Question: An asteroid orbiting the Sun has a perihelion distance of 1 AU. At aphelion, it is at 2 AU. What is the ratio of its speed at perihelion to aphelion?
Answer: This question is about the conservation of angular momentum. In other words, the product of (mass)x(speed)x(distance) should be always the same. Mass does not change in this case. Speed should change as the distance from the Sun changes since the product of the two should be the same. If we call the product (speed)x(distance)=1 for the ratio calculation, the speed at 1 AU is "1" and speed at 2 AU should be "1/2". So, the ratio between the speed at perihelion (1 AU) to aphelion (2 AU) is (1) divided by (1/2), which is 2.
Question: Kepler's 3rd Law says that the square of the period of an object orbiting the Sun goes as its orbital radius cubed. If a comet has an average orbital radius of 5 AU, how long does it take to complete one orbit?
Answer: Kepler's 3rd law says P2 = a3. Here, a = 5, and a3 = 5 x 5 x 5 = 125. So, this means P2 = 125. Then the period P is square root of 125 or P = 11.2 years.
Question: If you apply a force of 3 Newtons to a mass of 2 kg, it results in an acceleration of 1.5 m/sec2. What acceleration would result if you applied a force of 12 Newtons to a mass of 4 kg?
Answer:Newton's 2nd Law says F = ma, i.e. force is the product of mass and acceleration. You can see in the example that force (3 Newtons) is the product of mass (2 kg) and acceleration (1.5 m/sec2). In the question, you are given the information on the force and mass and are asked to calculate acceleration. So, for force of 12 Newtons and mass of 4 kg, you have "F = m x a" or "12 = 4 x a". Dividing both sides of the equal sign by 4, you get "a = 12/4 = 3", and the answer is 3.0 m/sec2.
Question:Suppose the moon of a planet has a mass of 1/(M)th the mass of the planet it is orbiting. What is the ratio of the force the moon applies to the planet compared to the force the planet applies to the moon? (Express your answer as a number.)
Answer:Newton's 3rd Law says there is an equal and opposite force for every force. If the moon is pulling on the planet with a gravitational force F, then the planet also pulls on the moon with the exactly same amount of gravitational force (and vice versa). So, the ratio of the forces is "1", regardless of the mass of the planet or the moon.
Question:In the distant past, the Moon was 4 times closer to the Earth than it is currently. How big was the force on the Moon back then compared to the force now? (Express your answer as a number.)
Answer:The Newton's Law of Gravitation is shown above. Since we are talking about the same Earth and the same Moon as before, the only thing changing is the distance. When the Moon was 4 times closer, the distance "r" was 1/4 of today's value. Gravity is proportional to 1/(r2). So, the gravity earlier was 1/(1/4)2 = 1/(1/16) = 16 times stronger.
Question: Hydrogen atom emits radio wave photons with a characteristic wavelength of 21.12 cm. What is the observed wavelength of this light originating from a galaxy moving away from us with a velocity of 3,000 km/s?
Answer: First of all, the galaxy is moving away from us, so the wavelength of the light should be stretched out, larger than 21.12 cm. Now, as described in Mathematical Insight 6.3 of the Bennett (3rd edition) Chapter 6, "the difference between the observed and intrinsic wavelength of the light" divided by the intrinsic wavelength is V/c where "V" is the recession speed of the galaxy while "c" is the speed of light, i.e.,
