Estimate the kinetic energy of the Mars with respect to the Sun as the sum of the terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the Sun. [Assume the Mars is a uniform sphere with mass = 6.4×1023 kg , radius = 3.4×106 m , rotation period 24.7 h , orbital period 686

Estimate the kinetic energy of the Mars with respect to the Sun as the sum of the terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the Sun. [Assume the Mars is a uniform sphere with mass = 6.4×1023 kg , radius = 3.4×106 m , rotation period 24.7 h , orbital period 686

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 26P: A space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104...

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Estimate the kinetic energy of the Mars with respect to the Sun as the sum of the terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the Sun. [Assume the Mars is a uniform sphere with mass = 6.4×1023 kg , radius = 3.4×106 m , rotation period 24.7 h , orbital period 686 d and is 2.3×108 km from the Sun.]
One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?
The position of four point masses m1=4 kg, M2=2 kg, m3=12 kg,and Mr=4 kg are given by (1,0),(0,2),(1,-1) and (1,3) ,arerespectively. In unit vector notation find the net gravitational force on . Calculate the total potential energy of the system.
A satellite of mass 20000 Kg orbits the earth along a path of long 3 x 108 m calculate: a) The orbital speed of the satellite. b) The mechanical energy of the satellite at the orbit. (c) The orbital period G = 6.67 x 10-11 Nm2/Kg2 , ME = 6 x 1024 Kg ,  = 3.14 Note along a path not the radius
Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can dig a long tunnel from one side of the Earth straight through the center and exit the other end, any object falling into the tunnel will appear at the other end (i.e. the opposite side of the Earth) in just 2530 s (42.2 min). Call that time t. Let t be a function of G, M, and R, where G = 6.67 x 10^-11 m3 kg−1 s−2 is the Universal Gravitational Constant, M = 5.98 x 10^24 kg, and R = 6400 km. (a) From dimensional analysis alone find the expression for t, up to a numerical constant c.(b) Determine the value of c by using the above values in the expression found in part (a).
A 1950 kg weather satellite moves in a circular orbit with a gravitational potential energy of 1.69 x 1015 J with respect to Earth’s surface. At its location, free-fall acceleration is only 6.44 m/s2 . How high above Earth’s surface is the satellite?
An uncrewed mission to the nearest star, Proxima Centauri, is launched from the Earth's surface as a projectile with an initial speed of 43.1 km/s, just enough for the spacecraft to escape the Earth's gravity and leave the solar system. Ignoring air resistance and the Earth's rotation, what is the speed of the spacecraft when it is more than halfway to the star? Assume we are ignoring the effect of the Sun on the spacecraft.
A spaceship with m = 1.00 ✕ 104 kg is in a circular orbit around the Earth, h = 800 km above its surface. The ship's captain fires the engines in a direction tangent to the orbit, and the spaceship assumes an elliptical orbit around the Earth with an apogee of d = 3.00 ✕ 104 km, measured from the Earth's center. How much energy (in J) must be used from the fuel to achieve this orbit? (Assume that all the fuel energy goes into increasing the orbital energy and that the perigee distance is equal to the initial radius.)
What’s the linear speed of a point on the equator of a planet whose radius is 4.8 times that of Earth?
A rocket is projected upward from the earth's surface (r = RE) with an initial speed v0 that carries it to a distance r = 1.5 RE from the center of the earth. What is the launch speed v0? Assume that air friction can be ignored.
The small mass starts at rest and slides down the smooth surface of a cylinder of radius R. Find the angle têta at which the mass loses contact with the cylinder
The orbit of Earth around the Sun is almost circular:The closest and farthest distances are 1.47 * 10^8 km and 1.52 * 10^8 kmrespectively. Determine the corresponding variations in (a) totalenergy, (b) gravitational potential energy, (c) kinetic energy, and(d) orbital speed. (Hint: Use conservation of energy and conservationof angular momentum.)