ALLEN Leader Test Series/Joint Package Course/22-05-2022/Paper-2 A satellite revolves around a planet in circular orbit of radius R (much larger than the radius of the planet) with a time period of revolution T. If the satellite is stopped and then released in its orbit (Assume that the satellite experiences gravitational force due to the planet only). ((A) t will fall into the planet (B) The time of fall of the satellite is nearly 5. T V8 (C))The time of fall of the satellite into the planet is nearly (D) It cannot fall into the planet so time of fall of the satellite is meaningless एक उपग्रह किसी ग्रह के चारों ओर ग्रह की त्रिज्या से बहुत अधिक त्रिज्या R वाली वृत्ताकार कक्षा में T आवर्तकाल से घूर्णन करता है। यदि उपग्रह को इसकी कक्षा में रोक दिया जाये तथा फिर छोड़ दिया जाए तो (माना उपग्रह पर केवल ग्रह के कारण ही गुरूत्वाकर्षण बल लगता है।) (A) यह ग्रह में गिर जाएगा। (B) उपग्रह को गिरने में लगभग T T√2 8 समय लगेगा। (C) उपग्रह को ग्रह में गिरने में लगभग TV2 समय लगेगा। 8 (D) यह ग्रह पर नहीं गिर सकता इसलिए उपग्रह को गिरने में लगा समय ज्ञात करना अर्थहीन है। Space for Rough Work/कच्चे कार्य के लिए स्थान

ALLEN Leader Test Series/Joint Package Course/22-05-2022/Paper-2 A satellite revolves around a planet in circular orbit of radius R (much larger than the radius of the planet) with a time period of revolution T. If the satellite is stopped and then released in its orbit (Assume that the satellite experiences gravitational force due to the planet only). ((A) t will fall into the planet (B) The time of fall of the satellite is nearly 5. T V8 (C))The time of fall of the satellite into the planet is nearly (D) It cannot fall into the planet so time of fall of the satellite is meaningless एक उपग्रह किसी ग्रह के चारों ओर ग्रह की त्रिज्या से बहुत अधिक त्रिज्या R वाली वृत्ताकार कक्षा में T आवर्तकाल से घूर्णन करता है। यदि उपग्रह को इसकी कक्षा में रोक दिया जाये तथा फिर छोड़ दिया जाए तो (माना उपग्रह पर केवल ग्रह के कारण ही गुरूत्वाकर्षण बल लगता है।) (A) यह ग्रह में गिर जाएगा। (B) उपग्रह को गिरने में लगभग T T√2 8 समय लगेगा। (C) उपग्रह को ग्रह में गिरने में लगभग TV2 समय लगेगा। 8 (D) यह ग्रह पर नहीं गिर सकता इसलिए उपग्रह को गिरने में लगा समय ज्ञात करना अर्थहीन है। Space for Rough Work/कच्चे कार्य के लिए स्थान

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#86
Problem 2. Satellite orbits. The geostationary orbit is a unique circular orbit above the equator of a planet, for which the orbital period is equal to the rotation period of the planet. For Earth, the geostationary orbit is 4.22 x 104 km from the centre of the Earth. The Earth rotates in 23 hours and 56 minutes. a) A failed satellite, whose apogee distance is at Earth's geostationary orbit, has only half the required orbital speed of a geostationary satellite at apogee. Calculate the perigee distance of the orbit of this failed satellite. b) If another planet has twice the size of Earth and the same average density as Earth, while rotating in the same amount of time, calculate the radius of the geostationary orbit for this planet.
Mercury orbit has a semi major axis a=5.791 x1010 m with an eccentricity e= 0.2056. Mercury Sun a MMercury = 3.3011 × 1023 kg a) What is the velocity of Mercury at the aphelion (point of maximum distance to the Sun)? b) What is the total mechanical energy of Mercury? c) What is the velocity of Mercury at the perihelion (point of minimum distance to the Sun)? d) What is the velocity of Mercury when its distance from the Sun is 0.371 AU? (1 AU = 1.496 x 1011 m) e) What is the orbital period of Mercury? (Only for this question you can the assume that the orbit is circular, with a radius equal to the semi major axis) f) If the period observed for Mercury is 87.969 earth days, compare (calculate percent difference) with the period you calculated in question e). Consider the value given in f) as the actual (i.e. experimental) one. Is the value obtained theoretically in question e) accurate?
Integrated Concepts - Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it? (c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last? (d) If its mass is 0.500 g, what is the average force it exerts on the satellite? (e) How much energy in joules is generated by the collision? (The satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)
Example 4. A satellite is orbiting a circular orbit at an altitude of 900 km, at which atmosphere density is 5.46 x 10-13kg/m³. The satellite has mass 150kg, cross sectional area 1.50m², and drag coefficient 2. a) Calculate the rate of change of orbit radius da/dt in units of m/s. b) Make an estimate of the time (in years) that will take the satellite to reach the Earth.
Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.
Needs Complete solution.
8-24. An Earth satellite has a perigee of 300 km and an apogee of 3,500 km above Earth's surface. How far is the satellite above Earth when (a) it has rotated 90° around Earth from perigee and (b) it has moved halfway from perigee to apogee?
With what orbital speed will a satellite circle Jupiter if placed at a height of 6.50 10 6 m above the surface of the planet? The mass of Jupiter is 1.90 ✕ 1027 kg and the radius of Jupiter is 7.14 ✕ 107 m. (Dont use scientific notation, use regular notation, example 50000)