Aplanet is in an elliptical orbit around a distant star. at periastron (the point of closest approach to the star), the planet is rp=4.50×108 km from the star and is moving with a speed of vp=18.5 km/s . when the planet is at apastron (the point of greatest distance from the star), it is ra=9.10×108 km from the star. how fast is the planet moving at apastron? va=? km/s

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

Next a skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 15 with the horizontal. the rope moves parallel to the slope with a constant speed of 0.69 m/s. the force of the rope does 800 3 of work on the skier as the skier moves a distance of 8.4 m up the incline. (a) if the rope moved with a constant speed of 2.2 m/s how much work would the force of the rope do on the skier as the skler moved a distance of 8.4 m up the incline? at what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.69 m/s and (c) 2.2 m/s?

You are driving directly behind a pickup truck, going at the same speed as the truck. a crate falls from the bed of the truck to the road. (a) will your car hit the crate before the crate hits the road if you neither brake nor swerve? (b) during the fall, is the horizontal speed of the crate more than, less than, or the same as that of the truck?