In this example we are going to calculate the weight of an object on the surface

Question

In this example we are going to calculate the weight of an object on the surface of the planet Mars and at a position well above the Martian surface. Suppose you’re involved in the design of a mission carrying humans to the surface of Mars, which has radius RMars=3.38×106mand mass mMars=6.42×1023kg. The earth weight of the Mars lander is 39,200 N. Calculate the weight Fg of the Mars lander and the acceleration due to Mars’s gravity, gMars, (a) at the surface of Mars, and (b) at 6.00×106mabove the surface of Mars (corresponding to the orbit of the Martian moon Phobos).

Part A - Practice Problem:

At a certain point in its orbit, the International Space Station is 430 km above the surface of the earth. If an object’s weight were determined to be 4.1 N at that altitude, what would the object weigh back on the earth’s surface?

Express your answer in newtons to three significant figures.

Explanation / Answer

weight on earth = 39200 N

mass of mars lander = 39200/9.8 = 4000 kg

now gravity at mars,

(A) on surface, g = GM/R2 = (6.67 x 10-11 x 6.42 x 1023)/(3.38 x 106)2 = 3.748 m/s2

weight of mars lander = 4000 x 3.748 = 14993 N

(B) on given height, g = GM/(h+R)2 = (6.67 x 10-11 x 6.42 x 1023)/(9.38 x 106)2 = 0.4867 m/s2

weight of mars lander = 4000 x 0.4867 =1947 N

PART-A

mg' = mgR2/(R+h)2

4.1 = weight on surface x (R/(R+h))2

weight on surface = 4.1 x (6800/6370)2 = 4.672 N

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