Conceptual Physics - Chapter 14: Satellite Motion (Review)

What is the maximum possible speed of impact upon the earth's surface for a far-away object initially at rest that falls to the earth due only to the earth's gravity?

11.2 km/s

What is the escape speed on the moon?

2.4 km/s

What speed would be needed if an ejected particle started at a distance from the sun equal to the earth's distance from the sun?

42.2 km/s

If you drop a ball from rest, how far will it fall vertically in the first second? If we instead move our hand horizontally and drop it (throw it), how far will it fall vertically in the first second?

A ball dropped from rest accelerates 10 m/s^2 and falls a vertical distance of 5 during the first second. If we instead move our hand horizontally and drop the ball, it will also fall a vertical distance of 5 meters in the first second.

Why doesn't gravitational force change the speed of a satellite in circular orbit?

A satellite in circular orbit around the earth is always moving perpendicular to gravity and parallel to the earth's surface at constant speed. Since it doesn't move in the direction of gravity, gravitational force does not change the speed of the satellite.

A satellite can orbit at 5 km above the moon, but not at 5 km above the earth. Why?

A satellite in orbit at 5 km from Earth would burn up due to friction in the atmosphere.

Describe an ellipse.

An ellipse is a specific curve: the closed path taken by a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant.

Ellipse

An oval-shaped curve that is the path of a point that moves such that the sum of its distances from two fixed points (foci) is constant.

Does the period of a satellite increase or decrease as its distance from the earth increases?

As its distance from the earth increases, the period of a satellite also increases.

Neglecting air resistance, what will happen to a projectile that is fired vertically at 8 km/s? At 12 km/s?

At 8 km/s, the projectile will achieve orbit around the Earth, while 12 km/s will thrust the projectile out of orbit since it is greater than 11.2 km/s.

Why do you suppose that a space shuttle is sent into orbit by firing it in an easterly direction (the direction in which the earth spins)?

Communications with a satellite will be much easier if it travels the same direction in orbit as the Earth rotates. If it moved in the opposite direction, it would whiz by any Earth location at incredible speed.

Although the escape speed from the surface of the earth is 1.2 km/s, couldn't a rocket with enough fuel escape at any speed? Why or why not?

Escape speeds infer that the speed is the initial speed. With sustained speed, the object could theoretically escape with a speed lower than 11.2 km/s.

Focus (pl. foci)

For an ellipse, one of the two points for which the sum of the distances to any point on the ellipse is a constant. A satellite orbiting the earth moves in an ellipse that has the earth at one focus.

Why do you suppose that sites close to the equator are preferred for launching satellites? (Hint: Look at the spinning earth from above either pole and compare it to a spinning turntable.)

From the perspective of space, positions near the equator rotate much more slowly than positions at the poles. Therefore, it would be easier to launch satellites near the equator.

Where in an elliptical orbit is the speed of a satellite maximum?

In an elliptical orbit, the speed would be the largest at the closest point (perigee).

Where in an elliptical orbit is the speed of a satellite minimum?

In an elliptical orbit, the speed would be the slowest at the farthest point (apogee).

Would you expect the speed of a satellite in close circular orbit about the moon to be less than, equal to, or greater than 8 km/s? Why?

Less than 8 km/s; the moon has less mass and therefore a weaker gravitational pull than the Earth.

If the earth somehow acquired more mass, with no change in its radius, would escape speed be less than, equal to, or more than 11.2 km/s? Why?

More than 11.2 km/s

How fast would a particle have to be ejected from the sun to leave the solar system?

More than 620 km/s

Why does most of the work done in launching a rocket take place when the rocket is still close to the earth's surface?

Most of the work is done near the earth's surface because the force of gravity is highest closest to Earth. Also, before the rocket leaves the atmosphere, there is air resistance to overcome.

Does gravity do any net work on a satellite in an elliptical orbit during one full orbit? Explain your answer.

No; work done to move the satellite in one direction is cancelled out by work done to move the satellite the other direction on the other side of the ellipse.

If a cannonball is fired from a tall mountain, gravity changes its speed all along its trajectory. But if it is fired fast enough to go into circular orbit, gravity does not change its speed at all. Why?

Once the cannonball is in orbit, it moves at a 90-degree angle to the force of gravity. Therefore, gravity has no effect on its speed.

If Pluto were somehow stopped short in its orbit, it would fall into the sun rather than around it. About how fast would it be moving when it hit the sun?

Since Pluto is so far from the sun, it would be moving at a tremendous speed towards the sun.

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

Since the Earth rotates very quickly, the satellites that seem to hover are actually moving at very high speeds.

Why does the force of gravity do no work on a satellite in circular orbit, but does do work on a satellite in an elliptical orbit?

The angle at which the gravitational force is against the satellite is not perpendicular, meaning there is a net force, changing the speed.

What do the distances 8000 m and 5 m have to do with a line tangent to the earth's surface?

The curvature of our earth drops a vertical distance of nearly 5 m for every 8000 m tangent to its surface.

Escape speed

The minimum speed necessary for an object to escape permanently from a gravitational field that holds it.

How does the direction of motion of a satellite in circular orbit compare with the curve of the earth's surface?

The motion of a satellite is perpendicular to the gravity of the Earth, meaning that it moves in a motion.

Apogee

The point in a satellite's elliptical orbit farthest from the center of the earth.

Perigee

The point in a satellite's elliptical orbit where it is nearest the center of the earth.

If an astronaut in an orbiting space shuttle wished to drop something to Earth, how could this be accomplished?

The space shuttle should attempt to orbit at the same speed as the rotation of the Earth and get closer to it. Then an object dropped might have a chance to land near the chosen target.

Why does gravitational force change the speed of a satellite in elliptical orbit?

The speed in an elliptical motion varies due to the change in gravitational force. The satellite slows and speeds up depending on the distance from the Earth and the direction. It acts as a falling object.

Does the speed of a satellite around the earth depend on its mass? Its distance from the earth? The mass of the earth?

The speed of a satellite depends greatly on the mass of the Earth and its distance from Earth. The mass of the satellite is very small in comparison to the mass of the Earth and therefore does not influence the speed.

Period

The time required for a complete orbit.

The sum of PE and KE for a satellite in a circular orbit is constant. Is this sum also constant for a satellite in an elliptical orbit?

Yes; at every point in an elliptical orbit, the sum of the KE and PE is also constant.