Calculating Escape Velocity and Energy Requirements for Ceres

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The gravitational field strength at the surface of Ceres is 0.15 N/kg, and the gravitational potential is 85 kJ/kg. The minimum escape velocity from Ceres is calculated to be 410 m/s. To determine the minimum energy required to escape, the discussion suggests using kinetic energy formulas, specifically E = mv²/2, where mass can be assumed as 1 kg for simplicity. Additionally, it is noted that calculating energy may require integrating the force over the distance to infinity, indicating a need for further clarification on the correct approach.
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The asteroid Ceres has mass of 7 times 10 to the power of 20 kg and radius of 550000 m.

a)What is the gravitational field strength at the surface of Ceres? DONE 0.15 N kg to the power of -1

b)What is the gravitational potential at the surface of Ceres?DONE 85 kilo J kg to the power of -1

c)What is the minimum escape velocity from the surface?DONE 410 m s to the power of -1

d)What is the minimum energy required to escape from Ceres? i do not know this part. Could I use a formulae of Kinetik energy? Please help me.
 
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I'm not an expert yet. Therefore I'm not sure of my post.

I think this formula may be helpful:

v2 = 2gh

You have v (= minimum escape velocity) and g (= gravitational field strength).
You can figure out h (= height),

and you already know:
Ep = mgh
E = mv2 / 2

You need mass for calculating energy. Can you use 1 kg mass in the formula? I don't know...
 
Last edited:
The energy required is the energy it takes to go from the surface of the asteroid to infinity. So, unless I'm mistaken, you must integrate the force over that distance.
 
Thank you both.
However, is someone really suru about right formulae?
 
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