Download Newton`s Gravity Applied (PowerPoint)

Theme 4 – Newton’s Gravity Applied
ASTR 101
Prof. Dave Hanes
Orbiting Near, Around,
and Away from the Earth
Let’s consider:
 Ballistic missiles on Earth
 Artificial satellites
 Geosynchronous satellites
 Actually escaping the Earth
 The loss of planetary atmospheres
 Exploring the Solar System
A definition: Ballistic Motions
Objects moving only under the influence of gravity
(no rockets firing, no air resistance, etc) are said
to be moving ballistically. (Newton’s imagined
cannonball was such an object.)
That is: launch it fast, then shut off the motors or
driving force and let it coast thereafter.
1. ICBMs: The Cold-War Dread
2: Artificial Satellites
There are literally tens of thousands of them.
http://science.nasa.gov/iSat/?group=science&satellite=20580
These include telecommunications satellites, ‘spy’ satellites,
weather satellites, resource-monitoring satellites,
astronomical satellites (like the Hubble), etc…
Low-Altitude Satellites
Example: International Space Station
The ISS orbits the Earth not far above the atmosphere
(to avoid drag), at a speed of ~ 7 km/sec
It orbits the Earth once every 90 minutes. (For the
astronauts, this yields 16 sunrises every 24 hours!)
Enjoy the experience!
http://apod.nasa.gov/apod/ap130331.html
A High-Altitude Satellite
with a Long Orbital Period
The moon is 380,000 km away, and orbits once a month!
3. Geosynchronous Satellites
As we saw, the ISS is nearby, has a short period;
but the Moon is remote, has a long period.
Now consider placing a satellite at an intermediate
distance, chosen to that it orbits the Earth once
every 24 hours.
What is the point?
Geostationary Satellites
4. ‘Escaping’ the Earth
The ideal: fire rockets rapidly, furiously and
briefly!
This sheds excess mass as quickly as possible (by
using up the fuel, but we also get rid of
unwanted ‘stages’ of the rocket)
When the fuel is all gone, coast!
But There Are Limitations
How much acceleration can a human body
withstand?
http://www.youtube.com/watch?v=3UEYxf4fl_A
We can’t launch astronauts (or delicate electronic
equipment, for that matter) like bullets out of a gun!
Escape Speeds
(no need to memorize these!)
11.2 km /sec to
escape Earth
(40,000 km/h)
7 km/sec is enough
to attain a circular
orbit
5. The Loss of Planetary Atmospheres
Atoms and molecules in the atmosphere ‘jostle’ and collide all
the time. In the outer parts, some can pick up enough speed to
escape. The atmosphere slowly dissipates into space.
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Smaller objects (like the moon) have too little gravity to retain
an atmosphere.
In cooler planets, the gases move more slowly, are less likely
to ‘boil off.’
The lighter gases (Hydrogen, Helium) escape most readily.
Atmospheres
are ‘Boiling
Off’ into
Space
6. Spacecraft in the Solar System
Note Two Features:
1.
1.
We carry some fuel on board to make
later modest ‘course corrections’
We use the (easily calculated)
gravitational force of other planets to
help steer and accelerate our space craft
en route to its target.
Remember Newton’s Third Law
As we pass (say) Jupiter, its gravitational force
affects the orbit of our space craft.
The same force acts on Jupiter (in the opposite
direction), so our passing spacecraft slightly
‘tweaks’ that planet’s orbit!
But Jupiter is so massive that the effects are
immeasurably small. Still, it’s not ‘free.’
Weightlessness
How Strong?
How strong is the pull of the Earth’s gravity at the altitude
of the International Space Station?
Orbital Altitude
= 370 km above sea level
= 6741 km from center of Earth
The ISS is 5.8% farther from the center than we are, and
the force of gravity is 12% weaker (inverse-square law).
But it is not zero! So why are the astronauts ‘weightless’?
Remember Also
The moon moves in its curved orbit because of the
Earth’s gravity . Although that force is weakened
by distance, it is still not zero – even at the great
distance of the moon.
(If it were, the moon would simply move off in a
straight line. That’s Newton’s first law.)
So the astronauts certainly don’t “escape the
Earth’s gravity.”
Think About Weight
Two definitions:
1)
2)
To a physicist: weight is a force.
You and me: weight is our perception of
a force acting on us - a reaction
(Newton’s third law again).
The Meaning of ‘Weight’
You stand on the scale
Gravity pulls you down with a
certain force: your weight
The scale (and floor) resist
that with an equal and opposite
force (fundamentally due to the
interactions of atoms)
Your perception of that force on
your feet is your sensation of weight
Remove the Perception!
If you remove the reaction (the upward
force on your feet), you will feel weightless
When you are free fall, you are weightless.
Not the Same as True Weightlessness
Strong air
resistance
The feel of the water,
air tanks, etc
Perfect Sensation
In the Space Station, you are
falling towards the ground at
exactly the same rate as the
ISS itself, and ‘float’ weightless
within it. (Of course your
‘sideways’ orbital motion keeps
you from hitting the ground!)
https://www.youtube.com/watch?v=XHL1opjFR7Y
The ‘Vomit Comet’
Special flights in aircraft can give rise to brief episodes of
weightlessness at the ‘top of the arc’ This is used in moviemaking: see “Apollo 13” and also
https://www.youtube.com/watch?v=LWGJA9i18Co
https://www.youtube.com/watch?v=Gsnyqu7xq9c
The Critical Point
As Galileo said, “all things
fall equally [under the
influence of gravity].”
If launched side by side, a
battleship and a baseball
would continue to orbit the
Earth in parallel.
BUT:
Massive Objects Remain Massive
Imagine an orbiting battleship, with you orbiting alongside.
It is ‘weightless’. But a push from you will not move it much! It
still has all its mass.
When you push it, the reaction force (remember Newton’s 3rd
law) will push back on you. You move as a result.
You drift apart – but you’re doing most of the moving!
Astronauts can’t throw girders around like toothpicks!
Learning About the Planets
We can use gravity to learn about the planets – in
particular, their masses.
(That is, how much material they contain
in total. That’s obviously important if we are to
understand their nature.)
Note that this is not simply their size! Big things
can be low in mass – a beach ball, for one.
The Mass of the Earth
See what gravitational influence
it has on a nearby object – drop
a ball!
The time it takes to hit the ground
tells you the size of the force and
thus the mass of the Earth.
(It doesn’t tell you about the ball,
because a heavier ball would
fall in exactly the same way.)
What We Learn
The mass of the Earth is trillions and trillions of
tons. But knowing its size as well, we can work
out that it is about 5 times as dense as water – a
big chunk of rock!
Rocks near the surface are not that dense, so it
must be denser near the middle.
And so on…
Other Objects
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Mars, Jupiter: watch the moons, which are
orbiting under the influence of those planets.
Venus, Mercury: they have no moons, but we
can send space probes there to see how they
behave. Or watch their influence on passing
asteroids, say.
Sun: the orbits of the planets tell us about the
mass of the Sun.
Surprise!
The small inner planets are dense, and (we infer) rocky.
But the outer planets are much less dense – indeed, Saturn
is less dense overall than water. (A toy model of it would
float in a bathtub!) They must be very different.
The Sun is comparable to Jupiter in density – it’s clearly not
a “big hot rock”! These huge objects are in fact gaseous
and (as we know now) mostly hydrogen and helium, the
lightest elements.