Astronomy Module 4

How many times greater is the force of gravity on a 8 kg object lying on the surface of a moon than on a 8 kg object orbiting at a distance of 1 moon radii above the surface?

1

An asteroid follows a circular orbit around the Sun with a radius of 5 AU. Which of the following is closest to its orbital period?

11 years

For the Earth, the perihelion is approximately 92 million miles and the aphelion is approximately 94 million miles. This information allows us to describe the Earth's orbit as:

Nearly circular orbit

A rocket engine accelerates its exhaust gas in one direction, moving the rocket in the other direction. Which law explains this phenomenon?

Newton's third law

Which of the following statements is consistent with Kepler's second law?

Planets always move faster when they are close to the Sun than when they are farther away.

Isaac Newton developed a theory of gravity by first considering Galileo's experiment of dropping objects of different masses from the Leaning Tower of Pisa. Galileo found that, when air resistance is negligible, all objects took the same amount of time to hit the ground when dropped from the top of the tower. Watch the AstroTour on Velocity, Acceleration, and Inertia, and then choose the answer that best describes what Galileo's experiment implies.

The acceleration of all objects dropped from the tower is the same.

Suppose that Planet Q has 4 times the mass as compared to Earth, and orbits the Sun at a distance of 2 AU. How does the amount of gravitational force exerted on Planet Q by the Sun compare to the amount of gravitational force exerted on Earth by the Sun?

The force on Earth and Planet Q are equal.

The interactive shows you a top-down view of a hypothetical solar system. The panel on the left will show you the orbit of the planet. The panel on the right will allow you to customize your solar system with different eccentricities. Play with the different eccentricities (0.0, 0.1, 0.4, and 0.8), paying attention to the relationship between semimajor axis and major axis. Select the answer below that best describes this relationship.

The major axis is twice the semimajor axis.

Kepler's laws of planetary motion were formulated using data recorded by:

Tycho Brahe.

Watch the AstroTour on Kepler's Laws and choose the statement below that directly follows from Kepler's second law of planetary motion.

Venus is traveling faster when it is at perihelion (the closest distance to the Sun) than when it is at aphelion (the farthest distance from the Sun).

In the law of gravity, G is

a constant related to the strength of the gravitational force.

Kepler's second law is a direct manifestation of:

conservation of angular momentum.

Sort each of the examples below by which of Newton's Laws of Motion is being demonstrated by each example.

Inertia Law (1st Law): An object in space can keep moving forever. Force Law (2nd Law): Massive objects weigh more.; Pushing a cart harder increases its speed.; Braking harder stops a car sooner. Reaction Law (3rd Law): Rockets expel exhaust backward.; Two cars collide and recoil from impact.; Swimmers move by pushing water.

What is the effect on the force of gravity between two objects if the mass of one object remains unchanged while the distance to the second object and the second object's mass are both doubled?

It always decreases.

Suppose the Sun suddenly quadrupled its mass, while Earth remained at the same distance from it. By how much does the force on the Earth change?

It increases by 4x.

The astronomer who formulated the three general laws of planetary motion was:

Johannes Kepler.

The interactive shows you a top-down view of a hypothetical solar system. The panel on the left will show you the orbit of the planet. The panel on the right will allow you to customize your solar system with different eccentricities. Play around with each of the eccentricities and notice how the system changes. Using this information, label the figure below with the appropriate titles.

Left to Right: C, B, D, A

A comet moves on an elliptical orbit around the Sun. Where is the comet's velocity largest?

perihelion

Which of the following values are the same whether one is standing on Earth or on the Moon?

the value of G; one's mass

Rank the following planets in order of increasing orbital speed they would have in a circular orbit around a star using their given orbital radii and stellar masses. Planet Orbital Radius (1011 m) Stellar Mass (kg) A 1 2×1030 B 3 2×1030 C 3 2×1031 D 5 2×1031 E 5 5×1031

B, A, D, C, E

Using the information about the different pairs of two massive objects below, rank the scenarios by the strength of the force of gravity between them from weakest to strongest. Scenario Mass 1 (× 1024 kg) Mass 2 (× 1024 kg) Distance (× 1010 m) A 40 10 10 B 10 1 10 C 4 10 2 D 1 1 1

B, D, A, C

We know that the mass, period, and semimajor axis are all related according to Kepler's third law. If the mass of the central body remains constant, increasing the period means the semimajor axis must also increase. If the mass of the central body remains constant and the period is decreased, then the semimajor axis must also decrease. This means the relationship between semimajor axis and period is a direct relationship. Interestingly, however, the relationship is not linear; it is a power law because solving the equation for period and semimajor axis we find P2≈a3. Now let's think about this relationship critically. The formula P2=4π2GMa3 will condense to P2=a3 when M⊙=1. The period is measured in years, and the semimajor axis is measured in AU in this form. As an example, if we know the period of a system is 8 years, what is the semimajor axis in AU?

4 AU

Using the table of information about planets in a fictional solar system below, rank the planets in order of length of orbital period (year), from shortest to longest. Planet Planet Mass (ME) Planet Radius (RE) Average Orbital Radius (AU) A 20 10 0.5 B 10 5 2 C 0.25 7.2 10 D 2 0.6 1 E 4 3 20

A, D, B, C, E

Astronomers discover four planets orbiting a Sun-like star. They determine the following information about the planets; Planet A is 0.2 AU from the star, Planet B has a period of 20 yrs, Planet C has a period of 10 yrs and Planet D is 1 AU from the star. What is the correct order of planets from closest to furthest distance from the star?

A, D, C, B

Suppose that Planet Q has the same mass as the Earth, yet orbits the sun at a distance of 5 AU. How does the amount of gravitational force exerted on Planet Q by the sun compare to the amount of gravitational force exerted on Earth by the sun?

Force on Earth is 25 times as large.

Newton determined that the force of gravity on an object is proportional to its mass, causing its mass to be canceled out (Newton's second law) and resulting in a constant acceleration. If the laws of physics are universal, then Newton should be able to apply his discoveries about gravity on Earth to the motion of the planets in our Solar System. Newton's third law says that for every force there is an equal reaction force in the opposite direction. What does this imply about the force of gravity associated with a person standing on the Earth?

The Earth's gravity pulls downward on the person, and the person's gravity pulls upward on the Earth.

An object travels at 10 m/s through interstellar space. If no forces act upon it, it will:

continue with the same velocity.

Planets in the solar system follow:

elliptical orbits with the Sun at one focus.

The gravitational force experienced by Earth due to the Moon is ________ the gravitational force experienced by the Moon due to Earth. (Note that the Moon is about 1% of the mass of Earth.)

equal to

The orbital periods of planets ________ with their average distance from the Sun.

increase