Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 11, Problem 55P
To determine
The minimum required speed relative to Earth to launch a projectile from the surface of Earth to escape from the solar system.
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We are planning a human exploration mission to Mars. We will first place our spacecraft into a circular around Mars and then send down a lander.
a) If we want the spacecraft to orbit at an altitude of 170 km above the Martian surface, what will the velocity and orbital period of the spacecraft?
b) When we land astronauts on the surface of Mars, what acceleration due to gravity in terms of g’s (i.e. as a fraction of the Earth’s gravitational acceleration) will the astronauts experience? You are permitted to use an online resource (e.g. Google) to find the necessary information about Mars that you might need in solving this problem.
Мon
Gravity:
on
off
O Gravity Force
Velocity
>
Path U
Grid
Star Mass
0.5
Our Sun
1.5
2.0
Planet Mass
0.5
Earth
1.5
2.0
Fast
392 Earth Days
Normal
Clear
Slow
Planetary motion.
A planet or asteroid orbits the Sun in an elliptical path'. The diagram shows two points of interest:
point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A.
At these two points (and only these two points), the velocity v of the planet is perpendicular to the
corresponding "radius" vector ỉ, from the Sun to the planet. An arbitrary point Q is also shown.
P
A
TP
A
Suppose the asteroid's speed at aphelion is vA = 900 m/s, and it's distance from the sun there is ra =
35 AU (AU is the "astronomical unit", commonly used in planetary astronomy).
a) Determine the planet's speed vp at perihelion.
b) Determine the planet's distance rp from the Sun (in AU) at perihelion.
Chapter 11 Solutions
Physics for Scientists and Engineers
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- Table D/2 Solar System Constants 6.673(10 1") m³/(kg · s²) 3.439(10 8) ft* /(lb - sec*) 5.976(1024) kg 4.095(1023) lb- sec² / ft Universal gravitational constant G Mass of Earth me Period of Earth's rotation (1 sidereal day) 23 h 56 min 4 s 23.9344 h 0.7292(10 4) rad /s 0.1991(10 °) rad /s Angular velocity of Earth Mean angular velocity of Earth-Sun line w = Mean velocity of Earth's center about Sun 107 200 km /h 66,610 mi / hr Body Surface Gravitational Acceleration m/s² (ft/sec?) Mean Distance to Sun km Eccentricity of Orbit Period of Orbit solar Mean Diameter km Mass Relative to Escape Velocity km/s (mi/sec) (mi) days (mi) Earth Sun 1392 000 333 000 274 616 (865 000) (898) (383) Мoon 384 3984 0.055 27.32 3 476 0.0123 1.62 2.37 (238 854) (2 160) (5.32) (1.47) Mercury 57-3 x 106 87.97 0.054 0.206 5 000 3.47 4.17 (35.6 x 106) (3 100) (11.4) (2.59) Venus 108 x 106 0.0068 224.70 12 400 0.815 8.44 10.24 (67.2 x 106) (7 700) (27.7) (6.36) Earth 149.6 x 106 0.0167 365.26 12 7422 9.8213…arrow_forwardYou are exploring a distant planet. When your spaceship is ina circular orbit at a distance of 630 km above the planet’s surface, the ship’sorbital speed is 4900 m/s. By observing the planet, you determine its radiusto be 4.48 * 10^6 m. You then land on the surface and, at a place where theground is level, launch a small projectile with initial speed 12.6 m>s at anangle of 30.8 above the horizontal. If resistance due to the planet’s atmosphereis negligible, what is the horizontal range of the projectile?arrow_forwardCalculate the speed v witrh which a projectile should be launched from the Earth so as to reach a height equal to one fourth of Earth's radius R.arrow_forward
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