Question

Consider the previous problem and include the fact that Earth has an orbital speed about the Sun of 29.8 km/s. (a) What speed relative to Earth would be needed and in what direction should you leave Earth? (b) What will be the shape of the trajectory?

a) 29.8 km/s, perpendicular to Earth's orbital motion
b) 29.8 km/s, parallel to Earth's orbital motion
c) Greater than 29.8 km/s, perpendicular to Earth's orbital motion
d) Less than 29.8 km/s, perpendicular to Earth's orbital motion

Answer 1

To leave Earth, you would need a speed greater than Earth's orbital speed and depart perpendicular to Earth's orbital motion. The shape of the trajectory would depend on the speed and direction of departure.

Step-by-step explanation:

(a) To leave Earth, you would need a speed relative to Earth greater than Earth's orbital speed around the Sun, which is 29.8 km/s.

This is because you need to overcome Earth's gravitational pull and also match the velocity of Earth's orbit around the Sun. The direction you should leave Earth would be perpendicular to Earth's orbital motion, which means you should depart in a direction that is perpendicular to the plane of Earth's orbit.

(b) The shape of the trajectory would depend on the speed and direction of departure. If the speed relative to Earth is greater than Earth's orbital speed, the shape of the trajectory would be hyperbolic.

If the speed relative to Earth is equal to Earth's orbital speed, the shape of the trajectory would be parabolic. If the speed relative to Earth is less than Earth's orbital speed, the shape of the trajectory would be elliptical.