# Homework Help: What is the gravitational force if the distance is tripled

1. Oct 17, 2004

### ameriland_06

I am currently in a High School Physics class..... i am completely lost with what we are doing, if anyone is really good at physics and has msn messenger please add me at ameriland_06@Hotmail.com If you don't have messenger if you could just e-mail me...

here are some of the questions i have....
1) The gravitational force between two masses is 36 N. What is the gravitational force if the distance is tripled

2) A science fiction writer invents a planet that has twice the radius and eight times the mass of earth. What is the acceleration due to gravity on this planet.

3) A spaceship travels from the earth directly toward the sun. At what distance from the center of the earth do the gravitational forces of the sun and the earth on the ship exactely cancel?

2. Oct 17, 2004

### chroot

Staff Emeritus
1) You know Newton's law of universal gravitation, right?

$$F = G \frac{m_1 m_2}{r^2}$$

If r is tripled, the denominator of the fraction increased by a factor of nine, and thus the force decreases by a factor of nine.

2) The acceleration due to gravity can be found this way:

$$F = ma$$

$$a = F / m$$

$$F = G \frac{M m}{r^2}$$

$$a = \frac{G M}{r^2}$$

Plug in the numbers.

3) You will have one version of newton's law of universal gravitation describing the force due to the Sun, and another due to the force due to the Earth. Equate them and solve for the distances.

- Warren

3. Oct 17, 2004

### ameriland_06

in the 2nd to last formula what does the Mm stand for?? and wouldn't that be the formula that i would use on 3)

4. Oct 17, 2004

### chroot

Staff Emeritus
ameriland,

In all cases, Newton's law of universal gravitation is applied to two masses. You can call those masses M and m, or m1 and m2, or anything else you like.

In problem 2, you're looking for the gravitational acceleration experienced by some test body (call its mass m) in the gravitational field of the earth, with mass M. As you can see, the mass of the test body ends up cancelling out.

- Warren

5. Oct 17, 2004

### ameriland_06

this all is extremely confusing to me... is there a specific site that might help me better understand it all??

6. Oct 17, 2004

### chroot

Staff Emeritus
Ameriland,

You're on the best site there is.

- Warren

7. Oct 17, 2004

### ameriland_06

2) A science fiction writer invents a planet that has twice the radius and eight times the mass of earth. What is the acceleration due to gravity on this planet.

ok on this problem i did this, a=GM/R squared ...... is that the formula i'd use?

3) A spaceship travels from the earth directly toward the sun. At what distance from the center of the earth do the gravitational forces of the sun and the earth on the ship exactely cancel?

On this problem would i use the formula F=G(Mm/r squared) and if i did would the M be the mass of the sun and m be the mass of the earth??? i don't really understand on this one?

also do you have any type of messenger so it would be easier to communicate?

Last edited: Oct 17, 2004
8. Oct 17, 2004

### chroot

Staff Emeritus
2) You are correct. Make sure you understand where that formula comes from though; don't just blindly apply it.

3) Consider a test mass m in between the Sun and Earth. Call the Sun's mass $M_s$ and the earth's mass $M_e$. The force on the test mass due to the Sun, when at a distance $r_s$ from the Sun, is

$$F_s = G \frac{M_s m}{r_s^2}$$

Similarly, the force due to the earth is

$$F_e = G \frac{M_e m}{r_e^2}$$

Solve for when $F_s = F_e$:

$$\frac{M_s}{r_s^2} = \frac{M_e}{r_e^2}$$

You can use now solve for the ratio between the two distances. You'll find that one distance is a multiple of the other. Knowing that the total distance between the Sun and Earth is 93 million miles, you can determine both distances.

- Warren

9. Oct 17, 2004

### JasonRox

For number 3...

You got a=GM/r.

Remember doing something like this...

3x+5y=4
6x+11y=3

...and you had to find x and y.

Well for number 3, you need to find where a equals for the Sun and Earth.

In other words, you get the formula of Earth and the Sun, and you work them together.

10. Oct 17, 2004

### ameriland_06

ok well.... i keep getting a wrong answer?? can anyone please tell me the correct answer??? and i have more problems

1) to place a satellite into circular orbit 1500 km above the surface of the earth, what velocity must be given to the satellite?

2) what is the ratio of the gravitation force between the moon and the sun to the gravitational force between the earth and the moon. Is it more accurate to say that the moon orbits the sun or the earth?

also i'd like to check my answers on a few of these....
1) A body orbits the sun at a distance ten time sthe mean distance of earth's orbit from the sun
a. find the period of the body in years.... i got 3.18 X 10^-7
b. Determine the speed of the body...... i got 1.49 X 10^-3

2) A 2240-kg communications satellite is in a circular orbit at a height of 35,800 km above the surface of the earth. What is the gravitational force on the satellite? what graction is this of its weight at the surface of the earth?
i got g=9.44 X 10^-8
and i got the weight at the earth's surface to be 21952 N
*not sure if i did this one right*

3)A science fiction writer invents a planet that has twice the radius and eight times the mass of the earth. What is the acceleration due to gravity on this planet??
i got 2.497 X 10^-22
*don't think this is right either*

11. Oct 17, 2004

### JasonRox

As much as we love physics and math, we still hate doing assignments. We like doing what we want to do.

Unfortunately we like helping people who put an effort in there work.

Did you put any effort?

If yes, show us some.

By giving me what you got, it won't tell me what you did wrong or what you need help on. I can stand here for hours and come up with an infinite amount of possibilities on how you got that answer. That would be a waste of my time, which I am not willing to sacrifice.

Don't get me wrong, I love helping. In fact, I even tutored for free multiple times.

When I tutor, I actually assign homework and I won't tutor the next session until it is done. It can be all wrong, but don't come back with a blank paper that says "I got 4.565423."

Tutors are no different than teachers. They want to see work.

Last edited: Oct 17, 2004
12. Oct 17, 2004

### ameriland_06

welll i don't know how to type out the formulas and what i plugged in?? and if i've put any effort into it, i've been working on this for the past 6 hours straight and i keep getting stuck...

13. Oct 17, 2004

### JasonRox

Have you tried reading the chapter?

14. Oct 17, 2004

### chroot

Staff Emeritus
1) Centripetal acceleration is always a = v^2 / r. Plug in the radius of the orbit (NOT the altitude) and the acceleration due to gravity at that radius, and solve for the velocity.

2) This is just a straightforward application of Newton's law of universal gravitation.

The other answers are basically the same two equations combined in the same ways. Many of your answers are obviously wrong. If a body is orbiting the Sun, but further away than the Earth is, it will be moving slower than the Earth.

Also, remember to put units on your answers. "1.49 X 10^-3" is meaningless.

Can you please show me how you got the answer "g=9.44 X 10^-8" to question number 2?

- Warren

- Warren

15. Oct 17, 2004

### ameriland_06

yes i've read our chapters and they just don't describe these types of problems... do you have any type of messenger so it would be easier for me to communicate to you what i'm doing on these problems??

16. Oct 17, 2004

### ameriland_06

ok... on 2) here is what i did.... g=Gm/d(squared) so g=(6.67X10^-11 X 5.97X10^24)/(3.58X10^7 + 6.38X10^6)*squared* forgot to square the distance in my first try.... would .2238 N be a better answer?

Last edited: Oct 17, 2004
17. Oct 17, 2004

### chroot

Staff Emeritus
Question 2 was not asking for the gravitational acceleration of the satellite. It was asking for the gravitational force. Just use the law of universal gravitation:

$$F = G \frac{M m}{r^2}$$

where M is the mass of the earth and m is the mass of the satellite.

- Warren

18. Oct 17, 2004

### ameriland_06

ok... i did that formula and got 501.34 N does that sound right??? If so to find the weight at the earth's surface would i just do Mass times Gravity? mass being 2240 kg and the gravity being 501.34 N??

and when you say this 1) Centripetal acceleration is always a = v^2 / r. Plug in the radius of the orbit (NOT the altitude) and the acceleration due to gravity at that radius, and solve for the velocity.

the orbital radius? would that be the earth's radius plus the altitude??

Last edited: Oct 17, 2004
19. Oct 17, 2004

### chroot

Staff Emeritus
Yes.
At the earth's surface, gravitational acceleration is 9.8 m/s^2. Weight is mg.
Yes.

- Warren

20. Oct 18, 2004

### ameriland_06

Thanks for everyone's help... I think i now have a better grasp of whats going on