# Change in gravitation potential energy in space

1. Nov 25, 2012

### Lolagoeslala

1. The problem statement, all variables and given/known data
an object of mass 750 kg is lifted from the earth's surface to a height of 6.8 x 10^6 m above its surface. Calculate the change in gravitational potential energy for the object.

3. The attempt at a solution

I used this formula ΔEg = Eg2 - Eg1
ΔEg = -(GMm/r2) - (-GMm/r1)

Eg2 = -(GMm/r2)
Eg2 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.8x10^6m)+(6.37x10^6m)
Eg2 = -2.27 x 10^10 J

Eg1 = -(GMm/r1)
Eg1 = -(6.67x10^-11 Nm^2/kg^2)(5.98 x10^24kg)(750kg)/(6.37x10^6m)
Eg1 = -4.7x 10^10 J

ΔEg = Eg2 - Eg1
ΔEg = -2.27 x 10^10 J + 4.7x 10^10 J
ΔEg = 2.43 x 10^10 J

Is my process correct?

2. Nov 25, 2012

### haruspex

Yes. But do be careful with parentheses: /(6.8x10^6m)+(6.37x10^6m)

3. Nov 25, 2012

### Lolagoeslala

Is in like when im adding them?
Are all the calculation right.. i really had trouble with them...
like adding the exponents above the 10...

4. Nov 25, 2012

### haruspex

Most likely you knew what you intended when you wrote /(6.8x10^6m)+(6.37x10^6m), and therefore treated it as /((6.8x10^6m)+(6.37x10^6m)) when you used it, but it's confusing for others (including examiners!), and might confuse you sometime.
I did a sanity check. The altitude doubled the radius, and then some, so the energy should halve, and then some - which it did.

5. Nov 25, 2012

### Lolagoeslala

so it is correct?

6. Nov 25, 2012

### haruspex

I believe so, but I did not check the arithmetic in detail.