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A projectile is launched vertically upward from a planet of mass M and radius R; its initial speed is V2 times the escape speed Derive an expression for its speed as a function of the distance from the planet's center. orbit 5 800 kmn above Forthi

A projectile is launched vertically upward from a planet of mass M and radius R; its initial speed is V2 times the escape speed Derive an expression for its speed as a function of the distance from the planet's center. orbit 5 800 kmn above Forthi

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NO.61

58. A projectile is launched vertically upward from a planet of mass M and radius R; its initial speed is V2 times the escape speed Derive an expression for its speed as a function of the distance r from the planet's center. 59. A spacecraft is in circular orbit 5800 km above Earth's surface CH How much will its altitude decrease if it moves to a new circular orbit where (a) its orbital speed is 10% higher or (b) its orbital m period is 10% shorter? 60. Two meteoroids are 150,000 km from Earth's center and head- ing straight toward Earth, one at 6 km/s, the other at 12 km/s. At what speeds will they strike Earth? 61. The New Horizons mission to Pluto had the fastest launch speed of any space probe-16.26 km/s. Assuming this speed was achieved at negligible altitude compared with Earth's radius, find CH sloob ol gaibeoT2 New Horizons' speed when it crossed the Moon's orbit. 62. A satellite is in an elliptical orbit at altitudes ranging from 230 to 890 km. At its highest point, it's moving at 7.23 km/s. How fast is it moving at its lowest point? 63. A missile's trajectory takes it to a maximum altitude of 1500 km. If its launch speed is 6.2 km/s, how fast is it moving at the peak of its trajectory? 64. A 750-kg spacecraft has total energy -0.57 TJ and is in circtliar rhitol radius (b) its kinetic
Transcribed Image Text:58. A projectile is launched vertically upward from a planet of mass M and radius R; its initial speed is V2 times the escape speed Derive an expression for its speed as a function of the distance r from the planet's center. 59. A spacecraft is in circular orbit 5800 km above Earth's surface CH How much will its altitude decrease if it moves to a new circular orbit where (a) its orbital speed is 10% higher or (b) its orbital m period is 10% shorter? 60. Two meteoroids are 150,000 km from Earth's center and head- ing straight toward Earth, one at 6 km/s, the other at 12 km/s. At what speeds will they strike Earth? 61. The New Horizons mission to Pluto had the fastest launch speed of any space probe-16.26 km/s. Assuming this speed was achieved at negligible altitude compared with Earth's radius, find CH sloob ol gaibeoT2 New Horizons' speed when it crossed the Moon's orbit. 62. A satellite is in an elliptical orbit at altitudes ranging from 230 to 890 km. At its highest point, it's moving at 7.23 km/s. How fast is it moving at its lowest point? 63. A missile's trajectory takes it to a maximum altitude of 1500 km. If its launch speed is 6.2 km/s, how fast is it moving at the peak of its trajectory? 64. A 750-kg spacecraft has total energy -0.57 TJ and is in circtliar rhitol radius (b) its kinetic
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