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Gravitational fields questions

1. There is a graph that shows T^2 against r^3, the question askes it to calculate the planets mass, what do I do with the graph?
2. Question : All vector fields have an associated scalar potential. For this question assume earth has a radius of 6400km and a mass of 6x10^24 kg.
Given the gravitational potential Vg is 63 MJ kg^-1 at earths surface calculate Vg at an altitude equal to earths radius?
Calculate the gravitational potential energy of a 10kg ball at an altitude equal to three times earths radius?

Any one who can help me with how I work any of these out, thank you in advanced

Reply 1

Eimmanuel

Study Forum Helper

Original post by heathersmusical

1. There is a graph that shows T^2 against r^3, the question askes it to calculate the planets mass, what do I do with the graph?
......
Any one who can help me with how I work any of these out, thank you in advanced

For Q1, you need to know the following relationship:

T^2 = \dfrac{4 \pi^2}{GM} r^3

where G is the gravitational constant and M is the mass of the planet.

So you can find the mass of the planet by determining the gradient of the T^2 against r^3 graph. The gradient is

\text{Gradient} = \dfrac{4 \pi^2}{GM}

Reply 2

Eimmanuel

Study Forum Helper

Original post by heathersmusical

....
2. Question : All vector fields have an associated scalar potential. For this question assume earth has a radius of 6400km and a mass of 6x10^24 kg.
Given the gravitational potential Vg is 63 MJ kg^-1 at earths surface calculate Vg at an altitude equal to earths radius?
Calculate the gravitational potential energy of a 10kg ball at an altitude equal to three times earths radius?

Any one who can help me with how I work any of these out, thank you in advanced

For Q2, you need to know that gravitational potential for a mass M is defined by

V_g = -\dfrac{GM}{r}

https://www.s-cool.co.uk/a-level/physics/gravitational-potential-energy/revise-it/gravitational-potential

So the Vg at an altitude equal to earths radius is

V_g = -\dfrac{GM_E}{2R_E}

where M_E is the mass of Earth and R_E is the radius of the Earth.

Note that there are at least 2 ways of doing this for this question. You should be familiar with them.

Reply 3

heathersmusical

Thank you so much !!

Original post by Eimmanuel

For Q2, you need to know that gravitational potential for a mass M is defined by

V_g = -\dfrac{GM}{r}

https://www.s-cool.co.uk/a-level/physics/gravitational-potential-energy/revise-it/gravitational-potential

So the Vg at an altitude equal to earths radius is

V_g = -\dfrac{GM_E}{2R_E}

where M_E is the mass of Earth and R_E is the radius of the Earth.

Note that there are at least 2 ways of doing this for this question. You should be familiar with them.