Exam 4: Gravitation and the Waltz of the Planets

A spacecraft that has been put into a circular orbit around the Sun (in the same plane as Earth's orbit) with a sidereal period of 2.25 years is unobservable behind the Sun once every:

The synodic period of a superior planet in motion around the Sun, as viewed from Earth, is defined as the time between:

In the geocentric Ptolemaic model that described the apparent motions of planets against the background sky as viewed from a stationary Earth, at what distance with respect to its deferent is a particular planet on its epicycle when it appears to stop moving for a short period in its motion against the background?

Consider a spacecraft in a circular orbit. Suppose a rocket thruster is fired, increasing the speed of the spacecraft. What will be its subsequent orbit? (See Figure 4-22, Universe, 11th ed.) ​ ​

According to Kepler's law, the approximate sidereal period of an asteroid moving around the Sun at a distance of about 2.8 au in the asteroid belt is:

At what distance would a planet have to orbit the Sun to have its synodic period equal to its sidereal period, assuming circular orbits for Earth and the planet?

The eccentricity of Venus's orbit is e = 0.007. Suppose a Planet X is discovered with an orbital eccentricity of e = 0.014. This tells us that:

As Venus orbits the Sun, by what factor, as viewed from Earth, does its angular size change from smallest to largest? (See Figures 4-13 and 4-14, Universe, 11th ed.(in the text))

The original form of Kepler's third law is P² = a³, where P is the period of the orbital motion and a is the semimajor axis of the elliptical orbit. Newton's form of the third law, however, is $P^{2}=\left[\frac{4 \pi^{2}}{G\left(m_{1}+m_{2}\right)}\right] a^{3}$ , where m₁ and m₂ are the masses involved. Three of the motions listed below can be analyzed with the original form of the law, and one requires Newton's form. Which one requires Newton's form?

A body moves through space with a certain speed. How many forces are needed to make this object move in a circle?

An inner planet is observed (through a telescope) to have a gibbous shape whenever it is close to:

If we could observe a planet in orbit around the Sun but very far away, as its distance approached infinity, its synodic period would approach:

The sidereal period of Jupiter is almost 12 years. Its synodic period is:

Newton's second law states that acceleration produced by a force is:

Galileo's early observations of the sky with his newly made telescope included the:

Greatest elongation in a planetary orbit occurs when the angle between:

Which one of the following relationships represents Newton's most important contribution to physics?

If you drop an object near Earth's surface it will have an acceleration of 9.8 m/s². If, instead, you throw the object downward, its acceleration (after it leaves your hand) will be:

If a planet moves around the Sun in a circular orbit, how many forces act on it?

Titan, the largest satellite of Saturn, orbits Saturn with a semimajor axis of 1.22 × 10⁹ m and an orbital period of 1.38 × 10⁶ s (about 16 days). Use the formula in Box 4-4 to compute the combined mass of Saturn and Titan. What is the result, in kilograms?