Explanation Given information: Minimum distance between the comet and the sun = 1 2 r E . Mean distance from the sun to earth. r E = 150 × 10 6 k m . Periodic time of the comet = 76 y e a r s . Concept used: If the trajectory is an elliptical orbit. 1 r 0 + 1 r 1 = 2 G M h 2 r 0 − Minimum distance from the center of the earth r 1 − Maximum distance from the center of the earth G − Universal gravitational constant M − Mass of the earth h − Angular momentum per unit mass Periodic time ( τ ) τ = 2 π a b h a = 1 2 ( r 0 + r 1 ) b = r 0 r 1 r 0 − Minimum distance from the center of the earth r 1 − Maximum distance from the center of the earth h − Angular momentum per unit mass Calculation: g = 9.81 m s − 2 R E a r t h = 6.37 × 10 6 m Radius at the closet point to the sun. r 0 = 1 2 r E r E = 150 × 10 6 k m r 0 = 1 2 × 150 × 10 9 m = 75 × 10 9 m Since. M S u n = 332.8 × 10 3 × M E a r t h and G M E a r t h = g R E a r t h 2 . G M S u n = 332.8 × 10 3 × G M E a r t h G M S u n = 332.8 × 10 3 × g R E a r t h 2 G M S u n = 332.8 × 10 3 × 9.81 m s − 2 × ( 6.37 × 10 6 m ) 2 G M S u n = 1.325 × 10 20 m 3 s − 2 Since the trajectory is an elliptical orbit

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 12.3, Problem 12.108P

To determine

The maximum distance from the sun reached by the comet.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 12.107P

Chapter 12.3, Problem 12.109P

Students have asked these similar questions

It was observed that during the Galileo spacecraft’s first flyby of the earth, its minimum altitude was 600 mi above the surface of the earth. Assuming that the trajectory of the spacecraft was parabolic, determine the maximum velocity of Galileo during its first flyby of the earth.

A space probe is to be placed in a circular orbit of radius 4o00 km about the planet Mars. As the probe reaches A, the point of its original trajectory closest to Mars, it is inserted into a first elliptic transfer orbit by reducing its speed. This orbit brings it to Point B with a much reduced velocity. There the probe is inserted into a second transfer orbit by further reducing its speed. Knowing that the mass of Mars is 0.1074 times the mass of the earth, that ra= 9004 km and rg= 180 004 km, and that the probe approaches A on a parabolic trajectory, determine the time needed for the space probe to travel from A to Bon its first transfer orbit. Approach trajectory Second transfer orbit В 4000 km First transfer orbit The time needed for the space probe to travel from A to B on its first transfer orbit is |h.

A spacecraft approaching the planet Saturn reaches point A with a velocity vA of magnitude 68.8 × 103 ft/s. It is to be placed in an elliptic orbit about Saturn so that it will be able to periodically examine Tethys, one of Saturn’s moons. Tethys is in a circular orbit of radius 183 × 103 mi about the center of Saturn, traveling at a speed of 37.2 × 103 ft/s. Determine (a) the decrease in speed required by the spacecraft at A to achieve the desired orbit, (b) the speed of the spacecraft when it reaches the orbit of Tethys at B.

Chapter 12 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 12.1 - A 1000-Ib boulder B is resting on a 200-Ib...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Prob. 12.CQ4P Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Prob. 12.F2P Ch. 12.1 - Objects A, B, and C have masses mA, mB, and...Ch. 12.1 - Blocks A and B have masses mAand mB, my...Ch. 12.1 - Blocks A and B have masses mAand mB, my...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The maximum distance from the sun reached by the comet.

Solution Summary: The author calculates the maximum distance from the sun reached by the comet.

Concept explainers

Videos

The maximum distance from the sun reached by the comet.

Want to see the full answer?

Chapter 12 Solutions