. A spaceship of mass m has its engines switched off and is moving in a circular orbit at height R above the surface of a planet of mass M and radius R. a) Derive an expression for total mechanical energy E of the orbiting spaceship, in terms of G, m, M and R. b) Derive an expression for the minimum speed V the spaceship would need to escape from this orbit into deep space, in terms of system parameters. (The engines can’t fire for the whole trip; they can only give the spaceship one boost so it obtains this velocity. Ignore all other celestial objects.)

Note that GmM/r^2 = ma = MV^2/r

After dividing we have that the velocity of the spaceship will be

V = √GM/R

Now to find the mech. Energy,

But mechanical energy = 1/2 MV^2

Therefore mechanical energy of the spaceship will be

(a) mech. Energy= 1/2m(√GM/R)^2

(b) escape velocity V = √GM/R already calculated above.

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.

wavelength divides in half and speed stays the same.