In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?

In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 4OQ

See similar textbooks

Similar questions

Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)
(a) What is the acceleration due to gravity on the surface of the Moon? (b) On the surface of Mars? The mass of Mars is SW 6.4181023kg and its radius is 3.38106m .
(a) Using the data in the previous problem for the asteroid Vesta which has a diameter of 520 km and mass of 2.671020kg , what would be the orbital period for a space probe in a circular orbit of 10.0 km from its surface? (b) Why is this calculation marginally useful at best?
A huge cannon is assembled on an almost airless planet. The planet has a radius of 5 x 10^6 m and a mass of 2.6 x 10^24 kg. The cannon fires a 10 cm radius sphere straight up at 5000 m/s. a) Assuming the planet is completely airless you should calculate what maximum height above the surface the sphere reaches. b) An observation satellite orbits the planet at a height of 1000 km. Does the projectile reach this height? If so what speed does it have as it goes past the satellite? c) Drag on this planet is actually D=0.005 A v2 (a measly 1% of drag on Earth) for the first 100 m ( and zero after that). Estimate or determine how much energy is lost due to this effect? Verbally comment on why it's an estimate.
A submarine of mass 200 kg is sent into a newly discovered "liquid" planet , i.e. the planet is a spherical mass of liquid with a mass M = 8.00 x1024 kg and a radius of R=1.17 x10' m. Assume that the liquid has uniform density throughout the planet. What is the gravitational force on the submarine when its distance from the center of the planet is r=0.4R (in Newtons)? G = 6.67 x 10-11 N. m2/kg²
At the Sun’s surface, the gravitational force between the sun and a 5.00 kg mass of hot gas has a magnitude of 1370 N. Assuming that the sun is spherical and has a mass of 2 x 1030 kg, what is the sun’s mean radius?
An asteroid has a mass of 3.66 × 10kg and a radius of 8.2 × 10m. If a 25 kg mass is dropped from 10 m above the “ground” of the asteroid, how long will it take the mass to fall to the ground?
Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg and a radius of 1821 km How high would this material go on earth if it were ejected with the same speed as on Io? (REarth = 6370 km, mEartg=5.96×1024kg) NOTE: Your answer suggests that you have assumed constant gravitational acceleration over the whole height of the ejected debris. Note that the gravitational field changes quite significantly over this height.
The mean diameters of X and Y, two planets in the same solar system, are 6.5 x 10³ km and 1.2 x 104 km, respectively. The mass of x is 0.21 times the mass of Y. The value of g on Y is 8.1 m/s². (a) What is the ratio of the mean density of X to that of Y (Px / Py)? (b) What is the value of g on X? m/s² (c) The mass of Y is 4.372 x 1024 kg. What is the escape speed on X? m/s
The dwarf planet Pluto has a radius of 1.15 x 10^6 m and a mass of 1.2x10^22 kg . What is the value of g on the surface of Pluto?
The escape speed from a distant planet is 39 km/s. If the acceleration of gravity on the planet surface is 11.5 m/s2, what is the radius of the planet?
Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg and a radius of 1821 km. For this calculation, ignore any variation in gravity over the 500 km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?