How high can you jump on Ceres?

If you assumed standard atmosphere, pressure and room temperature, so you don't need a space suit, how high could you jump on Ceres?

The surface gravity there is about 0.27 m/s^2.

First, let's assume that on earth, I can jump ~ 2ft, or 0.6m high.

Using equations for conservation of energy, we can determine my jumping velocity (really my landing velocity):

m*g*h = 0.5*m*v^2
or
v^2 = 2gh

Since g on earth is 9.8m/s^2, and my jump height is 0.6m

v^2 = 11.77 (m/s)^2
v = 3.43 m/s

Using the same equation in reverse to get my jump high on Ceres

11.77 = 2 * 0.27 * h
h = 21.8m

Originally posted by forkedknight
First, let's assume that on earth, I can jump ~ 2ft, or 0.6m high.

Using equations for conservation of energy, we can determine my jumping velocity (really my landing velocity):

m*g*h = 0.5*m*v^2
or
v^2 = 2gh

Since g on earth is 9.8m/s^2, and my jump height is 0.6m

v^2 = 11.77 (m/s)^2
v = 3.43 m/s

Using the same equation in reverse to get my jump high on Ceres

11.77 = 2 * 0.27 * h
h = 21.8m

What about the best humans can do? I think the present record is a bit over 8 feet! 2.44 meters! Would it be linear, since that would be 4 times higher, so Would that come out to 87.2 meters on Ceres?

Originally posted by sonhouse
What about the best humans can do? I think the present record is a bit over 8 feet! 2.44 meters! Would it be linear, since that would be 4 times higher, so Would that come out to 87.2 meters on Ceres?

To answer your question...yes the relation ship is linear. However, as it is, the equation is only good for vertical leap. That limits it it to standing still, and jumping without changing your body's center of mass with respect to the extended body. I don't think anyone has a true vertical leap of 8 ft here on earth.

If we consider that we could be assisted with our jump we can get even higher. The escape velocity on Ceres is reportedly 510 m/s. If we decide to not exceed 500 m/s to avoid an error in the escape velocity number then we get a height of:

500 / (2 * 0.27) = 926 m (rounded)

That same apparatus on earth would only get us 25.5 m [5 giraffes - see below], which is an impressive jump but gives you the idea of the escape velocity. Most people with a reasonably good arm can throw a ball this high, so we could stand on Ceres and 'throw' ball-massed satellites into orbit. That would save on gas! (https://what-if.xkcd.com/44/)

Would it be part jump and part push as Ceres would move away from us.

Originally posted by divegeester
Would it be part jump and part push as Ceres would move away from us.

Of course that is always true, but the momentum imparted to Ceres would be very small. Ceres has a mass of approximately 895.8E18 kg, whilst an average human has a mass of 80.7 kg. That is a HUGE difference and Ceres would move an very insignificant amount.

Originally posted by GastelEtswane
If we consider that we could be assisted with our jump we can get even higher. The escape velocity on Ceres is reportedly 510 m/s. If we decide to not exceed 500 m/s to avoid an error in the escape velocity number then we get a height of:

500 / (2 * 0.27) = 926 m (rounded)

That same apparatus on earth would only get us 25.5 m [5 giraffes - see ...[text shortened]... row' ball-massed satellites into orbit. That would save on gas! (https://what-if.xkcd.com/44/)

Job listing for the year 2145: Ceres needs people with good throwing arm to launch small payloads from surface, baseball pitchers may apply. Good working conditions, sign on bonus, one month vacation per year, very high salary...

Originally posted by sonhouse
Job listing for the year 2145: Ceres needs people with good throwing arm to launch small payloads from surface, baseball pitchers may apply. Good working conditions, sign on bonus, one month vacation per year, very high salary...

Only Ceres-ious applicants should apply?

Originally posted by GastelEtswane
Only Ceres-ious applicants should apply?

Good one🙂