a) Calculate the weight of a 100kg mass on the surface of the Earth using Newton

ID: 1344187 • Letter: A

Question

a) Calculate the weight of a 100kg mass on the surface of the Earth using Newton’s Law of Gravitation.

b) Repeat these calculations for altitudes above the surface of the Earth of 100km, 200km, 500km, 1000km, 2000km, 5000km, and 10,000km.

c) What is the percentage of the weight at 500km (Orbit of Hubble Telescope) to the weight on the surface of the Earth?

d) Plot the weight versus altitude using a program like Excel.

e) Based on these results, are you weightless if you are in orbit around the Earth?

a) weight = force exrted by earth on it

Fg = GMm/ R^2

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / (6371 x 10^3)^2 = 981.36 N

b) now R = (6371 + h ) x 10^3 m

for h = 100 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +100) x 10^3)^2 = 951.27 N

for h = 200 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +200) x 10^3)^2 = 922.53 N

for h = 500 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +500) x 10^3)^2 = 843.73 N

for h = 1000 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +1000) x 10^3)^2 = 733.15 N

for h = 2000 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +2000) x 10^3)^2 = 568.45 N

for h = 5000 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +5000) x 10^3)^2 = 305.39 N

for h = 10000 km

Fg = 6.67 x 10^-11 x 5.972 x 10^24 x 100 / ((6371 +10000) x 10^3)^2 = 148.63 N

c) % = ( 843.73 / 981.36) x 100 =85.98 %

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.