Question Number 215952 by ajfour last updated on 22/Jan/25
Commented by ajfour last updated on 22/Jan/25
$${A}\:{satellite}\:{been}\:{revolving}\:{about}\:{Earth}\:{in} \\ $$$${orbit}\:{of}\:{radiud}\:{R}_{{E}} \:.\:{If}\:{somewhere}\:{its} \\ $$$${velocity}\:{is}\:{increased}\:{by}\:\mathrm{25\%}\:{it}\:{would} \\ $$$${go}\:{in}\:{an}\:{ellipse}\:{now}.\:{But}\:{where}\:{such} \\ $$$$\:{ellipse}\:{crosses}\:{orbit}\:{of}\:{radius}\:\mathrm{2}{R}\:{it}\:{is}\: \\ $$$${given}\:{an}\:{impulse}\:\left({hopefully}\:{be}\:{by}\:\right. \\ $$$${ejecting}\:{some}\:{mass}\:{at}\:{a}\:{certain}\: \\ $$$${direction}\:{with}\:{some}\:{v}_{{rel}} .\:{Find}\:{the}\: \\ $$$${Impulse}\:{exchange}\:\boldsymbol{{J}}\:{it}\:{exchanges}\:{to}\: \\ $$$${make}\:{it}\:{suddenly}\:{adopt}\:{the}\:{orbit}\:{of}\: \\ $$$${radius}\:\mathrm{2}{R}. \\ $$