Originally Posted by

**Devon Keogh**

But using logic does it not seem that jumping would extend your orbit for a tiny amount of time and slow you down in relation to the sun then you will land on a slightly different point.

It is like jumping up on a line around the sun (orbiting the sun), when you land, you will be on a different point on that orbital line.

Technically yes, if you could jump

*exactly* straight up, took account of the rotation of the earth, corrected for the wind, and didn't move for a [real] year after landing. But you can't measure the other aspects of the jump well enough to detect the orbital effect.

Now for the effect of changing a real orbit by the amount you could jump on the planet. The height you can reach is given by

h = constants / (acceleration of gravity) = C/g

On a planet with 1/4 the gravity of the earth , you would jump to new h = 1 / (1/4) = 4h. So, as you said, you would jump four times as high. The orbital period of an orbit through the position you get to is a bit harder to do. The orbital period is

T = constants X square root (orbital radius cubed)

= C sqrt(R

^{3}) = C R

^{3/2}
and all the constants depend on properties of the sun, not the planet.

Now, how much can you change the radius of the orbit by jumping? The radius of the new orbit is the sum of your initial distance from the center of the planet plus the distance you jump in a direction away from the sun. The size of your jump is in fact small compared with every other distance in the problem, and under these conditions the effect of the jump is proportional to the first power of the jump. So your understanding is correct: The effect of moving to an orbit that you could touch by jumping, but at a place where the planet wasn't affecting your motion, is 4 times as much on the smaller planet as it is on earth.

I wouldn't be surprised if you had questions about this even though I agree with your result. If the questions involve the mathematics, please let me know what math you are comfortable with so that I can adjust the description to fit.