite
G
• F is never canceled out because all masses are positive quantities
G
• FG is extremely important in astronomy because of the huge masses and huge
separations
8. Newton’s version of Kepler’s ﬁrst law
• Four types of orbits are possible: circular, elliptical, parabolic and hyperbolic.
• To have a circular orbit there must be a perfect balance of motion by gravity →
extremely unlikely
• Many combinations of motion and gravity produce elliptical orbits → very likely
• Objects on parabolic and hyperbolic orbits never return, so we never see them
9. Newton’s version of Kepler’s third law: p = 4π2 a3
G(M 1M 2
• We measure p and a
• G, π

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