How far from the center of the earth is the center of mass of the earth + moon s

alka8q7 2021-11-18 Answered
How far from the center of the earth is the center of mass of the earth + moon system? Data for the earth and moon can be found inside the back cover of the book.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ryan Willis
Answered 2021-11-19 Author has 15 answers
The center of mass of a system consists of a set of obect numbered i=1,2,3... where i has mass mi and is located at position (xi,yi) is given by:
xcm=1Mimixi (1)
ycm=1mimiyi (2)
Given
From the back cover of the book, the mass of earth is me=5.98×1024 kg, the mass of Moon is mm=7.36×1022 kg, and the distnace between them is R=3.84×108 m
Calculations
We can conisder Earth and Moon to be along a straight line, and we ca take this straight line to be the x-axis.
Also we take the origin to be at the center of Earth, so Earths position is xe=0 and Moon's position is xm=R
Since our system consists of Earrth and Moon only, we can write equation (1) for our system as follows:
xcm=mexe+mmxmme+mm
Now , we enter the given values, so we get:
xcm=0+(7.36×1022 kg)(3.84×108 m)7.36×1022+5.98×1024 kg=4.67×106m
xcm=4.67×106 m
Therefore, the center of mass of the Earth-Moon system is at 4.67×106 m from the center of Earth which is less than Earth's radius 6.37×16m
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-08
A 500 g ball swings in a vertical circle at the end of a1.5-m-long string. When the ball is at the bottom of the circle,the tension in the string is 15 N.
What is the speed of the ball at that point?
asked 2020-11-22
The specific heat of lead is 0.030 cal/g.C. 300 grams of leadshot at 100C is mixed with 100 grams of water at 70C in an insulated container. The final temperature of the mixture is:
A) 100C
b) 85.5C
c)79.5C
d) 74.5C
e)72.5C
asked 2021-01-06

A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1
a) At which of the labeled x-coordinates is the force on the marble zero?
b) Which of the labeled x-coordinates is a position of stable equilibrium?
c) Which of the labeled x-coordinates is a position of unstable equilibrium?
image

asked 2021-04-21
The arm weighs 44.0 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force t in the deltoid muscle and the force s of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.
t=N
s=N
asked 2022-03-28

An aeroplane starting from airport A flies 300kms East then 250 km at 30°West of North and then 150 km north to arrive at airpot B

Calculate vector position of each displacement in unit vector notation 

asked 2021-11-11
Use differentiation to find a power series representation for f(x)=1(1+x)2, What is the radius of convergence?
asked 2021-12-30

Find the solution of the following Second Order Differential Equation
y9y=0,y(0)=2,y(0)=0

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question