physics question?

Question

On October 14, 2012, Felix Baumgartner, with a mass of 71 kg, set a record for the highest parachute jump when he jumped from a platform 38,000 m about the surface of the Earth.

a) What was Felix’s weight just before he jumped off the platform?

b) What was the strength of Earth’s gravity field at the location he jumped off the platform?

c) When Felix jumped from the platform what was his weight as a percentage of his weight on Earth’s surface?

Answer 1

g_(altitude) = g_{(sea level)}[r_e/(r_e + h)]²

g_{(sea level)} = 9.80665 m/s²

r_e (mean) = 6371.009 km = 6371009 m

g_(altitude) = 9.80665[6371009/(6371009 + 38000)]²

g_(altitude) = 9.80665[6371009/6409009]²

g_(altitude) = 9.80665[0.99407]²

g_(altitude) = 9.80665(0.988177)

g_(altitude) = 9.6907 m/s²

W = mg_(altitude)

W = (71)(9.6907) = 688 N = 690 N

Strength of the Earth's gravity field where he jumped: 9.6907 N/kg

Weight as a ratio of weight on the Earth's surface: 0.988177 = 98.8%

In case you were wondering about the equation I used initially:

Newton's Universal Law of Gravitation is F = GmM/r_e² where m is the mass of some random object on earth and M is the mass of the earth, G is the Universal Gravitational Constant and r_e is the radius of the earth.

But we also know (Newton's 2nd Law) that F = ma so:

ma = GmM/r_e² and, since "m" is on both sides, it cancels out and we can change the acceleration to "g", the acceleration of gravity. So we have:

g = GM/r_e² and this is the "g" at a distance from the center of the earth of "r_e" (or at sea level) so it would be better to say:

g_{(sea level)} = GM/r_e²

We can manipulate this equation by multiplying both sides by r_e² to get:

(r_e²)g_{(sea level)} = GM

Then we can repeat this for a distance of r_e plus h (an altitude of "h") to get:

(r_e + h)²g_(altitude) = GM

Since both equations equal "GM", we can set them equal to each other:

(r_e²)g_{(sea level)} = (r_e + h)²g_(altitude)

Then we can solve for g_(altitude) :

g_(altitude) = g_{(sea level)}[r_e²/(r_e + h)²] or

g_(altitude) = g_{(sea level)}[r_e/(r_e + h)]²