Homework Help

The average distance separating Earth and the Moon (center to center) is 384 000...

user profile pic

z0di4c | Student, College Freshman | eNotes Newbie

Posted March 20, 2010 at 1:41 PM via web

dislike 0 like

The average distance separating Earth and the Moon (center to center) is 384 000 km.

The average distance separating Earth and the Moon (center to center) is 384 000 km. Use the data in Table 7.3 to find the net gravitational force exerted by Earth and the Moon on a 3.00 104 kg spaceship located halfway between them.

Body Mass (kg) Mean Radius (m) Period (s) Distance from Sun (m) T2/r3 (s2/m3) Mercury 3.18 1023 2.43 106 7.60 106 5.79 1010 2.97 10-19 Venus 4.88 1024 6.06 106 1.94 107 1.08 1011 2.99 10-19 Earth 5.98 1024 6.37 106 3.156 107 1.496 1011 2.97 10-19 Mars 6.42 1023 3.37 106 5.94 107 2.28 1011 2.98 10-19 Jupiter 1.90 1027 6.99 107 3.74 108 7.78 1011 2.97 10-19 Saturn 5.68 1026 5.85 107 9.35 108 1.43 1012 2.99 10-19 Uranus 8.68 1025 2.33 107 2.64 109 2.87 1012 2.95 10-19 Neptune 1.03 1026 2.21 107 5.22 109 4.50 1012 2.99 10-19 Pluto ~1.4 1022 ~1.5 106 7.82 109 5.91 1012 2.96 10-19 Moon 7.36 1022 1.74 106 - - - Sun 1.991 1030 6.96 108 - - -

2 Answers | Add Yours

Top Answer

user profile pic

deviander | Student, Undergraduate | Honors

Posted March 20, 2010 at 2:28 PM (Answer #1)

dislike 1 like

Lol...ur in college man...w/e here's my answer.

The net gravitational force is the difference from the gravitational force from the Earth and the gravitational force from the Moon.

We also know the distance between the ship and the moon equals the distance between the ship and the earth, which is 192000km, or 1.92x10⁸m.

F=G●m1●m2 / r²

for the Earth:
F=G●m1●m2 / r²
F=(6.67428x10¯¹¹N (m/kg)²)●(5.98x10²⁴kg)●(3.00x10⁴kg) / [(1.92x10⁸m)²]
F=32.48063x10¹N or 324.8063N;

for the Moon:
F=G●m1●m2 / r²
F=(6.67428x10ˉ¹¹N (m/kg)²)●(7.36x10²²kg)●(3.00x10⁴kg) / [(1.92x10⁸m)²]
F=39.97616x10ˉ¹ or 3.997616N;

The net gravitational force then would be:
324.8063-3.997616
=320.808684 or 3.20808684x10²N

Assuming all the numbers in the question is given to 3 significant digits, the answer should be rounded to 3 significant digits too, which would be 3.21x10²N.

Final answer: 3.21x10²N towards / from the Earth

user profile pic

neela | High School Teacher | Valedictorian

Posted March 20, 2010 at 4:34 PM (Answer #2)

dislike 0 like

Let the distance between the  earth and moon be R and space ship. and the masses of  earth ,  moon and the spaceship be M1, M2 and m respectively.

Then the the gravitational force on the spaceship by earth  on the space ship by earth located at a distance R/2 is:

F1 = GM1*m/(R/2)^2 towards earth.

Similarly the the Gravitational force on the space ship by the moon is given by:

F2 = GM2*m/(R/2)^2  towards moon.

Since the spaceship is on the line between earth and the resulatant of forces F1 and F2 is F1+F2 = G*m(M2-M1)/(R/2)^2.

F1+F2 =

4G*m (M2-M1)/R^2 = 4*6.67428*10^-11*3*10^4*(5.98*10^24 -  7.36*10^22)/(384000000)^2, taking the force towards earth as positive and towards moon being in opposite direction as negative

= 320.8086539 N

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes