If a rope was tied around a ball the size of the sun, how much more length would it take to lift it 3 feet up?

Question

I made a bet about how many more feet of rope you would have to add to make the rope hover 3 feet above the surface of the ball.

Answer 1

I remember a problem like that from Ask Marilyn. The answer is 18.85 feet.

You would be increasing the radius by 3 feet, therefore the diameter by 6 feet.

Since the circumference and the diameter are directly proportional, you'd only need to add 6π feet (about 18.85 feet) to the rope.

old circumference = 2π × old radius = π × old diameter

new circumference = 2π × (old radius + 3)
= π × (old diameter + 6)
= π × old diameter + 6π

So since the old circumference was π × old diameter, the new circumference = old circumference + 6π. So you'd have to add 6π, or about 18.85, feet to the rope.

The original radius is irrelevant. p_carroll is wrong. esse est percipi is wrong too.

Answer 2

about 117,008 feet (35.7 km) if only one point on the rope is raise 3ft above the sun.

Sight, all done.
assuming the sun's radius is 695,500 km = 2,281,824,147 feet
(calculation not shown, too long to explain)
but after several steps you get
the resulting length - the actual length = 117008.204382 feet
So it would take about 117,008 more feet of rope to make the rope hover 3 feet above the surface of the sun.

p_carroll has the correct concept.
if you mean like the rope is above the surface by 3 ft at every point, then the answer is 6π.

if you mean that only one point on the rope is raise 3ft above the sun, c = 2πΔr would be wrong because it give you the circumference of the rope if it was circular, however if you raise it above the surface, it will be straight untill it touches the surface.

Answer 3

The answer requires you to calculate two lengths.

The first length is how much rope is required to go around the sun at its present size.

The second length is how much rope is required to go around the sun if the rope is 3 feet above the sun's surface (i.e., the same as increasing the radius by 3 feet).

Subtract the first length from the second length and you have your answer.

Note that the answer is an irrational number.

Answer 4

You would need 3 more feet to lift the rope 3 feet from the surface.

Answer 5

3 Feet?

Answer 6

The answer is

2π(Δr) where Δr is the desired change in radius. In this case

Δr = 3 feet

2π(Δr) = 2π(3) = 6π ≈ 18.85 feet

Answer 7

when you know the answer...apply at NASA for some kind of employment as I'm sure you will be accepted.

P.S. Tell the aliens I said Hello