Gravitational fields question - pls help!
A space rocket of mass 1500kg travelled from the Earth to the Moon, a distance of 3.8 x 10^8 m.
When the space rocket was mid-way between the Earth and the Moon, calculate the force of gravitational attraction on it due to the Earth.
I used F = GMm/r^2 with r = distance from Earth to Moon/2 + radius of Earth and got 15 N. Textbook however says answer is 16.6 N. Was I not supposed to include the radius of the Earth in the calculation and if so, why not?
When the space rocket was mid-way between the Earth and the Moon, calculate the force of gravitational attraction on it due to the Earth.
I used F = GMm/r^2 with r = distance from Earth to Moon/2 + radius of Earth and got 15 N. Textbook however says answer is 16.6 N. Was I not supposed to include the radius of the Earth in the calculation and if so, why not?
Original post by G.Y
A space rocket of mass 1500kg travelled from the Earth to the Moon, a distance of 3.8 x 10^8 m.
When the space rocket was mid-way between the Earth and the Moon, calculate the force of gravitational attraction on it due to the Earth.
I used F = GMm/r^2 with r = distance from Earth to Moon/2 + radius of Earth and got 15 N. Textbook however says answer is 16.6 N. Was I not supposed to include the radius of the Earth in the calculation and if so, why not?
When the space rocket was mid-way between the Earth and the Moon, calculate the force of gravitational attraction on it due to the Earth.
I used F = GMm/r^2 with r = distance from Earth to Moon/2 + radius of Earth and got 15 N. Textbook however says answer is 16.6 N. Was I not supposed to include the radius of the Earth in the calculation and if so, why not?
The calculation is always from the centre of mass.
F = mg = m x (GM)/R2
F = 1500 x (6.67x10-11 x 6x1024)/(3.8x108 / 2)2
F = 16.63 N
Original post by uberteknik
The calculation is always from the centre of mass.
F = mg = m x (GM)/R2
F = 1500 x (6.67x10-11 x 6x1024)/(3.8x108 / 2)2
F = 16.63 N
F = mg = m x (GM)/R2
F = 1500 x (6.67x10-11 x 6x1024)/(3.8x108 / 2)2
F = 16.63 N
So you don't include the radius of the Earth in the calculation? But doesn't that mean it's not from the centre of mass? Or do you assume that the distance from the Earth to the Moon that is given includes the radius of the Earth in the value?
Original post by G.Y
So you don't include the radius of the Earth in the calculation? But doesn't that mean it's not from the centre of mass? Or do you assume that the distance from the Earth to the Moon that is given includes the radius of the Earth in the value?
Correct. Do not include the radius of the moon and earth unless the question directs you to do so.
I agree, it's not explicitly stated, therefore an unambiguous standard must be adopted because orbits and diameters are never perfect spheres or circles.
e.g. the lunar distance most often used is an average value because the lunar orbit is not circular and varies by 50,000km perigee to apogee, etc. (go ahead and see what that does to the calculation).
Gravity is a function of mass and gravitational acceleration is vectored towards the centre of mass.
ergo. always use the centre of mass for distances, unless and otherwise, explicitly stated in the question.
(edited 6 years ago)
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