Question

Suppose an object is launched from Earth with 0.52 times the escape speed. How many multiples of Earth's radius (RE 6.37 x 106 m) in radial distance will the object reach before falling back toward Earth? The distances are measured relative to Earth's center, so a ratio of 1.00 would correspond to an object on Earth's surface. For this problem, neglect Earth's rotation and the effect of its atmosphere For reference, Earth's mass is 5.972 x1024 kg. Your answer is a ratio and thus unitless Enter only a number in the answer box

Answer 1

Escape velocity is given by

2GM

M is the mass of earth and R is its radius.

Let the object rises to a height h (measured from the center) before falling back to earth.

Applying principle of conservation of energy,

Total Energysurface - Total Energyh

GMm 1 or, R 2

GM Or,_ GM GM + 0.2704 ×

1 0.2704 1

or, - (0.2704 1)-

or,R = 07296 = 1.371 Or,_ - R 0.7296