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A 2.400×10^22kg moon orbits a 7.200×10^24kg planet with an orbital radius of 2.500×10^8m. Calculate the gravitational potential at the point half way between the centres of the planet and its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

The potential at the midpoint = Potential due to moon + Potential due to planet

(edited 5 years ago)

Original post by BobbJo

The potential at the midpoint = Potential due to moon + Potential due to planet

I got like 1.929x10^6 but its wrong

Original post by Kimberley_P

I got like 1.929x10^6 but its wrong

Yes it's wrong. Post the working

Potential varies inversely as distance so the formula is

$\phi =- \dfrac{GM}{r}$

make sure to use correct formula

i did ((-2.4x10^22*6.674x10^-11)/2.5x10^8)+((--7.2x10^24*6.674x10^-11)/(2.5x10^8/2))

==-3.848x10^6 but still its wrong. so could you help me please???

==-3.848x10^6 but still its wrong. so could you help me please???

Original post by Kimberley_P

i did ((-2.4x10^22*6.674x10^-11)/2.5x10^8)+((--7.2x10^24*6.674x10^-11)/(2.5x10^8/2))

==-3.848x10^6 but still its wrong. so could you help me please???

==-3.848x10^6 but still its wrong. so could you help me please???

first one should be 1.25 x 10^8 in the denominator

Original post by BobbJo

first one should be 1.25 x 10^8 in the denominator

Thank You

HI, I have another question related to this which I can't solve

Calculate the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

F5.16 A 2.400×10^22 kg moon orbits a 7.200×10^24 planet with an orbital radius of 2.500×10^8m. Calculate the gravitational potential at the point half way between the centres of the planet and its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

=-3.857x10^6 J/kg

Calculate the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

F5.16 A 2.400×10^22 kg moon orbits a 7.200×10^24 planet with an orbital radius of 2.500×10^8m. Calculate the gravitational potential at the point half way between the centres of the planet and its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

=-3.857x10^6 J/kg

Original post by Kimberley_P

HI, I have another question related to this which I can't solve

Calculate the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

F5.16 A 2.400×10^22 kg moon orbits a 7.200×10^24 planet with an orbital radius of 2.500×10^8m. Calculate the gravitational potential at the point half way between the centres of the planet and its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

=-3.857x10^6 J/kg

Calculate the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

F5.16 A 2.400×10^22 kg moon orbits a 7.200×10^24 planet with an orbital radius of 2.500×10^8m. Calculate the gravitational potential at the point half way between the centres of the planet and its moon. You should take the Universal gravitational constant to be 𝐺=6.674×10^−11Nm^2kg^−2. [Note: more significant figures are used in this question than appear in earlier printings of the book.]

=-3.857x10^6 J/kg

draw a diagram to show the relative positions, then the distances to use are clearer

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point (6.8 - 2.5) x10^8 m from its centre

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point 4.3 x10^8 m from its centre

Original post by BobbJo

draw a diagram to show the relative positions, then the distances to use are clearer

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point (6.8 - 2.5) x10^8 m from its centre

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point 4.3 x10^8 m from its centre

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point (6.8 - 2.5) x10^8 m from its centre

the gravitational potential at a point 6.800×10^8m from the centre of the planet in question F5.16 on the same side of the planet as its moon = gravitational potential due to planet at a point 6.8 x 10^8m from its centre + gravitational potential due to moon at a point 4.3 x10^8 m from its centre

thank you

Original post by username3249896

The potential at the midpoint = Potential due to moon + Potential due to planet

Could you pls explain why the two potentials need to be added and not subtracted?

Original post by student_here!

Could you pls explain why the two potentials need to be added and not subtracted?

In short, it is by "definition". Gravitational potential is a scalar, we are finding the "net" gravitational potential at a point due to 2 different masses, so we are summing them.

If you still have an issue, please start a new thread and describe your issue.

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