Handle two APIs at the same time

You can easily map planets and images based on their array index - given that:

you retrieve them in order

And since there are 8 planets there will be 8 images; So your Array.map function will look like:

 {planets.map((planet,index) => 
  (<Block 
  key = {planet.id}
  id = {planet.id}
  name = {planet.englishName}
  dateDiscovered = {planet.discoveryDate}
  mass = {planet.mass.massValue}
  massExp = {planet.mass.massExponent}
  image = images[index]
  
  />))}

You could useEffect and when the planets array changes, then you could iterate through the name of the planets in the planets array and call the image API.

React.useEffect(() => {
  async function fetchAllImages() {
    const allImages = [];

    for await (const planet of planets) {
      const { data }  = axios.get('https://images-api.nasa.gov/search',{
      params:{
        q: planet.name
      }})

      allImages.push(data);
    }

    setImages(allImages);
  }

  fetchAllImages();
}, [planets])

It's a really difficult problem to handle multiple API calls together. I don't exactly know if this will work but why don't you change const [images, setImages] =useState([]) to const [images, setImages] =useState({}) and

  axios.get('https://images-api.nasa.gov/search',{
 
 params:{
  q: name

 }})
 .then(res => setImages(images.concat(res.data.collection.items[0].links[0].href)))
} 

to

  axios.get('https://images-api.nasa.gov/search',{
 
 params:{
  q: name

 }})
 .then(res =>{ 
         images[name] = res.data.collection.items[0].links[0].href));
         setImages({...images});
     })
} 

Then you can loop with planets array picking URLs from images object based on plant name.

I suggest combining the two data fetches into a single effect hook callback. First fetch and filter the list of celestial bodies for true planets, then fetch the images and map the planets and images into a single array of planet data. Now simply pass image={planet.image} to Block.

function App() {
  const [planets, setPlanets] = useState([]);

  const getPlanets = async () => {
    const data = await fetch("https://api.le-systeme-solaire.net/rest/bodies"); //Await for first fetch promise to resolve
    const planets = await data.json(); //Await for data.json to resolve and save this planets

    // filter planet data
    const filteredPlanets = planets.bodies.filter(
      (planet) => planet.isPlanet && planet.name.indexOf("1") === -1
    );

    // define function here to avoid needing it as dependency
    // return GET request response image value
    const getImages = (name) => {
      return axios
        .get("https://images-api.nasa.gov/search", {
          params: {
            q: name
          }
        })
        .then((res) => res.data.collection.items[0].links[0].href);
    };

    // Fetch and await all images
    const planetImages = await Promise.all(
      filteredPlanets.map((planet) => getImages(planet.englishName))
    );

    // Merge planets and images arrays
    const planetsWithImages = filteredPlanets.map((planet, i) => ({
      ...planet,
      image: planetImages[i]
    }));

    setPlanets(planetsWithImages);
  };

  useEffect(() => {
    getPlanets();
  }, []);

  return (
    <div className="App">
      {planets.map((planet) => (
        <Block
          key={planet.id}
          id={planet.id}
          name={planet.englishName}
          dateDiscovered={planet.discoveryDate}
          mass={planet.mass.massValue}
          massExp={planet.mass.massExponent}
          image={planet.image} // <-- pass planet.image
        />
      ))}
    </div>
  );
}

I would add the images to the planet array, and remove the images array altogether.

On these lines...

    if(planets){
     planets.map(planet =>getImages(planet.englishName))
    }
   
  },[])

Your getImages function is fetching and storing the images in images

But since you are already mapping through your planets to get the planet names, instead of storing those images in a separate variable, return/store them in the planets array.

Maybe something like this...

if(planets){
    planets.map(planet => {
      const image = getImages(planet.englishName)
      return {...planet, image}
    })
  },[])

So now this line image = ??? is image = planet.image

And maybe do it all with one useEffect with something like this...

const getPlanets = async() => {
  const response = await fetch('https://api.le-systeme-solaire.net/rest/bodies')
  const data = await data.json()
  const planets = data.bodies.filter(planet =>planet.isPlanet && planet.name.indexOf('1') === -1)
    
  return planets
}      
 
const getImages = async (name) => {
  const response = await axios.get('https://images-api.nasa.gov/search', {params:{q: name}})
  const images = response.concat(res.data.collection.items[0].links[0].href)

  return images
}


useEffect(()=>{
      getPlanets()
        .then(planets => Promise.all(planets.map(async (planet) => {
          const image = await getImages(planet.englishName)
          return  {...planet, image }
        })))
        .then(planets => setPlanets(planets))
  },[])

*note I have not tested the above code but hopefully close to what you need.

import React, {useState, useEffect} from 'react';
import './App.css';
import axios from 'axios'
import Block from "./Block"


function App() {
  const [planets, setPlanets] = useState([])
  const [images, setImages] =useState([])
 

  const getPlanets = async()=>{
    const data = await fetch
    ('https://api.le-systeme-solaire.net/rest/bodies') //Await for first fetch promise to resolve
    const planets = await(data.json()) //Await for data.json to resolve and save this planets

    setPlanets(planets.bodies.filter 
        (planet =>planet.isPlanet && planet.name.indexOf('1')===-1)) 
    }      
 

  useEffect(()=>{
      getPlanets();
  },[])
  

  useEffect(() => {
    async function fetchAllImages() {
      const allImages = [];
  
      for await (const planet of planets) {
        const data  = await axios.get('https://images-api.nasa.gov/search',{
        params:{
          q: planet.englishName
        }})
        const res = await data.data.collection.items[0].links[0].href
        allImages.push(res);
      }
  
      setImages(allImages);
     

    }
  
    fetchAllImages();
  }, [planets])
  console.log(images)

  return (
    
   <div className="App">
     
 {planets.map((planet,index) => 
  (<Block 
  key = {planet.id}
  id = {planet.id}
  name = {planet.englishName}
  dateDiscovered = {planet.discoveryDate}
  mass = {planet.mass.massValue}
  massExp = {planet.mass.massExponent}
  image = {images[index]}
  
  />))}
  
   </div>
   
  );

}
export default App;