A Vogon Warship is in a circular orbit of radius 20km around a dwarf planet of m

Question

A Vogon Warship is in a circular orbit of radius 20km around a dwarf planet of mass 1.5x10^17 kg. The weapons officer inadvertantly fires the mass nullification beam at the planetoid, instantly eliminating all of it's mass. The Warship's mass is 1.0x10^5 kg. What is the subsequestn trajectory of the Vogon Warship? In Terms of it's Velocity and/or acceleration as appropriate?

The resulting reactor explosion leaves them without main-engine thrust or communications. They immediately turn on their 0.25-pound aft maneuvering thruster. This points directly behind them. They have 50 days (of 24 Earth hours each) oxygen remaining. They must travel 530 thousand km to a communications relay to call for help. Will they make it to the relay before they run out of oxygen?

Explanation / Answer

The velocity of the orbit is found using

v^2 = GM/r

v^2 = (6.67 X 10^-11)(1.5 X 10^17)/(20000)

v = 22.4 m/s

.25 pounds of force = 1.112 N

F = ma

1.112 = (1 X 10^5)(a)

a = 1.112 X 10^-5 m/s^2

d = 530000 m

Apply d = vot + .5at^2

530000 = (22.4 t) + (.5)(1.12 X 10^-5)t^2

In standard form, that is

5.56 X 10^-6t^2 + 22.4t -530000 = 0

Plug that into the quadratic equation and find the time roots

t = 23523 s or -4052300 sec

Since the time can not be negative, the time is the positive value of 23523 sec

Now lets find out how long the oxygen will last

(50)(24)(3600) = 4320000 sec

Since 4320000 sec is greater than 23523 sec, they will make it in time

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