Gravity Week HW

A vocabulary in context exercise in which students match words to definitions describing elliptical planetary orbits, applying ideas from Kepler's Laws of Planetary Motion.

1. Earth is located at one focus of the Moon's orbit. 2. According to Kepler's second law, Jupiter will be traveling most slowly around the Sun when at aphelion. 3. Earth orbits in the shape of a/an ellipse around the Sun. 4. The mathematical form of Kepler's third law measures the period in years and the semimajor axis in astronomical units (AU). 5. According to Kepler's second law, Pluto will be traveling fastest around the Sun when at perihelion. 6. The extent to which Mars' orbit differs from a perfect circle is called its eccentricity

Match the words in the left-hand column to the appropriate blank in the sentences in the right-hand column. Use each word only once.

1. The light from Polaris travels through space in the form of radiative energy. 2. Rapidly moving comets have more kinetic energy than slowly moving ones 3. An apple contains chemical potential energy that your body can convert into other forms energy. 4. Nuclear fusion in stars converts some of the mass-energy of hydrogen nuclei into light and heat. 5. Due to its much higher density, water heated to 80 degrees (Celsius) contains more thermal energy than air at the same temperature. 6. An asteroid that is moving farther from the Sun is gaining gravitational potential energy.

For at least the first few seconds, Loki was just accelerating freely (in free-fall!) under Earth's gravity. Roughly what acceleration was he experiencing?

10 m/s ^2

According to Kepler's third law (p2 = a3), if a planet were discovered with an average distance from the Sun of 100 AU, its period would be

1000 years

Jupiter orbits the Sun at an average distance of 5.203 AU and takes 11.86 years to complete each orbit. Based on these facts, which statement is true?

11.86 ^ 2=5.203 ^ 3

According to Kepler's third law (p2 = a3), an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to

4 astronomical units.

Assuming the acceleration from Part 1 and that he's accelerating freely, how fast was he going after he had been falling for 5 seconds?

50 m/s ^2

Match the correct laws to the examples in which they apply. Use each law only once.

An object moves at constant velocity if there is no net force acting on it explains why a spaceship with no forces acting on it will continue moving even if it has no fuel For planets orbiting the Sun, period (p) and orbital distance (a) obey the relation p2 = a3 explains why Earth orbits the Sun at a faster average speed than Mars. A line between a planet and its Sun sweeps out equal areas in equal times explains why Earth's orbital speed varies over the course of each year. For any force, there is an equal and opposite reaction force tells us that, when you are pushing on a table, the table is pushing up on you with a force that precisely balances the force of your push. Force equals mass times acceleration explains why applying a force to a baseball with your arm can cause the baseball to accelerate from rest to the speed at which it leaves your hand. The orbit of each planet is an ellipse, with the Sun at one focus explains why Earth's distance from the Sun varies over the course of each year.

Are they also weightless during launch to the station? How about during their return to Earth?

Astronauts are not weightless during either launch or return to Earth.

If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why?

Because air resistance has a greater effect on the larger ball.

Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton's theory of gravity? Neglect effects of air resistance.

Both balls fall to the ground in the same amount of time.

Explain your answer in the previous part.

During launch, astronauts are subjected to the force due to acceleration of the rocket. During return, they are subjected to the force due to deceleration of their ship by air resistance forces.

Which of the following statements correctly describes the law of conservation of energy?

Energy can change between many different forms, such as potential, kinetic, and thermal, but the total quantity of energy in the universe never changes.

The six statements below represent Newton's three laws of motion and Kepler's three laws of planetary motion. Match each statement to the scientist (Kepler or Newton) associated with it.

Kepler: A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times Kepler: The orbit of each planet about the Sun is an ellipse with the Sun at one focus. Newton: Force = mass x acceleration Kepler: More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship p2 =a3. Newton: An object moves at constant velocity if there is no net force acting upon it. Newton: For any force, there is an equal and opposite reaction force.

Eventually if Loki gets going fast enough, air resistance will start to become important. What is the result of air resistance?

Loki will eventually be falling with constant velocity Submit

Suppose an astronaut is working outside the Space Station and lets go off the handholds, so she is no longer attached to the Space Station in any way. Which of the following correctly explains what will happen?

Orbital speed does not depend on mass, so she will remain very close to the Space Station.

When space probe Voyager 2 passed by Saturn, its speed increased (but not due to firing its engines). What must have happened?

Saturn must have lost a tiny bit of its orbital energy.

Einstein's theory, like Newton's, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein's theory?

Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates.

You discover an asteroid that orbits the Sun with the same 1-year orbital period as Earth. Which of the following statements must be true?

The asteroid's average (semimajor axis) distance from the Sun is 1 AU

In Part A, you found that your weight will be greater than normal when the elevator is moving upward with increasing speed. For which of the following other motions would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed.

Which of the following statements about an ellipse is not true?

The focus of an ellipse is always located precisely at the center of the ellipse.

All of the following statements are true. Which one can be explained by Kepler's third law?

Venus orbits the Sun at a faster orbital speed than Earth.

Suppose you are in an elevator car when the elevator cable breaks. Which of the following correctly describes what happens and why.

You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate.

Suppose you drive from home to your child's school, pick her up, and drive back home, covering a total distance of 25 miles in 1 hour. Which of the following statements are true?

Your average speed for the trip is 25 miles per hour. Your velocity is different on the return home than it is on the way to school. You must accelerate when you reach the school.

On Earth, the______ tells us that the velocity of a falling object increases by about 10 m/s for each second it falls.

acceleration of gravity

Kepler's third law, p2 = a3, implies that

all orbits with the same semimajor axis have the same period. planets that are farther from the Sun move at slower average speeds than nearer planets. the orbital period of a planet does not depend on its mass. a planet's orbital period does not depend on the eccentricity of its orbit.

This diagram shows a graphical interpretation of Kepler's third law. Suppose there were a planet in our solar system that orbited the Sun with an average speed of 11 km/s. In terms of its average distance, this planet would be located:

between Jupiter and Saturn

Gravity follows an inverse square law. This means that if the distance between two masses is decreased by a factor of 4, the gravitational force between those two masses

increases by a factor of 16.

Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.

less than your normal weight at rest

An object's ______ is its mass times its velocity, and we say that it has angular momentum if it is rotating or turning on a curved path.

momentum

If your momentum is changing, then a(n) ______ must be acting on you

net force

In its original form, Kepler's third law states that p2 = a3 . What units must p and a use?

p must be years and a must be astronomical units.

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.

the Moon has a larger acceleration than Earth, because it has a smaller mass Submit

When you are standing on a scale in an elevator, what exactly does the scale measure?

the force you exert on the scale

The orbital period of a geosynchronous satellite is

the same as Earth's precise rotation period.

Why are astronauts (and other objects) weightless inside the International Space Station as it orbits Earth?

they are in free-fall

If you are in free-fall then your ____ will be zero

weight

If you stand on a scale on the Moon, your _____ will be different than it is on Earth but your _____ will be the same.

weight mass

In which of the following cases would you feel weightless?

while falling from a roof