How Far Does the Moon Fall Toward Earth in One Second?

Click For Summary
SUMMARY

The discussion focuses on calculating how far the Moon falls toward Earth in one second, given its orbital speed of 1024 m/s and a center-to-center distance of 384,400 km. Participants emphasize the need to apply centripetal acceleration and geometry to determine the vertical displacement of the Moon from its tangent line during this time. A diagram was provided to assist in visualizing the problem, indicating the importance of understanding angular displacement and gravitational effects on orbital mechanics.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with centripetal acceleration concepts
  • Basic geometry related to circles and tangents
  • Knowledge of orbital mechanics and angular displacement
NEXT STEPS
  • Study the equations of motion under uniform circular motion
  • Learn how to calculate centripetal acceleration in orbital contexts
  • Explore the concept of angular displacement and its applications
  • Review gravitational effects on satellite motion and orbits
USEFUL FOR

Students of physics, educators teaching orbital mechanics, and anyone interested in celestial dynamics and gravitational effects on satellite motion.

eunhye732
Messages
11
Reaction score
0
The center-to-center distance between Earth and Moon is 384400 km. The Moon completes an orbit in 27.3 days.
(b) If gravity were switched off, the Moon would move along a straight line tangent to its orbit, as described by Newton's first law. In its actual orbit in 1.00 s, how far does the Moon fall below the tangent line and toward the Earth?

part (a) was asking for the Moon's orbital speed which was 1024 m/s. for part (b) my question is I don't know what equation to use to solve for this. All i know is that I need to use centripetal acceleration but when?
thanks and i hope you can help~!
 
Physics news on Phys.org
The second part is a geometry problem.
Consider a circle with a tagent line drawn at one point. Now after 1.0 s, the moon (under gravity) moves through an angle of theta. I truly think this needs a diagram, so I've attached one now. We want to solve for y.

http://img400.imageshack.us/img400/503/745636345ew.gif
 
Last edited by a moderator:

Similar threads

Compute the distance between the Earth and the Moon
  • · Replies 5 ·
Replies
5
Views
2K
Where between the Moon and the Earth is the gravitational potential=0 ?
  • · Replies 21 ·
Replies
21
Views
3K
Universal Gravitation and/or Tidal Forces?
  • · Replies 1 ·
Replies
1
Views
1K
Universal Gravitation and/or Tidal Force
  • · Replies 1 ·
Replies
1
Views
2K
Calculating the Distance of a Zero Gravitational Field Between Earth and Moon
  • · Replies 2 ·
Replies
2
Views
2K
Calculating the fall of the moon in one second
  • · Replies 3 ·
Replies
3
Views
2K
What force needed to launch an object from moon to Earth
  • · Replies 14 ·
Replies
14
Views
3K
How does the position of the Moon affect gravitational pull and weight on Earth?
  • · Replies 33 ·
2
Replies
33
Views
21K
How Do You Calculate the Moon's Speed and Acceleration in Its Orbit?
  • · Replies 6 ·
Replies
6
Views
3K
Does an orbiting satellite speed up as it falls towards earth
  • · Replies 3 ·
Replies
3
Views
2K