Phobos obits Mars at a distance of 9376 km from the center of the planet and has a period of 0.3 189 days. Assume Phobos’s orbit is circular. Calculate the mass of Mars. (Hints: Use the circular orbit velocity formula in Reasoning with Numbers 4-1; make sure to convert relevant quantities to units of meters, kilograms. and seconds.)
To calculate:
The mass of Mars based on the distance and orbit angle of Phobos
Answer to Problem 5P
The mass of Mars =
Explanation of Solution
Given Information:
Radius of orbit = 9376 Km
Period of Orbit = 0.3189 Days
Formula Used:
Circular orbit velocity =
Also, VS=distance/time
Calculation:
Assume Phobos (Moons) orbit to be circular.
First convert the quantities into proper units
Now,
Circular Velocity =
Where, G = Gravitational Constant =
r = Radius of Planet. (m)
m= Mass of Planet (Kg)
Rewriting in terms of m
∴ m =
For finding circular velocity that is distance covered per unit time.
∴ VS =Distance/time
Distance between but circumference of orbit.
∴
∴ Moon must cover 5.9 x 107 m distance in 27552.96 sec
∴ its circular velocity must be,
∴ put all the Values in mass of Mars formula,
=
=
Conclusion:
Mass of Mars is
Want to see more full solutions like this?
Chapter 17 Solutions
Horizons: Exploring the Universe (MindTap Course List)
Additional Science Textbook Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Mathematical Methods in the Physical Sciences
The Physical Universe
University Physics Volume 2
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- Again using Appendix F, which planets might you expect to have extreme seasons? Whyarrow_forwardBetween mars and Jupiter the asteroid ceres orbits the sun at an average radius of 2.766 AU. Use kelpers third law to calculate the time in earth it takes for ceres to make one complete orbit. Round up your answer to the correct number of significant digits.arrow_forwardLet'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 yearsarrow_forward
- The asteroid Ceres has a mass of 9.39 x 1020 kg and an average radius of about 473 km (4.73 x 102 km). What is its escape velocity (in m/s)? 2GM (Hints: Use the formula for escape velocity, V. ; remember to convert units to m, kg, and s.) r m/s Could you jump off the asteroid? Yes Noarrow_forwardUse Kuiper Belt Object Haumea's eccentricity; e = 0.189, semimajor axis, a = 43.3 AU, and Period, P = 285 yrs, values to a) calculate its perihelion and aphelion distances with Dp = a (1 e) and D₂ = a (1 + e), b) verify if Haumea's a and P satisfy Kepler's third law for all objects orbiting the Sun: p2 = a³. Show your work. Paragraph Lato (Recom... a) Dp= Da= V b) p2= BI 19px... v U A L EQ 58° ...arrow_forwardI. 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:arrow_forward
- I would like you to compare the size of some of the largest moons of the solar system to their host planets. Using diameters of 12,700 km, and 140,000 km, 116,000 km for Earth, Jupiter, and Saturn respectively, please provide the ratios of the following moons to their host planets (you can use Table 12.1 from the book to get the diameters of the moons): Luna (Earth's moon), Io, Callisto, Ganymede, Europa, and Titan. After collecting those ratios, please tell me one thing that you notice that stands out about those results.arrow_forwardThe gravity on Mars is about 38% that of Earth's gravity. Let's say some cargo has a mass of 15 kg here on Earth. First, what would be the weight of that cargo in kilograms on Mars? Explain your answer. Second, what would be the mass of that cargo in kilograms on Mars? Explain your answer.arrow_forwardImagine you grew up on Mars, whose semi-major axis is 1.5 AU. In observing the planets over your lifetime from the Martian surface, what is the largest angular separation you would see between the Earth and the Sun? Take the orbits of the Earth and Mars to be circular.arrow_forward
- A Sense of Proportion: Mercury averages only 0.39 AU from the Sun, Venus 0.72 AU and Mars 1.52 AU. If you built a model solar system and represent the average distance from the Sun to Earth as 10 inches, how far would you place Mercury, Venus and Mars from the Sun?arrow_forwardEccentricity for Mars is 094 and semi major axis "a" is 227,9 10" Km; Calculate the perihelion and aphelion distances.arrow_forwardPluto has been hard to measure from Earth because of the atmosphere. In 2007 Young and Buie measured Pluto as having a diameter of 2322 km. In 2015 the New Horizons probe reached pluto and measured it up close and we now know the actual diameter is 2372 km. What was the percent error of the 2007 measurement? Enter your answer as a percent with a negative value if the 2007 measurement was too small and a positive value if it was too large.arrow_forward
- Horizons: Exploring the Universe (MindTap Course ...PhysicsISBN:9781305960961Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningFoundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning
- Stars and GalaxiesPhysicsISBN:9781305120785Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningAstronomyPhysicsISBN:9781938168284Author:Andrew Fraknoi; David Morrison; Sidney C. WolffPublisher:OpenStax