Two heavenly bodies both with radii of 7×10 3 miles and masses of 9×10 24 kg are

Question

Two heavenly bodies both with radii of 7×103 miles and masses of 9×1024 kg are separated by 2×107 miles. They are initially at rest. How fast are they moving just before their surfaces collide. Assume that you can ignore any effects having to do with the existence of atmospheres and that nothing significant exists in the space between the planets.

Consider the same setup as before, only one planet is twice the mass of the other (their radii are still the same size). What is the speed of the more massive planet just before their surfaces collide?

Explanation / Answer

Applying energy conservation,

PEi + KEi = PEf + KEF

-GM M / r + 0 = - G M M / (R + R) + 2 ( M v^2 / 2)

G M / 2 R - G M / r= v^2

v^2 = (6.67 x 10^-11 x 9 x 10^24)[1/(2 x 7 x 10^3 x 1609 m) - 1/(2 x 10^7 x 1609m)]

v = 5160 m/s .......Ans

--------------------

Applying momentum conservation,

0 = m v - 2 m V

v = 2 V

energy conservation,

-GM M / r + 0 = - G M M / (R + R) + (M v^2 /2 ) + (2 M V^2 / 2)

G M / 2 R - G M / r= (4 V^2 / 2) + (V^2) = 3 V^2

3v^2 = (6.67 x 10^-11 x 9 x 10^24)[1/(2 x 7 x 10^3 x 1609 m) - 1/(2 x 10^7 x 1609m)]

v = 2979 m/s .......Ans

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.