# 1. [6 points] A) What would be the force between a 85 meter diamete...

## Question

1. [6 points] A) What would be the force between a 85 meter diameter NEO (mass = 1 million metric tons) and a gravity tractor loaded with 1000 metric tons of rocks and parked at a constant distance of 85 meters from the center of mass of the NEO?
B) What would be the acceleration of the NEO as a result?
C) What would be the velocity change of the NEO after 1 year of operation?

2. [3 points] Your NEO bound spacecraft is hit by a stony meteoroid with the mass (2.5 gm) of a United States one cent coin (penny) traveling at 35 km/s.
A) What mass of TNT would contain an explosive power equal the kinetic energy of this meteoroid? If possible, compare the impact energy to the explosion of some familiar item.
B) Would the impact be capable of doing significant damage to your craft?

4. [6 points] You are using a gravity tractor to change the trajectory of an NEO on a collision course with Earth. Unless the trajectory is altered, the NEO will impact the Earth 20 years hence. The approximately 100 meter NEO has a mass of 1.57 billion kilograms. The force exerted on the NEO is related to the product masses of the tractor and the NEO (Newton’s Law of Gravity). You want to impart an acceleration of 2 x 10-9 m/sec2 to the NEO.
A) What should the mass of tractor be to produce a force sufficient to produce this acceleration?
B) Neglecting the mass of the physical tractor mechanism, what would be the size of a spherical boulder from the NEO which when attached to the tractor would produce the needed mass?

5. [5 points] Since the atmosphere of Jupiter has the same basic composition as the solar wind, it has been suggested that 3He could be harvested from the atmosphere of Jupiter by “floating” processing facilities (sort of like the Cloud City gas mining operation on the planet Bespin in the second Star Wars movie). For this question, assume that you could refuel your cargo rocket from the Jovian atmosphere and launch it from the top of the atmosphere where the escape velocity is 60 km/sec. The scenario would be to launch to a low circular orbit about Jupiter then use efficient low thrust propulsion to transfer the 3He cargo to market.
A) What would be the mass ratio (initial mass / final mass or [vehicle + cargo + fuel] / [vehicle + cargo]) of your vehicle to a low orbit about Jupiter assuming the ISP = 1000 sec (NERVA-type nuclear rocket).
B) What would the mass ratio be if you had access to a high thrust engine with an ISP = 3000 seconds?
C) Based on these results, how viable is this scenario?

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