Theme 4 – Newton’s Gravity Applied

ASTR 101Prof. 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 toescape Earth (40,000 km/h)

7 km/sec is enoughto 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.

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. We carry some fuel on board to make later modest ‘course corrections’

2. 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) To a physicist: weight is a force.

2) 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) resistthat with an equal and opposite force (fundamentally due to theinteractions of atoms)

Your perception of that force onyour 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

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 movie-making (see “Apollo 13”).

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!)

http://www.dump.com/weightlessnessspace/

The Critical Point

As Galileo said, “all things fall equally [under the influence of gravity].”

If launched side by side, abattleship and a baseballwould continue to orbit the Earth in parallel.

BUT:Massive Objects Remain

MassiveImagine 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 – dropa 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

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.