Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As ch

Question

Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 4.80 s ; the circumference of Mongo at the equator is 2.10×105 km ; and there is no appreciable atmosphere on Mongo.

a.) The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo?

= 9.77*10^25 kg

b.) If the Aimless Wanderer goes into a circular orbit 40,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?

=__________ hr

Explanation / Answer

determine the gravity on Mongo
v = u+ at
0 = 14 - a x 2.4 (same time up as down)
a =5.83m/s = g

Find radius of Mongo
C = 2pi r
r = 2.1x 10^5 / (2 x 3.14) = 3.34 x 10^4km = 3.34 x 10^7m

using g = Gm/r (m & r = mass and radius of mongo)
m = rg/G
m = 3.34 x 10^7 x 5.83 / 6.67 x 10^-11
m = 2.9 x 10^18kg

v^2 = Gm/r (where r is the radius of sattelite from centre of Mongo)
v^2 = 6.67 x 10^-11 x 2.9 x 10^18 / (3.34 + 4) x 10^7
v^2 = 2.64 m/s
v = 1.62m/s (this seems too low??)

T = 2 pi r / v
T = 2 x 3.14x7.34 x 10^7 / 1.62
T =2.84 x 10^8 secs = 79078.5hrs

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