roblem B.2: Distance of the Planets The table below lists the average distance R to the Sun and orbital period T of the first planets: Distance Orbital Period Mercury 0.39 AU 88 days Venus 0.72 AU 225 days Earth 1.00 AU 365 days Mars 1.52 AU 687 days (a) Calculate the average distance of Mercury, Venus and Mars to the Earth. Which one of these planets is the closest to Earth on average? (b) Calculate the average distance of Mercury, Venus and Earth to Mars. Which one of these planets is the closest to Mars on average? (c) What do you expect for the other planets? Hint: Assume circular orbits and use symmetries to make the distance calculation easier. You can approximate the average distance by using four well-chosen points on the planet's orbit.

roblem B.2: Distance of the Planets The table below lists the average distance R to the Sun and orbital period T of the first planets: Distance Orbital Period Mercury 0.39 AU 88 days Venus 0.72 AU 225 days Earth 1.00 AU 365 days Mars 1.52 AU 687 days (a) Calculate the average distance of Mercury, Venus and Mars to the Earth. Which one of these planets is the closest to Earth on average? (b) Calculate the average distance of Mercury, Venus and Earth to Mars. Which one of these planets is the closest to Mars on average? (c) What do you expect for the other planets? Hint: Assume circular orbits and use symmetries to make the distance calculation easier. You can approximate the average distance by using four well-chosen points on the planet's orbit.

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter21: The Birth Of Stars And The Discovery Of Planets Outside The Solar System

Section: Chapter Questions

Problem 24E: Kepler’s third law says that the orbital period (in years) is proportional to the square root of the...

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Use Kepler's Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun.Using Earth's time of 1 year and a mean distance of 93 million miles, the equation relating T (in years) and a (in million miles) is 804375T2=a3.Use that relation equation to determine the time required for a planet with mean distance of 206 million miles to orbit the Sun. Round to 2 decimal places. years
What would be the period of revolution of a hypothetical planet whose circular orbit around the sun has a radius of 1.75 AU? (Hint: 1 AU = 1 Astronomical Unit = 1.5*1011) a) 2.3 yrs b) 1.45 yrs c) 2.9 yrs
Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.
You land on a strange spherical planet X. As a curious physicist, you set out to make the following measurements: (1) you observe that planet X has no appreciable atmosphere, (2) you measure that if you throw a 0.25 kg stone vertically upwards with launch speed 10 m/s, it comes back to ground in 8 sec, and (3) you measure the equatorial circumference to be 250,000 km. What is the mass of planet X? [Hint: The value of g on the planet surface is related to its mass M and radius R by the formula g = GM/R2.] a) 9*1025 kg b) 2.3*1027 kg c) 6.9*1026 kg If you take your spaceship to a 10,000 km altitude circular orbit around planet X, what would be the orbital period of the spaceship? [Hint: Use the fact that the gravitational force causes the radial acceleration to calculate the orbital speed.] a) 4.89 hrs b) 9.78 hrs c) 19.56 hrs
A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 122 million kilometers. Its orbital eccentricity is 0.6. What is the planet's orbital period? And how do you find the planet's nearest and farthest orbital distances from its star?
Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Earth. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth years
Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Mercury. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth years
The table below lists the average distance R to the Sun and orbital period T of the first planets:Distance Orbital PeriodMercury 0.39 AU 88 daysVenus 0.72 AU 225 daysEarth 1.00 AU 365 daysMars 1.52 AU 687 days(a) Calculate the average distance of Mercury, Venus and Mars to the Earth.Which one of these planets is the closest to Earth on average?(b) Calculate the average distance of Mercury, Venus and Earth to Mars.Which one of these planets is the closest to Mars on average?(c) What do you expect for the other planets?Hint: Assume circular orbits and use symmetries to make the distance calculation easier. You canapproximate the average distance by using four well-chosen points on the planet’s orbit.
According to Kepler’s second law, where in a planet’s orbit would it be moving fastest? Where would it be moving slowest?
Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (Pa1.5) . For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.
The Moon requires about 1 month (0.08 year) to orbit Earth. Its distance from us is about 400,000 km (0.0027 AU). Use Kepler’s third law, as modified by Newton, to calculate the mass of Earth relative to the Sun.
If you visited another planetary system, would you be surprised to find planets older than Earth? Why or why not?