Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 10²ª kg, MMoon = 7.35 x 1022 kg, , d = 3.84 x 105 km.

a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 10²ª kg, MMoon = 7.35 x 1022 kg, , d = 3.84 x 105 km.

icon
Related questions
Question

Answer the question in full and detailed solutions, along with formulas used and therefore statement

 
a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 1024 kg, Mmoon = 7.35 x 102 kg, , d = 3.84 x 10° km.
Transcribed Image Text:a) Consider an astronaut with a mass of 78 kg floating some distance directly between two planets, one with mass M and one with mass m. Denote the distance between these planets by d. There is a point in between these planets where this astronaut feels an equal and opposite pull of gravity from the two planets. Come up with a general formula for this point depending on the two masses (M and m) and the distance (d). Show why the astronaut's mass does not matter. b) Use the formula you derived in part a) to find this point when the masses of the two planets are equal. c) Plug in the numbers for the Earth and Moon to solve for the distance using the following data: Mgarth = 5.98 x 1024 kg, Mmoon = 7.35 x 102 kg, , d = 3.84 x 10° km.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer