. 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.)

The star betelgeuse is about 600 light-years away. if it explodes tonight, a. we'll know because debris from the explosion will rain down on us from space.b. we'll know it immediately because it will be brighter than the full moon in the sky.c. we won't know about it until 600 years from now.d. none of the above.

To a of 4 x hz is 1. 0. mm nm nm

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?