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## Homework Statement

An object possesses 61.14 kg mass.

1. How much energy in kilojoules would be necessary so as to project the object from the surface of the moon to the Earth's atmosphere at the Karman Line of 100km Earthly elevation, at such a speed that the total travel time between lunar surface and Earth atmosphere would be 12 hours?

2. What would be the speed of the object as it collides with the Earth's atmosphere at the Karman line?

gravitational pull on the moon: 1.622 m/s^2

Earth's gravity: 9.80665 m/s^2

mass of the moon: 7.34767309 × 10^22 kilograms

Mass of the Earth: 5.972 * 10^24 kg

radius of the moon at surface: 1,737.287 km

radius of the Earth at Karman Line: 6,471 km

total distance between Earth's center and moon center: 392,580.569 km

distance between moon surface and Earth at Karman line (distance to be traversed in 12 hrs): 384,372.282 km

2. Homework Equations

2. Homework Equations

## The Attempt at a Solution

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I'm thinking that I'll have to construct a function that incorporates both the moon's and the Earth's gravity. This gets restated algebraically so that the function's product is time. Then I integrate from 0 to however many seconds there are in an hour.