Gravity question for Christmas.

[Loose rivets]

Captain Lofty Large is flying an SST at 50,000 ft. He weighs 100 kg at the surface. What is his weight at cruising alt. Do not correct for aircraft speed or the Earth’s rotation.

[Milt]

Mass the same but Weight reduced a smidgen resulting from the reduced value of gravity.

Perhaps 99.99 kg (for reduced gravity) then + or -
food , perspiration, reduced weight of internal gases.

He will still have the lead in his pencil !!

[enicalyth]

Assuming no trick to this and all the caveats, 99.5kg? Assume the old Admiralty spherical Earth and circumference is 21600 x 6080 = 131328000 feet therefore radius is 20901500 feet. Gravity is inversely proportional to square of distance. Lofty is at 20951500 feet. Do the sums (20901500^2) / (20951500^2) equals 0.995232767 sooooo allowing for the wind, Lofty weighs 99.5kg??
There's gotta be a catch to this and I've fallen for it. Go on! What's the punchline?

[Old Smokey]

Loose rivets,

To answer the question fully we also need to know the speed, such that the slight negative 'g' due to continuous pushover to follow the earth's curveature may be calculated.

Seasons Greetings,

Old Smokey

[Onan the Clumsy]

What about the position of the moon (and the sun)?

Albeit 50,000' is well below the LaGrange point, the moon, if directly overhead, would offset some of the gravitational loss due to the increased distance of Cpt Lofty from the mass of the Earth :8

[keithl]

Old Smokey - Pushover is surely a red herring? The a/c is at 1g while cruising and it is the gravity that stops it shooting off into space, not "pushing to follow the curve"?

[bookworm]

The a/c is at 1g while cruising and it is the gravity that stops it shooting off into space, not "pushing to follow the curve"?

Yes and no. The centrifugal force that arises from trying to stay still in a rotating frame, or alternatively the force required to provide the acceleration to make the thing go in a circle rather than a straight line, is a real effect.

The good news is that the force appropriate to hovering over a particular lat-lon position is conventionally incorporated into g, the acceleration of free fall, in addition to gravity. The bad news is that if the object in question is moving with respect to the earth, we're faced with coriolis force (http://www.pprune.org/forums/showthread.php?s=&threadid=156743) as well... :(

But our torturer in this case specifically excused us from thinking about earth rotation or aircraft speed.

(My money's on the pound of feathers, BTW ;))

[Old Smokey]

keithl,

You'd better tell that to NASA - They've been using the increased speed principal up to the point where 'g' in the 'pushover' to follow the earth's cureveature was reduced to zero for spacecraft to stay in orbit for some time now.

Very real, but all a bit tongue in cheek,

Best Regards,

Old Smokey

[Capt Pit Bull]

RTQ....

What is his WEIGHT, not how many G can he feel, or what is his mass.

His Mass remains 100 KG.

The G force he can feel:

- We can not tell, without knowing the aircraft speed / Earth rotation issues - but then again the question told us to ignore them.
- But it would be less than 1 G, because an aircraft in 'straight and level' flight is not actually moving in a straight line and hence the forces on the aircraft are not actually in balance, nor are they on the Pilot.
- The Pilot would experience the sensation of slightly less than 1 G, because the force holding him up (an upwards push from the seat) would have to be less than his weight in order for him to accelerate downwards enough to follow a curved path of constant altitude around the earth.
- Taken to an extreme, a la Old Smokey, a space shuttle crew in orbit *feel* weightless.
- However, since you can only sense your weight when there is something present to hold you up, the term 'weightless' in that context is a misnomer / bad physics. They are in Free Fall, but their weight remains very much present.

The Pilots Weight:
- is however slightly less than at the surface of the planet by virtue of an increased distance between centres of mass involved, A La Enicalyth. Assuming the maths given by Enic was correct, then the gravitational field at 50,000' is 9.95 Newtons per Kilogram, yielding a weight of:


995 Newtons

(Onan has a point but I'm ignoring it as there is no data in the question to support it)

[Deaf]

The exact change in the gravitional acceleration is rather complex to calculate but taking the simplistic 1944 Rubber Bible figure of:

-3.08600E-004 cm/sec2/m or
-3.08600E-006 m/sec2/m

for a mass of 100Kg and extending it to 16,940 m

we get -5.22768E-002 m/sec2/m or a reduction in his weight of, 5.23N due to the altitude. If he was over Halifax (Nova Scotia) at the time this would reduce his weight from 980.574N on the ground to 975.346N. if however he was over Bahia (Brazil) this would reduce his weight of 978.331N to 973.103N.

If I was sober I would use the more suitable methods given in Applied Geophysics (Telford et al)

[Loose rivets]

Season’s greetings.

Well, great to get so much interest. At the time I asked the question, I needed to keep it simple because of wine induced attenuation of the axon-to-dendrite junctions.

A trick? No, it was meant to be a simple question, a reduction of the storyline data below. I did wonder if anyone would extrapolate to the zero gravity nucleolus, then out again to start the calculation.

Having read Dan Brown’s Da Vinci Code, I noticed Angels and Demons on one of my kid’s book shelves, and in the first few pages the hero finds himself on a flight in a Boeing X-33 HSCT. You know, it’s the two hundred foot one, with silicon fibers in its titanium matrix. But it’s O.K., it runs on slush hydrogen. Its 20:1 thrust weight ration soon take our hero up to 60,000' and Mach15 on his way to Geneva from the U.S.

At some point, the captain tells our man that “you’re thirty percent lighter up there.” That’s what got me wondering. Since I only had my granddaughter’s crayons, and an old party hat to write on, I went to pprune for the answer. I guess with this enhanced data, it ups the anti a little. Any takers? But you can ignore the La Grange point without losing any street-cred. (The hours I’ve spent wondering what happens to spacetime at that point.)

While on the subject, I can’t resist asking cos I’m barred from using the word gravity at home; it’s called the g-word by Mrs Rivits and banned years ago. Does anyone has any knowledge of a gravitational model that suggests that matter is changing scale? By matter I mean the actual modification of spacetime that we perceive as particles, not just the distance between them. I suggested eons ago that a fabric of space, Ether 11 if you like, was curving because of an inflow to feed this scale-change. It seems to comply with GR and works tantalizingly well in explaining the difference between rotating and non-rotating black holes ( Hawking ), gravitational red shift etc., but breaks down because of the need to retain certain aspects of inertia. Discussion / mail with qualified bods has been met with polite interest and even a little puzzled nodding, but is usually followed with them walking away to get on with some serious work.