HOMEWORKQUESTIONS: WEEK 3

Fragments of fireworks beautifully illuminate the night sky, (a) What specific path is ideally traced by each fragment? (b) What paths would the fragments trace in a gravity-free region?

(a) a parabola (projectile) in gravity and no air resistance environment. (b) a straight line in gravity

As part of their training before going into orbit, astronauts experience weightlessness when riding in an airplane that is flown along the same parabolic trajectory as a freely falling projectile. A classmate says that gravitational forces on everything inside the plane during this maneuver cancel to zero. Another classmate looks to you for confirmation. What is your response?

At first it may seem to cancel, but it does not. They are experiencing a state of free fall, so therefore there is no support force, so that is why they are feeling weightlessness.

If you stopped an Earth satellite dead in it's tracks, it would simply crash into Earth. Why, then, don't the communications satellites that "hover motionless" above the same spot on Earth crash into Earth?

Communications satellites only look like they're not moving. This is because their orbital period coincides with Earth's daily rotation. The same idea can be applied as to why the sun and moon seem to follow you. It only appears that way, they coincide with our home planet rotating.

In 2000-2001, NASA's Near Earth Asteroid Rendezvous (NEAR) spacecraft orbited around the 20-mile-long asteroid Eros. Do you speculate that the orbital speed of this spacecraft is greater or less than 8 km/s? Discuss and defend your answer.

I would speculate that the orbital speed of the spacecraft is greater than 8 km/s. An object speed has to move 8 km/s during the 1 s to maintain the earth curvature or it could fall into the earth.

When a satellite in circular orbit slows, perhaps due to the firing of a "retro rocket," it ends up gaining more speed than it had initially. Why?

I would think that it ends up gaining more speed than it had initially because of the gravitational force. I would say this is because it is near (closer) to the earth resulting in gain speed than it had initially. The textbook provides an example when explaining that" a satellite acts like a projectile " (page 196). The example given was that a planet slows down away from the sun and increase speed once closer to the sun.

A projectile is launched vertically at 100 m/s. If air resistance can be ignored, at what speed will it return to its initial level?

Ignoring air resistance the projectile launched vertically at 100 m/s, it will fall and return to the same speed of 100 m/s. As soon as the projectile is launched, gravity is pulling on the object downwards. The gravity of the earth is 9.8 m/s, so that means that after ten seconds the projectile will have reached the highest point of its free fall and stop moving upwards. After it stops moving upwards, the projectile will continue to move downwards at a rate of 9.8 m/s a second until it reaches a speed of 100 m/s and hit the ground. The total time it would take for the projectile to rise and fall would be about twenty seconds. Ten seconds for the projectile to reach the highest point and another ten seconds after it begins to accelerate downwards to its initial position. However, the speed that is launched will be the same as it falls, 100 m/s.

In an accidental explosion, a satellite breaks in half while in circular orbit about Earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? Discuss what happens to the other half.

In the explosion, the satellite breaks in half while it is in orbit around the Earth. The half that is brought momentarily to rest will end up being pulled into the Earth, most likely causing it to burn and disintegrate in the Earths atmosphere, or end up crashing into the Earth. When it breaks off, it loses its horizontal velocity, and ends up being pulled in to the Earth. The other half, on the other hand acquires the momentum lost by the other half so it will possess a greater velocity. It will then move into a higher orbit.

How much time does it take for a complete revolution of a satellite in close orbit about the Earth?

It would take 90 minutes for a complete revolution of a satellite around the earth. Since the question states that it is in close orbit, the satellite travels fast. For instance, if the satellite had been farther, it would take a longer time for a full revolution to occur.

Which requires less fuel: launching a rocket to escape speed from the Moon or from Earth? Defend your answer.

Launching the rocket from the moon would require less fuel because if you launched the rocket from Earth the rocket engines need a minimum speed of 11.2 km/s. If the rocket does not maintain this they will not escape earth. While if you launched from the moon you only need to sustain 2.4 km/s to escape. Therefore, you are burning more fuel launching from Earth than you would if you launched from the moon.

Do your answers to the previous question depend on the angle at which the projectile is launched?

No, the vertical distance that the projectile falls beneath the straight-line path does not depend on the angle at which it is launched at. This is because when objects are in free fall, the same force of gravity acts upon them, and they have a constant acceleration of 10 m/s^2. Therefore, no matter the angle the projectile is launched, it will fall the same vertical distance.

Would the speed of a satellite in close circular orbit about Jupiter be greater than, equal to, or less than 8 km/s

The speed of the satellite in a closed circular orbit will be greater than 8 km/s, because the satellite over shoots a circular path and moves away from Earth, against the force of gravity . Figure (10. 27) shows that as it moves more away from earth it gains more speed and once it gets closer to earth it slows down.

Who gathered the data that showed planets traveling in elliptical paths around the Sun? Who discovered ellipti- cal orbits? Who explained them?

Tycho Brache gathered the data that showed the planets traveling in elliptical paths. Johannes Kepler discovered the fact that planets follow elliptical paths while traveling. Sir Isaac Newton explained these facts regarding the travels of planets.

A stone is thrown upward at an angle. What happens to the vertical component of it velocity as it rises? As it falls?

When the stone is thrown upward at an certain angle, the vertical component of its velocity decreases as it rises and increases as it falls.

Ignoring air resistance, could a satellite be put into orbit in a circular tunnel beneath the Earth's surface? Discuss.

Yes, a satellite can be put into orbit in a circular tunnel beneath the Earth's surface. The satellite is always moving in a direction perpendicular to the force of gravity that acts on it and the satellite moves at right angles to the gravitational force that acts on it. There will only a change in direction and no change in speed. The orbit of the satellite will be in has a focus of the center of the planet.

How could an astronaut in a space shuttle "drop" an object vertically to Earth?

if you drop the object vertically it would continue in a free fall and acceleration will increase the objects speed. If the football can travel in a straight line, it means there is no gravity pulling it down, unlike the case on the surface of the earth. The astronaut can simply give the object an initial push downward, the object will move vertically at a constant speed (not accelerating) until it hits the wall.