Question

A landing craft with mass 1.24×104 kg is in a circular orbit a distance 5.50×105 m above the surface of a planet. The period of the orbit is 5100 s . The astronauts in the lander measure the diameter of the planet to be 9.80×106 m . The lander sets down at the north pole of the planet.

A) What is the weight of an astronaut of mass 84.4 kg as he steps out onto the planet's surface?

Answer #1

Treat the mass of the landing craft as negligible (which it is,
compared to a planet)

G = 6.674*10^-11 (a constant)

t = sidereal (360°) orbit time = 5,100 seconds

m = astronaut mass = 84.4 kg

R = planet radius = 4.9*10^+6 metres

The orbital radius (r) = (5.50*10^5) + (4.9*10^6)

= 5.45*10^6 metres

Firstly, find the planet mass (M) in kg from :

M = ( 4 * π ² * r ³ ) / ( G * t ² )

= (4*π ²*(5.45*10^6)^3)/(6.67*10^-11*5100^2) = 3.683*10^24

Then get the force (f) in Newtons on the astronaut from :

f = ( G * M * m ) / R ²

= (6.67*10^-11*3.863*10^24*84.40/(4.9*10^6)^2 = 905.734Kg

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