Stars and Galaxies (MindTap Course List)
10th Edition
ISBN: 9781337399944
Author: Michael A. Seeds
Publisher: Cengage Learning
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Question
Chapter 1, Problem 2LL
To determine
Whether mercury follows a circular orbit or not.
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A planet's speed in orbit is given by V = (30 km/s)[(2/r)-(1/a)]0.5 where V is the planet's velocity, r is the distance in AU's from the Sun at that instant, and a is the semimajor axis of its orbit.
Calculate the Earth's velocity in its orbit (assume it is circular):
What is the velocity of Mars at a distance of 1.41 AU from the Sun?
What is the spacecraft's velocity when it is 1 AU from the Sun (after launch from the Earth)?
What additional velocity does the launch burn have to give to the spacecraft? (i.e. What is the difference between the Earth's velocity and the velocity the spacecraft needs to have?)
How fast will the spacecraft be traveling when it reaches Mars?
Does the spacecraft need to gain or lose velocity to go into the same orbit as Mars?
When the Earth passes directly between the Sun and Mars, the Earth and Mars are closest to each other. If Mars is 1.52 AU from the Sun and there are 1.5 x 108 km in 1 AU, how many times will the width of
the U.S. (2,530 miles) fit end-to-end between Mars and Earth?
Planets and Sun not drawn to
scale.
Mars
Earth
Sun
Part 1 of 4
Mars is 1.52 AU from the Sun. How many times further away from the Sun is Mars than the Earth? (The distances in AU are relative to the distance between the Sun and the Earth, so however many AU a
planet is away from the Sun is how many times farther it is from Sun than Earth.)
1.52✔
1.52 times further away
I. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius.
Average
Radius of
Orbit
Times of
Planet
R3
T2
T?/R3
Revolution
Mercury
5.7869 x 1010
7.605 x 106
Venus
1.081 x 1011
1.941 x 107
Earth
1.496 x 1011
3.156 x 107
1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?
II. Solve the given problems. Write your solution on the space provided before each number.
1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the
following:
a) Speed
b) Period
c) Radial Acceleration
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Chapter 1 Solutions
Stars and Galaxies (MindTap Course List)
Ch. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Prob. 3RQCh. 1 - What is the difference between the Moon and a...Ch. 1 - Prob. 5RQCh. 1 - Why are light-years more convenient than miles,...Ch. 1 - Prob. 7RQCh. 1 - Prob. 8RQCh. 1 - Prob. 9RQCh. 1 - Prob. 10RQ
Ch. 1 - What are the largest known structures in the...Ch. 1 - Prob. 12RQCh. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - Prob. 16RQCh. 1 - Prob. 1PCh. 1 - The equatorial diameter of the Moon is 3476...Ch. 1 - Prob. 3PCh. 1 - A typical galaxy is shown on the first page of the...Ch. 1 - Prob. 5PCh. 1 - Prob. 6PCh. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - If the speed of light is 3.0 105 km/s, how many...Ch. 1 - Prob. 10PCh. 1 - How long does it take light to cross the diameter...Ch. 1 - Prob. 12PCh. 1 - Prob. 13PCh. 1 - Prob. 1SPCh. 1 - Prob. 2SPCh. 1 - Prob. 3SPCh. 1 - Prob. 4SPCh. 1 - Prob. 1LLCh. 1 - Prob. 2LLCh. 1 - Prob. 3LLCh. 1 - Prob. 4LLCh. 1 - Prob. 5LLCh. 1 - Prob. 6LL
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Ex/13: The mean radius of earth is 6400 km. The acceleration due to gravity at its surface is 9.8 m/s². Estimate the mass of earth. "" 11 › (G = 6.67 × 10-¹¹ Nm²/kg²)arrow_forwardIf city is located in 2.8° north latitude and 46.0° east longitude. From there, you want to fly to a city in 7° north latitude and 52° east longitude. How much is the arc length of the big circle at 11000 m when the earth's radius is 6370 km? The arc length is 14223 km. Give your answer rounded to one kilmetre. Your last answer was interpreted as follows: 14223 XAnswer is incorrect. Keep centre of Earth as origin and define vectors to cities. Try again.arrow_forwardSaturn has an angular size of 16”, and an observed Synodic Period of 1.035yrs. Saturn’s moon, Titan orbits the planet with an angular separation of 192”, with a period of 15.9days. From these observations we can determine Saturn’s mass. Use the Sidereal Period of Saturn above to find the distance to Saturn from the Sun.arrow_forward
- Would you expect the distance between Earth and Mars to vary? Briefly explain your answer.arrow_forwardquestion 1 & 2 please , using 2 AU and the formulaarrow_forwardMars is 1.5 times as far away from the Sun as Earth. Earth’s axis is tilted at 23.5o compared to the ecliptic. The axis of Mars is tilted at 25o compared to the ecliptic. The atmosphere on Earth is 100 times as thick as the atmosphere on Mars. Which of the following statements is true? 1.)Mars is so cold that the water there is ice, while Earth does not have any ice 2.)When it is summer in Earth’s northern hemisphere, it is winter on Mars’ southern hemisphere 3.) Earth has seasons, Mars does not 4.) All of the water on Mars is frozen, while Earth has water in solid, liquid and gas formarrow_forward
- a) What is the semimajor axis of the spacecraft’s elliptical orbit around the Sun (in AU)? Hint: The semimajor axis of Earth’s orbit is 1 AU and the semimajor axis of Mars’ orbitis 1.52 AU. Consider the diagram above and assume for simplicity that the orbits of Earth and Mars are circular. b) What would be the period of the spacecraft’s orbit around the Sun (in Earth years)? c) Assuming that the spacecraft’s launch is timed properly to arrive at Mars, what is the time required (in days) for the spacecraft to reach Mars from Earth?arrow_forwardAssume that the planet's orbit is circular of radius R = 130 × 106 km and planet's period is T = 30 × 10° s. What is the magnitude of the vector J = r x r' (in units of square kilometers per second)? (Use decimal notation. Give your answer to three decimal places.) ||J|| = x10° km²/s Find the rate at which the planet's radial vector sweeps out area in units of square kilometers per second. (Use decimal notation. Give your answer to three decimal places.) dA x10° km²/s dtarrow_forwardAt its closest approach to Earth, Mars is 57.50 million kilometers away. How long (in minutes) would a radio signal sent from a future manned mission to Mars take to travel to Earth? (distance = speed x time) [55]arrow_forward
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Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY