Gravitational potential question

A spacecraft of mass 1.0 × 106 kg is in orbit around the Sun at a radius of 1.1 × 10^11 m
The spacecraft moves into a new orbit of radius 2.5 × 10^11 m around the Sun.
What is the total change in gravitational potential energy of the spacecraft?

A -6.76 x10^14
B -3.38 x 10^14
C 3.38 x 10^14
D 6.76 x10^14

I understand you have to find the change in gravitational potential then times this number by the mass to get the change in gravitational potential energy, i get the value of -6.76x10^14. But the answer is D. Why is the energy positive?
Does it have something to do that the gravitational potential energy is the energy needed to move an object from infinity to that point?
If you move an object from infinity to a point, the force is in the same direction as the displacement so the work is positive. But we are moving the satellite towards infinity, so the force pulling it back to earth is in the opposite direction to the displacement, so the work must be negative, but its not. Im so baffled. I hope i make some sort of sense?
Please could someone help me understand?

For Gravitational Potential energy it is assumed that at infinity it is equal to zero, as a object approaches a gravitating object it will gain Kinetic energy (as it accelarates to to the gravitational field of the object), this gain in energy cannot be from nowhere- this would violate the laws of conservation of energy, hence it is assumed that the potential energy is most negative when the radius of rotation approaches zero and most positive/ equal to zero when approaching infinity. Hence as you go away from/increase your radius of rotation from a gravitating object, you will gain potential energy (it will become less negative) and you will lose equal and opposite kinetic energy (it will become less positive)- therefore energy is conserved and at any point, the kinetic energy of the satellite is equal and opposite to the potential energy of the satellite. There is the theory.

Summary: you need to do work to move away from a gravitating object, therefore the change in potential energy will be positive...


Hope this helps!!

Ok oh, so when would the change in potential energy be negative? When it moves towards the gravitating object? why?

Yes the change in potential energy will be negative when moving towards the gravitating object and positive when moving away from a object. Even if you use the equation mgΔh, if you go from a high height of 5 metres to a height of 1 metre above the ground, you're Δh value will be 1-5=-4 and therefore your change in potential energy will be negative. As I said above this will be because as you move towards the gravitating object you will accelerate and therefore you will gain kinetic energy, therefore to conserve energy you must lost energy from your potential energy store. Is better to thing of the negative sign as the 'change in potential energy' instead of the object's current potential energy if what I said previously is confusing...

Hope this helps

Therefore the change in potential energy would also be negative when moving from infinity to the object. As the object moves towards the gravitating object it accelerates so gains KE so the change in potential energy must be negative to conserve energy. Now i know gravitational potential is just the change in gravitational potential energy divided by mass at that point in space. So is that why the gravitational potentials are negative?