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 11.0 m/s returns to the ground in 4.50 s ; the circumference of Mongo at the equator is 2.90×105 km ; and there is no appreciable atmosphere on Mongo.

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

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?

Explanation / Answer

Determine the gravity on Mongo
v = u+ at
0 = 11 - a x 2.25 (same time up as down)
a = 4.9 m/s = g

Find radius of Mongo
C = 2pi r
r = 2.9 x 10^5 / (2 x 3.14) = 4.62 x 10^4 km = 4.62 x 10^7 m

using g = Gm/r (m & r = mass and radius of mongo)
m = rg/G
m = 4.62 x 10^7 x 4.9/ 6.67 x 10^-11 = 3.39 x 10^18 kg

v^2 = Gm/r (where r is the radius of sattelite from centre of Mongo)
v^2 = 6.67 x 10^-11 x 3.39 x 10^18/ (4.62 + 4) x 10^7
v^2 = 2.62
v = 1.62 m/s

T = 2 pi r / v
T = 2 x 3.14 x 8.62 x 10^7 / 1.62
T = 3.34 x 10^8 secs = 92777.78 hrs

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