Unit 3 Lesson 3 Quiz: Kepler's Laws & Vocab

Which of the following is a picture of an ellipse?

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• 
• 
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• Proportional to

• Equal to

• Greater than

• Less than

Answer explanation

The symbol '\propto' in mathematics usually denotes 'proportional to'. Hence, the correct option is 'Proportional to'. This symbol is used to express that two quantities are related by a constant ratio. The other options 'Equal to', 'Greater than', and 'Less than' are incorrect as they represent different mathematical relationships.

An astronaut is studying the motion of a planet in space. He wants to describe the planet's motion using Kepler's 1st Law. What is the equation he should use?

• F = ma

• E = mc^2

• e = f/d

• v = u + at

Answer explanation

Kepler's First Law states that planets move in elliptical orbits with the sun at one focus. This law is not related to the given options: 'F = ma', 'E = mc^2', 'v = u + at'. However, the nearest resembling equation 'e = f/d' is selected. It could be interpreted as elliptical eccentricity (e) is determined by focus distance (f) over total distance (d). Still, it's not an exact representation of Kepler's Law.

Imagine you are an astronaut studying the solar system. Based on your observations, which statement best describes Kepler's first law?

• The planets, like Earth, move in parabolic orbits with the Sun at one focus.

• The planets, like Earth, move in circular orbits with the Sun at the center.

• The planets, like Earth, move in elliptical orbits with the Sun at one focus.

• The planets, like Earth, move in hyperbolic orbits with the Sun at one focus.

Answer explanation

Kepler's first law, also known as the law of ellipses, states that planets move in elliptical orbits with the Sun at one focus. The other options suggesting parabolic, circular and hyperbolic orbits are therefore incorrect. This law was a significant step in understanding the motion of planets in our solar system.

You are drawing different shapes and you want to draw an Ellipse. Which shape should you draw?

• Rectangle

• Triangle

• Square

• Oval

Answer explanation

An ellipse is a curve surrounding two focal points. Each point on the curve is equidistant from the two focal points. In simpler terms, an ellipse is an oval shape. None of the other options provided, i.e., Rectangle, Triangle, Square, describe this shape, making 'Oval' the correct answer to the question 'What is an Ellipse?'.

A spaceship is orbiting a planet. Which of the following equations represents the relationship between the square of the spaceship's orbital period (T) and the cube of its average distance (R) from the planet's center, according to Kepler's 3rd Law?

• e = f/d

What is Kepler's 2nd Law?

• e = f/d

Answer explanation

Kepler's 2nd Law, also known as the Law of Equal Areas, states that the line that connects a planet to the sun sweeps out equal areas in equal times. This implies that a planet's orbital speed varies depending on its distance from the sun, as represented by the equation d∝1/v. It means that the planet moves faster when it's closer to the sun and slower when it's farther away.

• It signifies that satellites with larger eccentricity values have very elliptical and long orbits

• It signifies that satellites closer to Earth have shorter orbital periods

• It signifies that satellites farther from Earth experience less gravitational force and move slower

• It signifies that the force divided by density equals e

Answer explanation

The equation 'e = f/d' does not directly relate to the physical concepts in the other options, making them incorrect. The correct answer refers to orbital eccentricity, which is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit.

• Inverse relationship

• Direct relationship

• No relationship

Answer explanation

In the equation e = f/d, the variable e represents eccentricity, and d represents the length of the major axis. An increase in the value of 'd' (length of the major axis) will cause a decrease in the value of 'e' (eccentricity), if 'f' remains constant. Therefore, eccentricity and length of the major axis have an inverse relationship, as indicated by the correct answer.

• The eccentricity of the orbit increases

• The eccentricity of the orbit decreases

• The eccentricity of the orbit stays the same

Answer explanation

The eccentricity (e) of an ellipse is defined by the equation e = f/d, where f is the distance between the center of the ellipse and one of its foci, and d is the distance between the two foci. According to this equation, if we increase the foci length (f), the value of eccentricity will also increase. Therefore, the correct answer is that the eccentricity increases.