# Mass of object in Escape velocity

1. Dec 4, 2011

### asmalik12

Why doesn't the escape velocity depend upon the mass of body?

2. Dec 4, 2011

### Staff: Mentor

Why doesn't the height reached by a tossed ball depend on the mass of the ball? Same thing. (As is often the case when dealing with gravity, the mass drops out.)

3. Dec 4, 2011

### D H

Staff Emeritus
It does. The correct equation is

$$v_e = \sqrt{\frac{2\,G(M+m)}r}$$

The capital M denotes the mass of the central body, the little m, the mass of the escaping body.

Now think about how big that little m needs to be to make any measurable difference in the velocity needed to escape Earth orbit. Escape velocity from LEO is about 11 km/s. Suppose we can measure velocity down to the micrometer/second range, or 10 significant digits. That corresponds to a mass of 1015 kg, or the mass of about 100 mountains.

We aren't going to launch a 100 mountain mass out of Earth orbit any time soon.

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