Astronomy and Cosmology
week 3 – Thursday 17 April 2003
Gravity
• Star Date
• Gravity lecture and applications
• Workshop: moons of Jupiter
break
• Minilecture by Geoff and Jonathan
• Friday: workshop report on Moon
• Friday: take Quiz 3
Guiding Questions
1. How did ancient astronomers explain the motions of the
planets?
2. Why did Copernicus think that the Earth and the other planets
revolved around the Sun?
3. What did Galileo see in his telescope that confirmed that
planets orbit the Sun?
4. How did Tycho Brahe attempt to test the ideas of Copernicus?
5. What paths do the planets follow as they move around the
Sun?
6. What fundamental laws of nature explain the motions of
objects on Earth as well as the motions of the planets?
7. Why don’t the planets fall into the Sun?
8. What keeps the same face of the Moon always pointed
toward the Earth?
Derive Kepler’s 3d law from
Newton’s second law:
F=ma
Gravitational force
F=GmM/r2
acceleration in circular orbit
a = v2/r
Solve for v2:
Speed v = distance/time = 2pr/T. Plug this into v2 and solve for T2:
This is Kepler’s third law: T = period and r = orbit radius.
Applying Kepler’s 3d law:
For objects orbiting the Sun,
a=radius in AU and p=period in years
A satellite is placed in a circular orbit around the Sun, orbiting
the Sun once every 10 months. How far is the satellite from
the Sun?
2
 10 
a = p =    _______
 12 
3
2
a  ______
Sidereal and Synodic periods:
A satellite is placed in a circular orbit around the Sun, orbiting
the Sun once every 10 months. How often does the satellite
pass between the Earth and the Sun?
1
1
1


sidereal period Earth ' s sidereal year synodic period
1 1 1
 
P E S
1
1 1
 
10
1 S
12
1
 ________________
S
S  ________________
We can use Newton’s gravity to
approximate the size of a black hole!
Gravitational energy  kinetic energy
GmM 1
2
 mv
r
2
Solve for r  ____________
Not even light can escape (v=c) if it is closer than r to a black
hole. This is the Schwarzschild radius:
R=_____________________