You plan to take a trip to the moon. Since you do not have a traditional...

60.1K

Verified Solution

Question

Physics

You plan to take a trip to the moon. Since you do not have atraditional spaceship with rockets, you will need to leave theearth with enough speed to make it to the moon. Some informationthat will help during this problem:
mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to center)
G = 6.67428 x 10-11 N-m2/kg2
1) On your first attempt you leave the surface of the earth at v= 5534 m/s. How far from the center of the earth will you get?
2) Since that is not far enough, you consult a friend whocalculates (correctly) the minimum speed needed as vmin = 11068m/s. If you leave the surface of the earth at this speed, how fastwill you be moving at the surface of the moon? Hint carefully writeout an expression for the potential and kinetic energy of the shipon the surface of earth, and on the surface of moon. Be sure toinclude the gravitational potential energy of the earth even whenthe ship is at the surface of the moon!

(Please inlude step-by-step solution or even an online video linkthat can teach me this as well)

Answer & Explanation Solved by verified expert

3.9 Ratings (573 Votes)

SOLUTION The gravitational force is F G M m r And it sits in a potential field given by Ur where F U is the gradient of this potential U G M m r You start off with kinetic energy given by K m v and it disappears into this potential energy reservoir so that the change in kinetic energy K because it starts at K and goes to 0 is the negative of the change in potential energy proportional to 1r 1r m v G M m 1r 1r As you can see your mass is unimportant and divides out so that you instead just get 1r 1r v 2 G M r 1 1r v 2 G M Using See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member