Orbital Motion = Kepler Explained

“Compromise”: planet moves in curved orbit

Planet wants to move in a straight line of constant velocity (Newton 1)

Sun’s gravitational pull forces planet into orbit by changing direction of planets velocity

It takes a stronger force to make a high speed planet move in an orbit

Cannon “Thought Experiment”

• http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html

Applications

• From the distance r between two bodies and the gravitational acceleration a of one of the bodies, we can compute the mass M of the other

F = ma = G Mm/r2 (m cancels out)

– From the weight of objects (i.e., the force of gravity) near the surface of the Earth, and known radius of Earth RE = 6.4103 km, we find ME = 61024 kg

– Your weight on another planet is F = m GM/r2

• E.g., on the Moon your weight would be 1/6 of what it is on Earth

Applications (cont’d)

• The mass of the Sun can be deduced from the orbital velocity of the planets: MS = rOrbitvOrbit

2/G = 21030 kg – actually, Sun and planets orbit their common center of mass

• Orbital mechanics. A body in an elliptical orbit cannot escape the mass it's orbiting unless something increases its velocity to a certain value called the escape velocity– Escape velocity from Earth's surface is about 25,000 mph (7

mi/sec)

From Newton to Einstein

• If we use Newton II and the law of universal gravity, we can calculate how a celestial object moves, i.e. figure out its acceleration, which leads to its velocity, which leads to its position as a function of time:

ma= F = GMm/r2

so its acceleration a= GM/r2 is independent of its mass!

• This prompted Einstein to formulate his gravitational theory as pure geometry.

Telescopes

From Galileo to Hubble: Telescopes use lenses and mirrors to focus and therefore collect light

Rain analogy: Collect light as you collect rain

Rain/light collected is proportional to area of umbrella/mirror, not its diameter

Light hits Matter: Refraction• Light travels at different speeds in vacuum, air,

and other substances• When light hits the material at an angle, part of it

slows down while the rest continues at the original speed – results in a change of direction– Different colors bend different amounts – prism,

rainbow

Application for Refraction

• Lenses use refraction to focus light to a single spot

Light hits Matter (II): Reflection• Light that hits a mirror is

reflected at the same angle it was incident from

• Proper design of a mirror (the shape of a parabola) can focus all rays incident on the mirror to a single place

Application for Reflection

• Curved mirrors use reflection to focus light to a single spot

Telescopes

• Light collectors

• Two types:– Reflectors

(Mirrors)– Refractors

(Lenses)

Refracting Telescopes

Reflecting Telescope

Problems with Refractors

• Different colors (wavelengths) bent by different amounts – chromatic aberration

• Other forms of aberration

• Deform under their own weight

• Absorption of light

• Have two surfaces that must be optically perfect

Telescope Size• A larger telescope gathers more light (more

collecting area)

• Angular resolution is limited by diffraction of light waves; this also improves with larger telescope size

Resolving Power of Telescopes

Atmospheric Limitations