Falling to Earth from 100,000 Miles - Can You Die by Impact?

[Evil_Klown]

Hi everyone -- I'm brand new here and didn't really know where to post this question. It's just that some friends and I were drinking beer last night and we began to wonder about something.

If you were on a stationary (non orbiting) platform 100,000 miles from Earth and you stepped off of it -- would you fall to earth?
Would the Earth move away from you too quickly to affect you?
Would it take you years to hit Earth -- or days?
Would you go into orbit around the Earth ... or just slam straight in?

We're not nearly smart enough to attempt a solution -- we were just wondering. Can anyone help? If so -- thanks.

Evil_Klown

 

[cristo]

I don't see how such a stationary platform could exist. What is the platform attached to? You are talking about dropping a body off this platform, and whether or not it would be affected by the Earth's graviational field (it would). However, so would this platform, and thus it souldn't be stationary.

 

[chaoseverlasting]

If the platform is not orbiting the planet, but its position is constant over time wrt the center of the planet, then depending on the mass of the body, the body would take a finite amount of time to fall to the planet providing you can neglect the gravitational effects of other heavenly bodies.

The gravitational force experienced by the body would be given by $$F_g=\frac{GMm}{r^2}$$. Since here $$r=1\times 10^5m$$, initially the force experienced would be very small, but would increase as the body came closer to the planet, hence increasing its acceleration and reducing time taken.

 

[HallsofIvy]

I'm going to assume you have a space station "stationary" in the sense that it is constantly directly above a fixed point on earth. At a particular altitude (stationary orbit) it would be any orbit. At any other altitude, something, such as rockets, would be required to keep it in position. What would happen would depend on the precise altitude. Below stationary orbit a person "stepping off" the space station would fall down- his horizontal speed would not be sufficient to keep him in "orbit". Of course, he would have some horizontal speed and would not fall "straight" down- he would impact at some distance to the west of the point directly below the space platform. If the station were above "stationary orbit" altitude, his speed would be too great for orbit and he would, in fact "fall up"- he move away from the earth.

 

[loom91]

As others have pointed out, the details of his motion will depend critically on the initial conditions, the motion of the platform in this case. Remember that 'stationery' is not a well-defined concept. It immediately begs the question stationary with respect to what?

Stationary with respect to Earth: this is known as a geostationary satellite. If it is at the altitude where it can be kept in orbit simply by Earth's gravitation and no expenditure of energy (such as by firing thrusters) is needed, then stepping out of it will not affect you. You will be stationary with respect to the satellite and join it in its geostationary orbit. If thrusters are being used, then the result will depend on the position of the platform as explained by HallsofIvy.

But note that even if you do fall down, you will not accelerate indefinitely. The viscous drag of air will cause you to accelerate only up to a maximum velocity, known as the terminal velocity. In fact, as the density of the atmosphere increases, you may even decelerate. The bottom line is that you will be completely vapourised long before you have a chance to hit the ground. This is not a recommended experiment in physics.

Molu