If we had no gravity how thick would a steel rope need to be to prevent the moon flying away?

Question

I think I can see the point on the moon where the old one was fixed, Coperincus still shows the radial ropes that spead the load. This was needed before the law of gravity was passed

Answer 1

My son had to calculate the answer to this for his physics class. Using the value he was given for the tensile strength of steel, and calculating the force of gravity between the Earth and the moon, we figured the cable would have to be something like 420 MILES in diameter!

Answer 2

The sun has about 2.2 times the gravitational force on the moon than does the earth. However, the earth and moon both orbit the sun together, so the moon's momentum is already at equilibrium with the sun's gravity. So there is a lot more force holding the moon in the sun's orbit than the earth's, but both orbits are stable. Those claiming the earth has more gravitational force on the moon than the sun are probably confusing it with tidal force, which is different. Using the formula a = Gm/r^2 to determine gravitational acceleration shows that the moon recieves about .000275 g's from the earth, and .000605 g's from the sun. Escape velocity from the sun at the moon's distance is also much higher than from the earth.

Answer 3

Gravity depends on just mass, moving or not.
Centrifugal forces depend on accelerated masses.

If there is no gravity, the weight of both earh and moon are zero kilograms, so you can choose a 380,000 km long human hair to hold earth and moon together. A steel cable would not be needed.

This is a prediction of general relativity, where gravitational (heavy) mass is set to be equal to accelerating (slow) mass.
When accelerating mass is 0 because gravitational mass is 0, the centrifugal force is 0 too, meaning that you don't need much to keep the objects together.

Answer 4

First of all you would have to ignore the 'wrapping' effect by assuming that the cable is attached to a railing on the earth.
Next, let's get the relevant numbers for the moon (from wiki):

Max. orbital speed 1.082 km/s (2420 mi/h)
Perigee 363,104 km (0.0024 AU)
Mass 7.3477×1022 kg (0.0123 Earths)

The steel cable would have to support the tension generated due to centripetal force. The equation for centripetal force is:

F_c = mass * (velocity)^2/ (radius of curvature)

The highest centipetal force would be experienced at perigee, where both the velocity is maximum and radius is minimum:

F_c_max = (7.3477×10^22 kg) * (1.082 km/s)^2 / (363,104 km)

=2.3691×10^17 N

Now we need to determine the diameter of the steel cable that can withstand this force. We want a steel cable thick enough so that it should not break. In fact, to be perfectly safe, it shouldn't even be close to breaking. Let's say the stress on the cable should be 1/2 of that required to break it (this means our factor of safety is 2). The tensile strength of carbon steels is in the range of 276-1882 MPa (where 1 Pa = 1 N/m^2).

The stress on the cable (Force divided by x-sectional area) is:

Stress_max = F_c_max/(0.5*pi*radius^2)

Suppose we use the steel with the highest tensile strength (1882 MPa). To account for the safety factor, Stress_max should be 1/2 of that 1882 MPa. Solving the above for radius, we have:

radius = 12660 m or 12.66 km

For the diameter, just double the radius. This asumes a solid chunk of steel. If you want a flexible cable, you would need to many individual strands of steel such that the total cross sectional area is described by the radius above.

Answer 5

The moon would fly away if gravity was turned off. And of course, the earth would fly away from the Sun. As the rope took the strain we would get dragged around and all sorts of odd trajectories would result (depending on which direction the moon was heading on release relative to our direction of travel) We could end up dragging the moon behind us, or spinning as a pair. If the earth continued its rotation about its axis, we may wind the the rope around us (assuming it was fixed on our equator) and reel the moon in, or get it twisting with us. All in all, a right old mess would result. best leave gravity switched on I say.

Oh.. I havn't answered your question, dang!

Answer 6

Ha Ha lovely thought. I think the Moon is weightless in space
so maybe some green gardening string might be enough to keep it on the leash. Yet what if it just flys at us. Why would I care becsue I would have floated away, oh I think I understand the question. IF we used a steel rope attatched to the moon whould we be able to reach it when whe are out of gravity.

Yea Yea, good one. Merry christmas

Answer 7

If there was no gravity, there would be no Moon to hold on to, and no Earth to tie it to! Planets and moons have no tensile strength by themselves in the way a rock does at the scales we are familiar with; there are as wobbly a jelly. Take away gravity and they would just fall apart.

Answer 8

I think your confused on the issue of gravity

Answer 9

LET
MASS OF THE EARTH=M
MASS OF THE MOON=m
DISTANCE BETWEEN THEM BE D
FORCE ACTING ON EACH OTHER=GMm/D^2
WHERE G=UNIVERSAL GRAVITATIONAL CONSTANT
YOUNGS MODULUS OF ELASTICITY OF STEEL(Y) IS AROUND 2*10^11 N/m^2
AREA OF CROSS SECTION=FORCE/Y
FROM AREA OF CROSS SECTION , BY USING A=pi R^2
WE CAN GET THE VALUE OF R

Answer 10

Hah