# Change in gravitation potential energy in space

## Homework Statement

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.

## 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?

haruspex
Homework Helper
Gold Member
2020 Award
Yes. But do be careful with parentheses: /(6.8x10^6m)+(6.37x10^6m)

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

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...

haruspex
Homework Helper
Gold Member
2020 Award
Is in like when im adding them?
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.

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.
so it is correct?

haruspex